Zhang-Suen thinning algorithm: Difference between revisions
(Added AppleScript.) |
(Added solution for Action!) |
||
Line 261: | Line 261: | ||
........................................................... |
........................................................... |
||
</pre> |
</pre> |
||
=={{header|Action!}}== |
|||
<lang Action!>PROC DrawImage(BYTE ARRAY image BYTE x,y,width,height) |
|||
BYTE i,j |
|||
BYTE POINTER ptr |
|||
Color=2 |
|||
FOR j=0 TO height-1 |
|||
DO |
|||
Plot(x,j+y) DrawTo(x+width-1,j+y) |
|||
OD |
|||
Color=1 |
|||
ptr=image |
|||
FOR j=0 TO height-1 |
|||
DO |
|||
FOR i=0 TO width-1 |
|||
DO |
|||
IF ptr^ THEN |
|||
Plot(i+x,j+y) |
|||
FI |
|||
ptr==+1 |
|||
OD |
|||
OD |
|||
RETURN |
|||
PROC Thinning(BYTE ARRAY image BYTE width,height) |
|||
DEFINE PTR="CARD" |
|||
DEFINE MAX="200" |
|||
PTR ARRAY change(MAX) |
|||
BYTE POINTER p1,p2,p3,p4,p5,p6,p7,p8,p9,p68,p24 |
|||
INT count,i |
|||
BYTE x,y,sum,step1 |
|||
step1=1 |
|||
DO |
|||
count=0 |
|||
p1=image p8=p1-1 p4=p1+1 |
|||
p2=p1-width p6=p1+width |
|||
p9=p2-1 p3=p2+1 |
|||
p7=p6-1 p5=p6+1 |
|||
FOR y=0 TO height-1 |
|||
DO |
|||
FOR x=0 TO width-1 |
|||
DO |
|||
IF p1^=1 AND x>0 AND y>0 AND x<width-1 AND y<height-1 THEN |
|||
sum=p2^+p3^+p4^+p5^+p6^+p7^+p8^+p9^ |
|||
IF sum>=2 AND sum<=6 THEN |
|||
sum=0 |
|||
IF p3^>p2^ THEN sum==+1 FI |
|||
IF p4^>p3^ THEN sum==+1 FI |
|||
IF p5^>p4^ THEN sum==+1 FI |
|||
IF p6^>p5^ THEN sum==+1 FI |
|||
IF p7^>p6^ THEN sum==+1 FI |
|||
IF p8^>p7^ THEN sum==+1 FI |
|||
IF p9^>p8^ THEN sum==+1 FI |
|||
IF p2^>p9^ THEN sum==+1 FI |
|||
IF sum=1 THEN |
|||
IF step1 THEN |
|||
p24=p4 p68=p6 |
|||
ELSE |
|||
p24=p2 p68=p8 |
|||
FI |
|||
IF p2^+p4^+p68^<3 AND p24^+p6^+p8^<3 THEN |
|||
change(count)=p1 count==+1 |
|||
FI |
|||
FI |
|||
FI |
|||
FI |
|||
p1==+1 p2==+1 p3==+1 p4==+1 p5==+1 |
|||
p6==+1 p7==+1 p8==+1 p9==+1 |
|||
OD |
|||
OD |
|||
step1=1-step1 |
|||
FOR i=0 TO count-1 |
|||
DO |
|||
p1=change(i) p1^=0 |
|||
OD |
|||
UNTIL count=0 |
|||
OD |
|||
RETURN |
|||
PROC Main() |
|||
BYTE ARRAY image1=[ |
|||
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||
0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 |
|||
0 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 |
|||
0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 |
|||
0 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||
0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||
0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 |
|||
0 1 1 1 0 0 1 1 1 1 0 0 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1 0 0 |
|||
0 1 1 1 0 0 0 1 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 |
|||
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] |
|||
BYTE ARRAY image2=[ |
|||
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||
0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 |
|||
0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 |
|||
0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 |
|||
0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 |
|||
0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 |
|||
0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||
0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||
0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||
0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||
0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||
0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|||
0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 |
|||
0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 |
|||
0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 |
|||
0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 |
|||
0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 |
|||
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] |
|||
BYTE width1=[32],height1=[10],width2=[59],height2=[18] |
|||
BYTE CH=$02FC |
|||
Graphics(7+16) |
|||
Color=1 |
|||
SetColor(0,0,$00) |
|||
SetColor(4,0,$04) |
|||
SetColor(1,0,$0C) |
|||
DrawImage(image1,0,0,width1,height1) |
|||
Thinning(image1,width1,height1) |
|||
DrawImage(image1,width1+10,0,width1,height1) |
|||
DrawImage(image2,0,height1+10,width2,height2) |
|||
Thinning(image2,width2,height2) |
|||
DrawImage(image2,width2+10,height1+10,width2,height2) |
|||
DO UNTIL CH#$FF OD |
|||
CH=$FF |
|||
RETURN</lang> |
|||
{{out}} |
|||
[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Zhang-Suen_thinning_algorithm.png Screenshot from Atari 8-bit computer] |
|||
=={{header|AppleScript}}== |
=={{header|AppleScript}}== |
Revision as of 21:08, 4 December 2021
You are encouraged to solve this task according to the task description, using any language you may know.
This is an algorithm used to thin a black and white i.e. one bit per pixel images.
For example, with an input image of:
################# ############# ################## ################ ################### ################## ######## ####### ################### ###### ####### ####### ###### ###### ####### ####### ################# ####### ################ ####### ################# ####### ###### ####### ####### ###### ####### ####### ###### ####### ####### ###### ######## ####### ################### ######## ####### ###### ################## ###### ######## ####### ###### ################ ###### ######## ####### ###### ############# ######
It produces the thinned output:
# ########## ####### ## # #### # # # ## # # # # # # # # # ############ # # # # # # # # # # # # # # ## # ############ ### ###
- Algorithm
Assume black pixels are one and white pixels zero, and that the input image is a rectangular N by M array of ones and zeroes.
The algorithm operates on all black pixels P1 that can have eight neighbours.
The neighbours are, in order, arranged as:
P9 | P2 | P3 |
P8 | P1 | P4 |
P7 | P6 | P5 |
Obviously the boundary pixels of the image cannot have the full eight neighbours.
- Define = the number of transitions from white to black, (0 -> 1) in the sequence P2,P3,P4,P5,P6,P7,P8,P9,P2. (Note the extra P2 at the end - it is circular).
- Define = The number of black pixel neighbours of P1. ( = sum(P2 .. P9) )
- Step 1
All pixels are tested and pixels satisfying all the following conditions (simultaneously) are just noted at this stage.
- (0) The pixel is black and has eight neighbours
- (1)
- (2) A(P1) = 1
- (3) At least one of P2 and P4 and P6 is white
- (4) At least one of P4 and P6 and P8 is white
After iterating over the image and collecting all the pixels satisfying all step 1 conditions, all these condition satisfying pixels are set to white.
- Step 2
All pixels are again tested and pixels satisfying all the following conditions are just noted at this stage.
- (0) The pixel is black and has eight neighbours
- (1)
- (2) A(P1) = 1
- (3) At least one of P2 and P4 and P8 is white
- (4) At least one of P2 and P6 and P8 is white
After iterating over the image and collecting all the pixels satisfying all step 2 conditions, all these condition satisfying pixels are again set to white.
- Iteration
If any pixels were set in this round of either step 1 or step 2 then all steps are repeated until no image pixels are so changed.
- Task
- Write a routine to perform Zhang-Suen thinning on an image matrix of ones and zeroes.
- Use the routine to thin the following image and show the output here on this page as either a matrix of ones and zeroes, an image, or an ASCII-art image of space/non-space characters.
00000000000000000000000000000000 01111111110000000111111110000000 01110001111000001111001111000000 01110000111000001110000111000000 01110001111000001110000000000000 01111111110000001110000000000000 01110111100000001110000111000000 01110011110011101111001111011100 01110001111011100111111110011100 00000000000000000000000000000000
- Reference
- Zhang-Suen Thinning Algorithm, Java Implementation by Nayef Reza.
- "Character Recognition Systems: A Guide for Students and Practitioners" By Mohamed Cheriet, Nawwaf Kharma, Cheng-Lin Liu, Ching Suen
11l
<lang 11l>V beforeTxt = |‘1100111
1100111 1100111 1100111 1100110 1100110 1100110 1100110 1100110 1100110 1100110 1100110 1111110 0000000’
V smallrc01 = |‘00000000000000000000000000000000
01111111110000000111111110000000 01110001111000001111001111000000 01110000111000001110000111000000 01110001111000001110000000000000 01111111110000001110000000000000 01110111100000001110000111000000 01110011110011101111001111011100 01110001111011100111111110011100 00000000000000000000000000000000’
V rc01 = |‘00000000000000000000000000000000000000000000000000000000000
01111111111111111100000000000000000001111111111111000000000 01111111111111111110000000000000001111111111111111000000000 01111111111111111111000000000000111111111111111111000000000 01111111100000111111100000000001111111111111111111000000000 00011111100000111111100000000011111110000000111111000000000 00011111100000111111100000000111111100000000000000000000000 00011111111111111111000000000111111100000000000000000000000 00011111111111111110000000000111111100000000000000000000000 00011111111111111111000000000111111100000000000000000000000 00011111100000111111100000000111111100000000000000000000000 00011111100000111111100000000111111100000000000000000000000 00011111100000111111100000000011111110000000111111000000000 01111111100000111111100000000001111111111111111111000000000 01111111100000111111101111110000111111111111111111011111100 01111111100000111111101111110000001111111111111111011111100 01111111100000111111101111110000000001111111111111011111100 00000000000000000000000000000000000000000000000000000000000’
F intarray(binstring)
‘Change a 2D matrix of 01 chars into a list of lists of ints’ R binstring.split("\n").map(line -> line.map(ch -> (I ch == ‘1’ {1} E 0)))
F chararray(intmatrix)
‘Change a 2d list of lists of 1/0 ints into lines of 1/0 chars’ R intmatrix.map(row -> row.map(p -> String(p)).join(‘’)).join("\n")
F toTxt(intmatrix)
‘Change a 2d list of lists of 1/0 ints into lines of '#' and '.' chars’ R intmatrix.map(row -> row.map(p -> (I p {‘#’} E ‘.’)).join(‘’)).join("\n")
F neighbours_array(x, y, image)
‘Return 8-neighbours of point p1 of picture, in order’ V i = image V (x1, y1, x_1, y_1) = (x + 1, y - 1, x - 1, y + 1) R [i[y1][x], i[y1][x1], i[y][x1], i[y_1][x1], i[y_1][x], i[y_1][x_1], i[y][x_1], i[y1][x_1]]
F neighbours_tuple(x, y, image)
‘Return 8-neighbours of point p1 of picture, in order’ V i = image V (x1, y1, x_1, y_1) = (x + 1, y - 1, x - 1, y + 1) R (i[y1][x], i[y1][x1], i[y][x1], i[y_1][x1], i[y_1][x], i[y_1][x_1], i[y][x_1], i[y1][x_1])
F transitions(neighbours)
V s = 0 L(i) 7 s += Int((neighbours[i], neighbours[i + 1]) == (0, 1)) R s + Int((neighbours[7], neighbours[0]) == (0, 1))
F zhangSuen(&image)
V changing1 = [(-1, -1)] V changing2 = [(-1, -1)] L !changing1.empty | !changing2.empty changing1.drop() L(y) 1 .< image.len - 1 L(x) 1 .< image[0].len - 1 V n = neighbours_array(x, y, image) V (P2, P3, P4, P5, P6, P7, P8, P9) = neighbours_tuple(x, y, image) I (image[y][x] == 1 & P4 * P6 * P8 == 0 & P2 * P4 * P6 == 0 & transitions(n) == 1 & sum(n) C 2..6) changing1.append((x, y)) L(x, y) changing1 image[y][x] = 0 changing2.drop() L(y) 1 .< image.len - 1 L(x) 1 .< image[0].len - 1 V n = neighbours_array(x, y, image) V (P2, P3, P4, P5, P6, P7, P8, P9) = neighbours_tuple(x, y, image) I (image[y][x] == 1 & P2 * P6 * P8 == 0 & P2 * P4 * P8 == 0 & transitions(n) == 1 & sum(n) C 2..6) changing2.append((x, y)) L(x, y) changing2 image[y][x] = 0 R image
L(picture) (beforeTxt, smallrc01, rc01)
V image = intarray(picture) print("\nFrom:\n#.".format(toTxt(image))) V after = zhangSuen(&image) print("\nTo thinned:\n#.".format(toTxt(after)))</lang>
- Output:
Just the example asked for in the task:
From: ........................................................... .#################...................#############......... .##################...............################......... .###################............##################......... .########.....#######..........###################......... ...######.....#######.........#######.......######......... ...######.....#######........#######....................... ...#################.........#######....................... ...################..........#######....................... ...#################.........#######....................... ...######.....#######........#######....................... ...######.....#######........#######....................... ...######.....#######.........#######.......######......... .########.....#######..........###################......... .########.....#######.######....##################.######.. .########.....#######.######......################.######.. .########.....#######.######.........#############.######.. ........................................................... To thinned: ........................................................... ........................................................... ....#.##########.......................#######............. .....##........#...................####.......#............ .....#..........#.................##....................... .....#..........#................#......................... .....#..........#................#......................... .....#..........#................#......................... .....############...............#.......................... .....#..........#...............#.......................... .....#..........#................#......................... .....#..........#................#......................... .....#..........#................#......................... .....#............................##....................... .....#.............................############............ .......................###..........................###.... ........................................................... ...........................................................
Action!
<lang Action!>PROC DrawImage(BYTE ARRAY image BYTE x,y,width,height)
BYTE i,j BYTE POINTER ptr
Color=2 FOR j=0 TO height-1 DO Plot(x,j+y) DrawTo(x+width-1,j+y) OD Color=1 ptr=image FOR j=0 TO height-1 DO FOR i=0 TO width-1 DO IF ptr^ THEN Plot(i+x,j+y) FI ptr==+1 OD OD
RETURN
PROC Thinning(BYTE ARRAY image BYTE width,height)
DEFINE PTR="CARD" DEFINE MAX="200" PTR ARRAY change(MAX) BYTE POINTER p1,p2,p3,p4,p5,p6,p7,p8,p9,p68,p24 INT count,i BYTE x,y,sum,step1
step1=1 DO count=0 p1=image p8=p1-1 p4=p1+1 p2=p1-width p6=p1+width p9=p2-1 p3=p2+1 p7=p6-1 p5=p6+1
FOR y=0 TO height-1 DO FOR x=0 TO width-1 DO IF p1^=1 AND x>0 AND y>0 AND x<width-1 AND y<height-1 THEN sum=p2^+p3^+p4^+p5^+p6^+p7^+p8^+p9^ IF sum>=2 AND sum<=6 THEN sum=0 IF p3^>p2^ THEN sum==+1 FI IF p4^>p3^ THEN sum==+1 FI IF p5^>p4^ THEN sum==+1 FI IF p6^>p5^ THEN sum==+1 FI IF p7^>p6^ THEN sum==+1 FI IF p8^>p7^ THEN sum==+1 FI IF p9^>p8^ THEN sum==+1 FI IF p2^>p9^ THEN sum==+1 FI IF sum=1 THEN IF step1 THEN p24=p4 p68=p6 ELSE p24=p2 p68=p8 FI IF p2^+p4^+p68^<3 AND p24^+p6^+p8^<3 THEN change(count)=p1 count==+1 FI FI FI FI p1==+1 p2==+1 p3==+1 p4==+1 p5==+1 p6==+1 p7==+1 p8==+1 p9==+1 OD OD step1=1-step1 FOR i=0 TO count-1 DO p1=change(i) p1^=0 OD UNTIL count=0 OD
RETURN
PROC Main()
BYTE ARRAY image1=[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 0 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] BYTE ARRAY image2=[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] BYTE width1=[32],height1=[10],width2=[59],height2=[18] BYTE CH=$02FC
Graphics(7+16) Color=1 SetColor(0,0,$00) SetColor(4,0,$04) SetColor(1,0,$0C)
DrawImage(image1,0,0,width1,height1) Thinning(image1,width1,height1) DrawImage(image1,width1+10,0,width1,height1)
DrawImage(image2,0,height1+10,width2,height2) Thinning(image2,width2,height2) DrawImage(image2,width2+10,height1+10,width2,height2)
DO UNTIL CH#$FF OD CH=$FF
RETURN</lang>
- Output:
Screenshot from Atari 8-bit computer
AppleScript
<lang applescript>-- Params: -- List of lists (rows) of "pixel" values. -- Record indicating the values representing black and white. on ZhangSuen(matrix, {black:black, white:white})
script o property matrix : missing value property changePixels : missing value on A(neighbours) -- Count transitions from white to black. set sum to 0 repeat with i from 1 to 8 if ((neighbours's item i is white) and (neighbours's item (i mod 8 + 1) is black)) then set sum to sum + 1 end repeat return sum end A on B(neighbours) -- Count neighbouring black pixels. set sum to 0 repeat with p in neighbours if (p's contents is black) then set sum to sum + 1 end repeat return sum end B end script set o's matrix to matrix set rowCount to (count o's matrix) set columnCount to (count o's matrix's beginning) -- Assumed to be the same for every row. repeat until (o's changePixels is {}) repeat with step from 1 to 2 set o's changePixels to {} repeat with r from 2 to (rowCount - 1) repeat with c from 2 to (columnCount - 1) if (o's matrix's item r's item c is black) then tell (a reference to o's matrix) to ¬ set neighbours to {item (r - 1)'s item c, item (r - 1)'s item (c + 1), ¬ item r's item (c + 1), item (r + 1)'s item (c + 1), item (r + 1)'s item c, ¬ item (r + 1)'s item (c - 1), item r's item (c - 1), item (r - 1)'s item (c - 1)} set blackCount to o's B(neighbours) if ((blackCount > 1) and (blackCount < 7) and (o's A(neighbours) is 1)) then set {P2, x, P4, x, P6, x, P8} to neighbours if (step is 1) then set toChange to ((P4 is white) or (P6 is white) or ((P2 is white) and (P8 is white))) else set toChange to ((P2 is white) or (P8 is white) or ((P4 is white) and (P6 is white))) end if if (toChange) then set end of o's changePixels to {r, c} end if end if end repeat end repeat if (o's changePixels is {}) then exit repeat repeat with pixel in o's changePixels set {r, c} to pixel set o's matrix's item r's item c to white end repeat end repeat end repeat return o's matrix -- or: return matrix -- The input has been edited in place.
end ZhangSuen
on join(lst, delim)
set astid to AppleScript's text item delimiters set AppleScript's text item delimiters to delim set txt to lst as text set AppleScript's text item delimiters to astid return txt
end join
on demo()
set pattern to "00000000000000000000000000000000
01111111110000000111111110000000 01110001111000001111001111000000 01110000111000001110000111000000 01110001111000001110000000000000 01111111110000001110000000000000 01110111100000001110000111000000 01110011110011101111001111011100 01110001111011100111111110011100 00000000000000000000000000000000"
set matrix to pattern's paragraphs repeat with thisRow in matrix set thisRow's contents to thisRow's characters end repeat ZhangSuen(matrix, {black:"1", white:"0"}) repeat with thisRow in matrix set thisRow's contents to join(thisRow, "") end repeat return join(matrix, linefeed)
end demo return demo()</lang>
- Output:
<lang applescript>"00000000000000000000000000000000 00111111100000000011111100000000 00100000100000000110000000000000 00100000010000000100000000000000 00100000100000000100000000000000 00111110100000000100000000000000 00000001100000000100000000000000 00000000100001000110000110001000 00000000010000000001111000000000 00000000000000000000000000000000"</lang> Alternative demo: <lang applescript>on demo()
set pattern to " ################# ############# ################## ################ ################### ################## ######## ####### ################### ###### ####### ####### ###### ###### ####### ####### ################# ####### ################ ####### ################# ####### ###### ####### ####### ###### ####### ####### ###### ####### ####### ###### ######## ####### ################### ######## ####### ###### ################## ###### ######## ####### ###### ################ ###### ######## ####### ###### ############# ###### " set matrix to pattern's paragraphs repeat with thisRow in matrix set thisRow's contents to thisRow's characters end repeat ZhangSuen(matrix, {black:"#", white:space}) repeat with thisRow in matrix set thisRow's contents to join(thisRow, "") end repeat return join(matrix, linefeed)
end demo return demo()</lang>
- Output:
<lang applescript>"
# ########## ####### ## # #### # # # ## # # # # # # # # # ############ # # # # # # # # # # # # # # ## # ############ ### ### "</lang>
AutoHotkey
Reads input from a text file and writes output to a different text file (first creating the file, if necessary). <lang AutoHotkey>FileIn := A_ScriptDir "\Zhang-Suen.txt" FileOut := A_ScriptDir "\NewFile.txt"
if (!FileExist(FileIn)) { MsgBox, 48, File Not Found, % "File """ FileIn """ not found." ExitApp } S := {} N := [2,3,4,5,6,7,8,9,2]
Loop, Read, % FileIn { LineNum := A_Index Loop, Parse, A_LoopReadLine S[LineNum, A_Index] := A_LoopField }
Loop { FlipCount := 0 Loop, 2 { Noted := [], i := A_Index for LineNum, Line in S { for PixNum, Pix in Line { ; (0) if (Pix = 0 || (P := GetNeighbors(LineNum, PixNum, S)) = 1) continue ; (1) BP := 0 for j, Val in P BP += Val if (BP < 2 || BP > 6) continue ; (2) AP := 0 Loop, 8 if (P[N[A_Index]] = "0" && P[N[A_Index + 1]] = "1") AP++ if (AP != 1) continue ; (3 and 4) if (i = 1) { if (P[2] + P[4] + P[6] = 3 || P[4] + P[6] + P[8] = 3) continue } else if (P[2] + P[4] + P[8] = 3 || P[2] + P[6] + P[8] = 3) continue
Noted.Insert([LineNum, PixNum]) FlipCount++ } } for j, Coords in Noted S[Coords[1], Coords[2]] := 0 } if (!FlipCount) break }
for LineNum, Line in S { for PixNum, Pix in Line Out .= Pix ? "#" : " " Out .= "`n" } FileAppend, % Out, % FileOut
GetNeighbors(Y, X, S) { Neighbors := [] if ((Neighbors[8] := S[Y, X - 1]) = "") return 1 if ((Neighbors[4] := S[Y, X + 1]) = "") return 1 Loop, 3 if ((Neighbors[A_Index = 1 ? 9 : A_Index] := S[Y - 1, X - 2 + A_Index]) = "") return 1 Loop, 3 if ((Neighbors[8 - A_Index] := S[Y + 1, X - 2 + A_Index]) = "") return 1 return Neighbors }</lang> Output:
####### ###### # # ## # # # # # # ##### # # ## # # # ## ## # # ####
C
Input and out images written from and to files. Format of input file is :
<Rows> <Columns> <Blank pixel character> <Image Pixel character> <Image of specified rows and columns made up of the two pixel types specified in the second line.>
The images before and after thinning are also printed on the console. <lang C>
- include<stdlib.h>
- include<stdio.h>
char** imageMatrix;
char blankPixel,imagePixel;
typedef struct{ int row,col; }pixel;
int getBlackNeighbours(int row,int col){
int i,j,sum = 0;
for(i=-1;i<=1;i++){ for(j=-1;j<=1;j++){ if(i!=0 || j!=0) sum+= (imageMatrix[row+i][col+j]==imagePixel); } }
return sum; }
int getBWTransitions(int row,int col){ return ((imageMatrix[row-1][col]==blankPixel && imageMatrix[row-1][col+1]==imagePixel) +(imageMatrix[row-1][col+1]==blankPixel && imageMatrix[row][col+1]==imagePixel) +(imageMatrix[row][col+1]==blankPixel && imageMatrix[row+1][col+1]==imagePixel) +(imageMatrix[row+1][col+1]==blankPixel && imageMatrix[row+1][col]==imagePixel) +(imageMatrix[row+1][col]==blankPixel && imageMatrix[row+1][col-1]==imagePixel) +(imageMatrix[row+1][col-1]==blankPixel && imageMatrix[row][col-1]==imagePixel) +(imageMatrix[row][col-1]==blankPixel && imageMatrix[row-1][col-1]==imagePixel) +(imageMatrix[row-1][col-1]==blankPixel && imageMatrix[row-1][col]==imagePixel)); }
int zhangSuenTest1(int row,int col){ int neighbours = getBlackNeighbours(row,col);
return ((neighbours>=2 && neighbours<=6) && (getBWTransitions(row,col)==1) && (imageMatrix[row-1][col]==blankPixel||imageMatrix[row][col+1]==blankPixel||imageMatrix[row+1][col]==blankPixel) && (imageMatrix[row][col+1]==blankPixel||imageMatrix[row+1][col]==blankPixel||imageMatrix[row][col-1]==blankPixel)); }
int zhangSuenTest2(int row,int col){ int neighbours = getBlackNeighbours(row,col);
return ((neighbours>=2 && neighbours<=6) && (getBWTransitions(row,col)==1) && (imageMatrix[row-1][col]==blankPixel||imageMatrix[row][col+1]==blankPixel||imageMatrix[row][col-1]==blankPixel) && (imageMatrix[row-1][col]==blankPixel||imageMatrix[row+1][col]==blankPixel||imageMatrix[row][col+1]==blankPixel)); }
void zhangSuen(char* inputFile, char* outputFile){
int startRow = 1,startCol = 1,endRow,endCol,i,j,count,rows,cols,processed;
pixel* markers;
FILE* inputP = fopen(inputFile,"r");
fscanf(inputP,"%d%d",&rows,&cols);
fscanf(inputP,"%d%d",&blankPixel,&imagePixel);
blankPixel<=9?blankPixel+='0':blankPixel; imagePixel<=9?imagePixel+='0':imagePixel;
printf("\nPrinting original image :\n");
imageMatrix = (char**)malloc(rows*sizeof(char*));
for(i=0;i<rows;i++){ imageMatrix[i] = (char*)malloc((cols+1)*sizeof(char)); fscanf(inputP,"%s\n",imageMatrix[i]); printf("\n%s",imageMatrix[i]);
}
fclose(inputP);
endRow = rows-2; endCol = cols-2; do{ markers = (pixel*)malloc((endRow-startRow+1)*(endCol-startCol+1)*sizeof(pixel)); count = 0;
for(i=startRow;i<=endRow;i++){ for(j=startCol;j<=endCol;j++){ if(imageMatrix[i][j]==imagePixel && zhangSuenTest1(i,j)==1){ markers[count].row = i; markers[count].col = j; count++; } } }
processed = (count>0);
for(i=0;i<count;i++){ imageMatrix[markers[i].row][markers[i].col] = blankPixel; }
free(markers); markers = (pixel*)malloc((endRow-startRow+1)*(endCol-startCol+1)*sizeof(pixel)); count = 0;
for(i=startRow;i<=endRow;i++){ for(j=startCol;j<=endCol;j++){ if(imageMatrix[i][j]==imagePixel && zhangSuenTest2(i,j)==1){ markers[count].row = i; markers[count].col = j; count++; } } }
if(processed==0) processed = (count>0);
for(i=0;i<count;i++){ imageMatrix[markers[i].row][markers[i].col] = blankPixel; }
free(markers); }while(processed==1);
FILE* outputP = fopen(outputFile,"w");
printf("\n\n\nPrinting image after applying Zhang Suen Thinning Algorithm : \n\n\n");
for(i=0;i<rows;i++){ for(j=0;j<cols;j++){ printf("%c",imageMatrix[i][j]); fprintf(outputP,"%c",imageMatrix[i][j]); } printf("\n"); fprintf(outputP,"\n"); }
fclose(outputP);
printf("\nImage also written to : %s",outputFile); }
int main() { char inputFile[100],outputFile[100];
printf("Enter full path of input image file : "); scanf("%s",inputFile);
printf("Enter full path of output image file : "); scanf("%s",outputFile);
zhangSuen(inputFile,outputFile);
return 0; } </lang>
Contents of input file : zhImage.txt
10 32 0 1 00000000000000000000000000000000 01111111110000000111111110000000 01110001111000001111001111000000 01110000111000001110000111000000 01110001111000001110000000000000 01111111110000001110000000000000 01110111100000001110000111000000 01110011110011101111001111011100 01110001111011100111111110011100 00000000000000000000000000000000
Console interaction :
Enter full path of input image file : zhImage.txt Enter full path of output image file : out.txt Printing original image : 00000000000000000000000000000000 01111111110000000111111110000000 01110001111000001111001111000000 01110000111000001110000111000000 01110001111000001110000000000000 01111111110000001110000000000000 01110111100000001110000111000000 01110011110011101111001111011100 01110001111011100111111110011100 00000000000000000000000000000000 Printing image after applying Zhang Suen Thinning Algorithm : 00000000000000000000000000000000 00111111100000000011111100000000 00100000100000000110000000000000 01000000100000000100000000000000 01000000100000001000000000000000 01111110100000001000000000000000 00000001000000000100000000000000 00000000100001000110000110001000 00000000010000000001111000000000 00000000000000000000000000000000 Image also written to : out.txt
Contents of out.txt :
00000000000000000000000000000000 00111111100000000011111100000000 00100000100000000110000000000000 01000000100000000100000000000000 01000000100000001000000000000000 01111110100000001000000000000000 00000001000000000100000000000000 00000000100001000110000110001000 00000000010000000001111000000000 00000000000000000000000000000000
C++
Compiled with --std=c++14 <lang CPP>#include <iostream>
- include <string>
- include <sstream>
- include <valarray>
const std::string input { "................................" ".#########.......########......." ".###...####.....####..####......" ".###....###.....###....###......" ".###...####.....###............." ".#########......###............." ".###.####.......###....###......" ".###..####..###.####..####.###.." ".###...####.###..########..###.." "................................" }; const std::string input2 { ".........................................................." ".#################...................#############........" ".##################...............################........" ".###################............##################........" ".########.....#######..........###################........" "...######.....#######.........#######.......######........" "...######.....#######........#######......................" "...#################.........#######......................" "...################..........#######......................" "...#################.........#######......................" "...######.....#######........#######......................" "...######.....#######........#######......................" "...######.....#######.........#######.......######........" ".########.....#######..........###################........" ".########.....#######.######....##################.######." ".########.....#######.######......################.######." ".########.....#######.######.........#############.######." ".........................................................." };
class ZhangSuen;
class Image { public:
friend class ZhangSuen; using pixel_t = char; static const pixel_t BLACK_PIX; static const pixel_t WHITE_PIX;
Image(unsigned width = 1, unsigned height = 1) : width_{width}, height_{height}, data_( '\0', width_ * height_) {} Image(const Image& i) : width_{ i.width_}, height_{i.height_}, data_{i.data_} {} Image(Image&& i) : width_{ i.width_}, height_{i.height_}, data_{std::move(i.data_)} {} ~Image() = default; Image& operator=(const Image& i) { if (this != &i) { width_ = i.width_; height_ = i.height_; data_ = i.data_; } return *this; } Image& operator=(Image&& i) { if (this != &i) { width_ = i.width_; height_ = i.height_; data_ = std::move(i.data_); } return *this; } size_t idx(unsigned x, unsigned y) const noexcept { return y * width_ + x; } bool operator()(unsigned x, unsigned y) { return data_[idx(x, y)]; } friend std::ostream& operator<<(std::ostream& o, const Image& i) { o << i.width_ << " x " << i.height_ << std::endl; size_t px = 0; for(const auto& e : i.data_) { o << (e?Image::BLACK_PIX:Image::WHITE_PIX); if (++px % i.width_ == 0) o << std::endl; } return o << std::endl; } friend std::istream& operator>>(std::istream& in, Image& img) { auto it = std::begin(img.data_); const auto end = std::end(img.data_); Image::pixel_t tmp; while(in && it != end) { in >> tmp; if (tmp != Image::BLACK_PIX && tmp != Image::WHITE_PIX) throw "Bad character found in image"; *it = (tmp == Image::BLACK_PIX)?1:0; ++it; } return in; } unsigned width() const noexcept { return width_; } unsigned height() const noexcept { return height_; } struct Neighbours { // 9 2 3 // 8 1 4 // 7 6 5 Neighbours(const Image& img, unsigned p1_x, unsigned p1_y) : img_{img} , p1_{img.idx(p1_x, p1_y)} , p2_{p1_ - img.width()} , p3_{p2_ + 1} , p4_{p1_ + 1} , p5_{p4_ + img.width()} , p6_{p5_ - 1} , p7_{p6_ - 1} , p8_{p1_ - 1} , p9_{p2_ - 1} {} const Image& img_; const Image::pixel_t& p1() const noexcept { return img_.data_[p1_]; } const Image::pixel_t& p2() const noexcept { return img_.data_[p2_]; } const Image::pixel_t& p3() const noexcept { return img_.data_[p3_]; } const Image::pixel_t& p4() const noexcept { return img_.data_[p4_]; } const Image::pixel_t& p5() const noexcept { return img_.data_[p5_]; } const Image::pixel_t& p6() const noexcept { return img_.data_[p6_]; } const Image::pixel_t& p7() const noexcept { return img_.data_[p7_]; } const Image::pixel_t& p8() const noexcept { return img_.data_[p8_]; } const Image::pixel_t& p9() const noexcept { return img_.data_[p9_]; } const size_t p1_, p2_, p3_, p4_, p5_, p6_, p7_, p8_, p9_; }; Neighbours neighbours(unsigned x, unsigned y) const { return Neighbours(*this, x, y); }
private:
unsigned height_ { 0 }; unsigned width_ { 0 }; std::valarray<pixel_t> data_;
};
constexpr const Image::pixel_t Image::BLACK_PIX = '#'; constexpr const Image::pixel_t Image::WHITE_PIX = '.';
class ZhangSuen { public:
// the number of transitions from white to black, (0 -> 1) in the sequence P2,P3,P4,P5,P6,P7,P8,P9,P2 unsigned transitions_white_black(const Image::Neighbours& a) const { unsigned sum = 0; sum += (a.p9() == 0) && a.p2(); sum += (a.p2() == 0) && a.p3(); sum += (a.p3() == 0) && a.p4(); sum += (a.p8() == 0) && a.p9(); sum += (a.p4() == 0) && a.p5(); sum += (a.p7() == 0) && a.p8(); sum += (a.p6() == 0) && a.p7(); sum += (a.p5() == 0) && a.p6(); return sum; }
// The number of black pixel neighbours of P1. ( = sum(P2 .. P9) ) unsigned black_pixels(const Image::Neighbours& a) const { unsigned sum = 0; sum += a.p9(); sum += a.p2(); sum += a.p3(); sum += a.p8(); sum += a.p4(); sum += a.p7(); sum += a.p6(); sum += a.p5(); return sum; } const Image& operator()(const Image& img) { tmp_a_ = img; size_t changed_pixels = 0; do { changed_pixels = 0; // Step 1 tmp_b_ = tmp_a_; for(size_t y = 1; y < tmp_a_.height() - 1; ++y) { for(size_t x = 1; x < tmp_a_.width() - 1; ++x) { if (tmp_a_.data_[tmp_a_.idx(x, y)]) { auto n = tmp_a_.neighbours(x, y); auto bp = black_pixels(n); if (bp >= 2 && bp <= 6) { auto tr = transitions_white_black(n); if ( tr == 1 && (n.p2() * n.p4() * n.p6() == 0) && (n.p4() * n.p6() * n.p8() == 0) ) { tmp_b_.data_[n.p1_] = 0; ++changed_pixels; } } } } } // Step 2 tmp_a_ = tmp_b_; for(size_t y = 1; y < tmp_b_.height() - 1; ++y) { for(size_t x = 1; x < tmp_b_.width() - 1; ++x) { if (tmp_b_.data_[tmp_b_.idx(x, y)]) { auto n = tmp_b_.neighbours(x, y); auto bp = black_pixels(n); if (bp >= 2 && bp <= 6) { auto tr = transitions_white_black(n); if ( tr == 1 && (n.p2() * n.p4() * n.p8() == 0) && (n.p2() * n.p6() * n.p8() == 0) ) { tmp_a_.data_[n.p1_] = 0; ++changed_pixels; } } } } } } while(changed_pixels > 0); return tmp_a_; }
private:
Image tmp_a_; Image tmp_b_;
};
int main(int argc, char const *argv[]) {
using namespace std; Image img(32, 10); istringstream iss{input}; iss >> img; cout << img; cout << "ZhangSuen" << endl; ZhangSuen zs; Image res = std::move(zs(img)); cout << res << endl;
Image img2(58,18); istringstream iss2{input2}; iss2 >> img2; cout << img2; cout << "ZhangSuen with big image" << endl; Image res2 = std::move(zs(img2)); cout << res2 << endl; return 0;
} </lang>
Output:
32 x 10 ................................ .#########.......########....... .###...####.....####..####...... .###....###.....###....###...... .###...####.....###............. .#########......###............. .###.####.......###....###...... .###..####..###.####..####.###.. .###...####.###..########..###.. ................................ ZhangSuen 32 x 10 ................................ ..#######.........######........ ..#.....#........##............. ..#......#.......#.............. ..#.....#........#.............. ..#####.#........#.............. .......##........#.............. ........#....#...##....##...#... .........#.........####......... ................................ 58 x 18 .......................................................... .#################...................#############........ .##################...............################........ .###################............##################........ .########.....#######..........###################........ ...######.....#######.........#######.......######........ ...######.....#######........#######...................... ...#################.........#######...................... ...################..........#######...................... ...#################.........#######...................... ...######.....#######........#######...................... ...######.....#######........#######...................... ...######.....#######.........#######.......######........ .########.....#######..........###################........ .########.....#######.######....##################.######. .########.....#######.######......################.######. .########.....#######.######.........#############.######. .......................................................... ZhangSuen with big image 58 x 18 .......................................................... .......................................................... ....#.##########.......................#######............ .....##........#...................####.......#........... .....#..........#.................##...................... .....#..........#................#........................ .....#..........#................#........................ .....#..........#................#........................ .....############...............#......................... .....#..........#...............#......................... .....#..........#................#........................ .....#..........#................#........................ .....#..........#................#........................ .....#............................##...................... .....#.............................############........... .......................###..........................###... .......................................................... ..........................................................
D
This uses the module from the Bitmap Task. And it performs no heap allocations. <lang d>import std.stdio, std.algorithm, std.string, std.functional,
std.typecons, std.typetuple, bitmap;
struct BlackWhite {
ubyte c; alias c this; static immutable black = typeof(this)(0), white = typeof(this)(1);
}
alias Neighbours = BlackWhite[9]; alias Img = Image!BlackWhite;
/// Zhang-Suen thinning algorithm. Img zhangSuen(Img image1, Img image2) pure nothrow @safe @nogc in {
assert(image1.image.all!(x => x == Img.black || x == Img.white)); assert(image1.nx == image2.nx && image1.ny == image2.ny);
} out(result) {
assert(result.nx == image1.nx && result.ny == image1.ny); assert(result.image.all!(x => x == Img.black || x == Img.white));
} body {
/// True if inf <= x <= sup. static inInterval(T)(in T x, in T inf, in T sup) pure nothrow @safe @nogc { return x >= inf && x <= sup; }
/// Return 8-neighbours+1 of point (x,y) of given image, in order. static void neighbours(in Img I, in size_t x, in size_t y, out Neighbours n) pure nothrow @safe @nogc { n = [I[x,y-1], I[x+1,y-1], I[x+1,y], I[x+1,y+1], // P2,P3,P4,P5 I[x,y+1], I[x-1,y+1], I[x-1,y], I[x-1,y-1], // P6,P7,P8,P9 I[x,y-1]]; }
if (image1.nx < 3 || image1.ny < 3) { image2.image[] = image1.image[]; return image2; }
immutable static zeroOne = [0, 1]; //** Neighbours n; bool hasChanged; do { hasChanged = false;
foreach (immutable ab; TypeTuple!(tuple(2, 4), tuple(0, 6))) { foreach (immutable y; 1 .. image1.ny - 1) { foreach (immutable x; 1 .. image1.nx - 1) { neighbours(image1, x, y, n); if (image1[x, y] && // Cond. 0 (!n[ab[0]] || !n[4] || !n[6]) && // Cond. 4 (!n[0] || !n[2] || !n[ab[1]]) && // Cond. 3 //n[].count([0, 1]) == 1 && n[].count(zeroOne) == 1 && // Cond. 2 // n[0 .. 8].sum in iota(2, 7)) { inInterval(n[0 .. 8].sum, 2, 6)) { // Cond. 1 hasChanged = true; image2[x, y] = Img.black; } else image2[x, y] = image1[x, y]; } } image1.swap(image2); } } while (hasChanged);
return image1;
}
void main() {
immutable before_txt = " ##..### ##..### ##..### ##..### ##..##. ##..##. ##..##. ##..##. ##..##. ##..##. ##..##. ##..##. ######. .......";
immutable small_rc = " ................................ .#########.......########....... .###...####.....####..####...... .###....###.....###....###...... .###...####.....###............. .#########......###............. .###.####.......###....###...... .###..####..###.####..####.###.. .###...####.###..########..###.. ................................";
immutable rc = " ........................................................... .#################...................#############......... .##################...............################......... .###################............##################......... .########.....#######..........###################......... ...######.....#######.........#######.......######......... ...######.....#######........#######....................... ...#################.........#######....................... ...################..........#######....................... ...#################.........#######....................... ...######.....#######........#######....................... ...######.....#######........#######....................... ...######.....#######.........#######.......######......... .########.....#######..........###################......... .########.....#######.######....##################.######.. .########.....#######.######......################.######.. .########.....#######.######.........#############.######.. ...........................................................";
foreach (immutable txt; [before_txt, small_rc, rc]) { auto img = Img.fromText(txt); "From:".writeln; img.textualShow(/*bl=*/ '.', /*wh=*/ '#'); "\nTo thinned:".writeln; img.zhangSuen(img.dup).textualShow(/*bl=*/ '.', /*wh=*/ '#'); writeln; }
}</lang>
- Output:
From: ##..### ##..### ##..### ##..### ##..##. ##..##. ##..##. ##..##. ##..##. ##..##. ##..##. ##..##. ######. ....... To thinned: ##..### #.....# #.....# #...### #...#.. #...#.. #...#.. #...#.. #...#.. #...#.. #...#.. #...#.. #####.. ....... From: ................................ .#########.......########....... .###...####.....####..####...... .###....###.....###....###...... .###...####.....###............. .#########......###............. .###.####.......###....###...... .###..####..###.####..####.###.. .###...####.###..########..###.. ................................ To thinned: ................................ ..#######.........######........ ..#.....#........##............. ..#......#.......#.............. ..#.....#........#.............. ..#####.#........#.............. .......##........#.............. ........#....#...##....##...#... .........#.........####......... ................................ From: ........................................................... .#################...................#############......... .##################...............################......... .###################............##################......... .########.....#######..........###################......... ...######.....#######.........#######.......######......... ...######.....#######........#######....................... ...#################.........#######....................... ...################..........#######....................... ...#################.........#######....................... ...######.....#######........#######....................... ...######.....#######........#######....................... ...######.....#######.........#######.......######......... .########.....#######..........###################......... .########.....#######.######....##################.######.. .########.....#######.######......################.######.. .########.....#######.######.........#############.######.. ........................................................... To thinned: ........................................................... ........................................................... ....#.##########.......................#######............. .....##........#...................####.......#............ .....#..........#.................##....................... .....#..........#................#......................... .....#..........#................#......................... .....#..........#................#......................... .....############...............#.......................... .....#..........#...............#.......................... .....#..........#................#......................... .....#..........#................#......................... .....#..........#................#......................... .....#............................##....................... .....#.............................############............ .......................###..........................###.... ........................................................... ...........................................................
Elena
ELENA 5.0 :
<lang elena>import system'collections; import system'routines; import extensions; import extensions'routines;
const string[] image = new string[]{
" ", " ################# ############# ", " ################## ################ ", " ################### ################## ", " ######## ####### ################### ", " ###### ####### ####### ###### ", " ###### ####### ####### ", " ################# ####### ", " ################ ####### ", " ################# ####### ", " ###### ####### ####### ", " ###### ####### ####### ", " ###### ####### ####### ###### ", " ######## ####### ################### ", " ######## ####### ###### ################## ###### ", " ######## ####### ###### ################ ###### ", " ######## ####### ###### ############# ###### ", " "};
int[][] nbrs = new int[][] {
new int[]{0, -1}, new int[]{1, -1}, new int[]{1, 0}, new int[]{1, 1}, new int[]{0, 1}, new int[]{-1, 1}, new int[]{-1, 0}, new int[]{-1, -1}, new int[]{0, -1}
};
int[][][] nbrGroups = new int[][][] {
new int[][]{new int[]{0, 2, 4}, new int[]{2, 4, 6}}, new int[][]{new int[]{0, 2, 6}, new int[]{0, 4, 6}}
};
extension zhangsuenOp : Matrix<CharValue> {
proceed(r, c, toWhite, firstStep) { if (self[r][c] != $35) { ^ false }; int nn := self.numNeighbors(r,c); if ((nn < 2) || (nn > 6)) { ^ false }; if(self.numTransitions(r,c) != 1) { ^ false }; ifnot (self.atLeastOneIsWhite(r,c,firstStep.iif(0,1))) { ^ false }; toWhite.append(new { x = c; y = r; }); ^ true } numNeighbors(r,c) { int count := 0; for (int i := 0, i < nbrs.Length, i += 1) { if (self[r + nbrs[i][1]][c + nbrs[i][0]] == $35) { count += 1 } }; ^ count; } numTransitions(r,c) { int count := 0; for (int i := 0, i < nbrs.Length, i += 1) { if (self[r + nbrs[i][1]][c + nbrs[i][0]] == $32) { if (self[r + nbrs[i + 1][1]][c + nbrs[i + 1][0]] == $35) { count := count + 1 } } }; ^ count } atLeastOneIsWhite(r, c, step) { int count := 0; var group := nbrGroups[step]; for(int i := 0, i < 3, i += 1) { for(int j := 0, j < group[i].Length, j += 1) { var nbr := nbrs[group[i][j]]; if (self[r + nbr[1]][c + nbr[0]] == $32) { count := count + 1; ^ true }; ^ false } }; ^ count > 1 } thinImage() { bool firstStep := false; bool hasChanged := true; var toWhite := new List(); while (hasChanged || firstStep) { hasChanged := false; firstStep := firstStep.Inverted; for(int r := 1, r < self.Rows, r += 1) { for(int c := 1, c < self.Columns, c += 1) { if(self.proceed(r,c,toWhite,firstStep)) { hasChanged := true } } }; toWhite.forEach:(p){ self[p.y][p.x] := $32 }; toWhite.clear() } } print() { var it := self.enumerator(); it.forEach:(ch){ console.print(ch," ") }; while (it.next()) { console.writeLine();
it.forEach:(ch){ console.print(ch," ") } } }
}
public program() {
Matrix<CharValue> grid := class Matrix<CharValue>.load(new { int Rows = image.Length; int Columns = image[0].Length; at(int i, int j) = image[i][j]; }); grid.thinImage(); grid.print(); console.readChar()
}</lang>
- Output:
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
Elixir
<lang elixir>defmodule ZhangSuen do
@neighbours [{-1,0},{-1,1},{0,1},{1,1},{1,0},{1,-1},{0,-1},{-1,-1}] # 8 neighbours def thinning(str, black \\ ?#) do s0 = for {line, i} <- (String.split(str, "\n") |> Enum.with_index), {c, j} <- (to_char_list(line) |> Enum.with_index), into: Map.new, do: {{i,j}, (if c==black, do: 1, else: 0)} {xrange, yrange} = range(s0) print(s0, xrange, yrange) s1 = thinning_loop(s0, xrange, yrange) print(s1, xrange, yrange) end defp thinning_loop(s0, xrange, yrange) do s1 = step(s0, xrange, yrange, 1) # Step 1 s2 = step(s1, xrange, yrange, 0) # Step 2 if Map.equal?(s0, s2), do: s2, else: thinning_loop(s2, xrange, yrange) end defp step(s, xrange, yrange, g) do for x <- xrange, y <- yrange, into: Map.new, do: {{x,y}, s[{x,y}] - zs(s,x,y,g)} end defp zs(s, x, y, g) do if get(s,x,y) == 0 or # P1 (get(s,x-1,y) + get(s,x,y+1) + get(s,x+g,y-1+g)) == 3 or # P2, P4, P6/P8 (get(s,x-1+g,y+g) + get(s,x+1,y) + get(s,x,y-1)) == 3 do # P4/P2, P6, P8 0 else next = for {i,j} <- @neighbours, do: get(s, x+i, y+j) bp1 = Enum.sum(next) # B(P1) if bp1 in 2..6 do ap1 = (next++[hd(next)]) |> Enum.chunk(2,1) |> Enum.count(fn [a,b] -> a " ", 1 => "#"} defp print(map, xrange, yrange) do Enum.each(xrange, fn x -> IO.puts (for y <- yrange, do: @display[map[{x,y}]]) end) end
end
str = """ ........................................................... .#################...................#############......... .##################...............################......... .###################............##################......... .########.....#######..........###################......... ...######.....#######.........#######.......######......... ...######.....#######........#######....................... ...#################.........#######....................... ...###############...........#######....................... ...#################.........#######....................... ...######....########........#######....................... ...######.....#######........#######....................... ...######.....#######.........#######.......######......... .########.....#######..........###################......... .########.....#######..#####....##################.######.. .########.....#######..#####......################.######.. .########.....#######..#####.........#############.######.. ........................................................... """ ZhangSuen.thinning(str)
str = """ 00000000000000000000000000000000 01111111110000000111111110000000 01110001111000001111001111000000 01110000111000001110000111000000 01110001111000001110000000000000 01111111110000001110000000000000 01110111100000001110000111000000 01110011110011101111001111011100 01110001111011100111111110011100 00000000000000000000000000000000 """ ZhangSuen.thinning(str, ?1)</lang>
- Output:
################# ############# ################## ################ ################### ################## ######## ####### ################### ###### ####### ####### ###### ###### ####### ####### ################# ####### ############### ####### ################# ####### ###### ######## ####### ###### ####### ####### ###### ####### ####### ###### ######## ####### ################### ######## ####### ##### ################## ###### ######## ####### ##### ################ ###### ######## ####### ##### ############# ###### # ########## ####### ## # #### # # # ## # # # # # # # # # ############ # # # # # # # # # # # # # # ## # ############ ## ### ######### ######## ### #### #### #### ### ### ### ### ### #### ### ######### ### ### #### ### ### ### #### ### #### #### ### ### #### ### ######## ### ####### ###### # # ## # # # # # # ##### # # ## # # # ## ## # # ####
Fortran
With F90 came standardisation of a variety of array manipulation facilities. Since the image array is to be inspected as a whole then adjusted rather than adjusted step-by-step as it is inspected, the first thought was to employ the special facility of the FOR ALL statement, which is that in an expression such as <lang Fortarn>FOR ALL (i = 2:n - 1) A(i) = (A(i - 1) + A(i) + A(i + 1))/3</lang> all right-hand-side expressions will be evaluated with the original values of the array, while in the less special array assignment <lang Fortran>A(2:N - 1) = (A(1:N - 2) + A(2:N - 1) + A(3:N))/3</lang> as in the case of the equivalent DO-loop, the processing will be with a mixture of old and new values as the loop proceeds.
So, that suggests something like <lang Fortran> FOR ALL (I = 2:N - 1, J = 2:M - 1)
WHERE(DOT(I,J) .NE. 0) DOT(I,J) = ADJUST(DOT,I,J)</lang>
This requires function ADJUST to be a "pure" function, and they are not supposed to perpetrate side effects, such as one reporting that any adjustment was made. Nor is it clear that array DOT must be presented as a parameter either as the entire array or as element DOT(i,j), or if not, that it can be global to function ADJUST - which would also be an impurity - and for that matter, variables I and J could be global also...
Instead, thought turned to more closely following the task specification, which involves producing a list of elements to be adjusted after an inspection pass. Given that array DOT is two-dimensional, it would be nice if an element could be indexed via an expression such as DOT(INDEX)
where INDEX was an array of two elements with INDEX(1) = i, and INDEX(2) = j, so as to access DOT(i,j) If this were possible, then obviously one could hope that array INDEX could be extended so as to store the multiple elements of a list of such locations to access, with a view to DOT(INDEX(1:n)) = 0
adjusting the image.
Alas, such a syntax form is not accommodated. However, F90 also introduced the ability to define and use compound data types, such as the type PLACE as used below. It is not possible to define a type of a special, recognised form, such as say "SUBSCRIPT LIST" that can be used as dreamt of above, so the components are just ordinary variables. Two ordinary arrays could be used, one for each of the two subscripts, or a compound type could be devised in a hint towards self-documentation. Thus, <lang Fortran> DOT(WHACK(1:WHACKCOUNT).I,WHACK(1:WHACKCOUNT).J) = 0</lang>
But it doesn't work... After a fair amount of head scratching, not at all assisted by the woolly generalities and inane examples of the compiler's "help" collection, it became apparent that the expression did not work through a list of indices as anticipated, but instead, for each value of the first index, all the values of the second index were selected. Thus, instead of the first change being DOT(WHACK(1).I,WHACK(1).J) only, it was DOT(WHACK(1).I,WHACK(1:WHACKCOUNT).J) that were being cleared. Accordingly, the fancy syntax has to be abandoned in favour of a specific DO-loop.
<lang Fortran> MODULE ZhangSuenThinning !Image manipulation.
CONTAINS SUBROUTINE ZST(DOT) !Attempts to thin out thick lines. INTEGER DOT(:,:) !The image in an array, rows down the page. TYPE PLACE !This records an array location. INTEGER I !Via its INTEGER J !Indices. END TYPE PLACE !A lot of baggage. TYPE(PLACE) WHACK(UBOUND(DOT,DIM = 1)*UBOUND(DOT,DIM = 2)) !Allow a whack for every dot. INTEGER WHACKCOUNT !Counts up those to be wiped out. LOGICAL WHACKED !Notes if any have been. INTEGER STEP,I,N,J,M !Assistants. INTEGER D9(9) !Holds a 3x3 portion. INTEGER HIT1(3,2),HIT2(3,2) !Lists of elements to inspect for certain tests. PARAMETER (HIT1 = (/2,6,8, 4,2,6/)) !Two stages. PARAMETER (HIT2 = (/4,8,6, 2,4,8/)) !Each with two hit lists. N = UBOUND(DOT,DIM = 1) !Number of rows. M = UBOUND(DOT,DIM = 2) !Number of columns.
Commence a pass.
10 WHACKED = .FALSE. !No damage so far. DO STEP = 1,2 !Each pass is in two stages. WHACKCOUNT = 0 !No dots have been selected for whitewashing. DO I = 2,N - 1 !Scan down the rows. DO J = 2,M - 1 !And the columns. Interior dots only. IF (DOT(I,J).NE.0) THEN !Rule 0: Is the dot black? Eight neighbours are present due to loop control. D9(1:3) = DOT(I - 1,J - 1:J + 1) !Yes. Form a 3x3 mesh. 1 2 3 not 9 2 3 D9(4:6) = DOT(I ,J - 1:J + 1) !As a 1-D array. 4 5 6 8 1 4 D9(7:9) = DOT(I + 1,J - 1:J + 1) !For eased access. 7 8 9 7 6 5 CALL INSPECT(D9,HIT1(1,STEP),HIT2(1,STEP)) !Apply rules one to four, as specified. END IF !So much for a black dot. END DO !On to the next column. END DO !On to the next row. IF (WHACKCOUNT.GT.0) THEN !Are any to be wiped out? DO I = 1,WHACKCOUNT !Yes! DOT(WHACK(I).I,WHACK(I).J) = 0 !One by one. END DO !On to the next victim.
Can't use DOT(WHACK(1:WHACKCOUNT).I,WHACK(1:WHACKCOUNT).J) = 0
WHACKED = .TRUE. !There has been a change. END IF !So much for changes. END DO !On to the second stage. IF (WHACKED) GO TO 10 !If there had been changes, perhaps there will be more. CONTAINS !Some helpers. SUBROUTINE INSPECT(BLOB,HIT1,HIT2) !Inspect a 3x3 piece according to the four levels of tests as specified. INTEGER BLOB(9) !The piece. BLOB(5) is DOT(I,J), and is expected to be 1. INTEGER HIT1(3),HIT2(3) !Two hit lists. INTEGER TWIRL(9) !traces the periphery of the piece. PARAMETER (TWIRL = (/2,3,6,9,8,7,4,1,2/)) !Cycle around the periphery. INTEGER B !A counter. !Rule: B = SUM(BLOB) - BLOB(5) !1: Count the neighbours having one, not zero. IF (2 <= B .AND. B <= 6) THEN ! The test. Can't have 2 <= B <= 6, alas. IF (COUNT(BLOB(TWIRL(1:8)) !2: Counting transitions. * .LT.BLOB(TWIRL(2:9))) .EQ.1) THEN ! The test of 0 --> positive. IF (ANY(BLOB(HIT1).EQ.0)) THEN !3: At least one must be white. IF (ANY(BLOB(HIT2).EQ.0)) THEN !4: Of two sets of three. WHACKCOUNT = WHACKCOUNT + 1 !Another one down! WHACK(WHACKCOUNT) = PLACE(I,J) !This is the place. END IF !Now back out of the nested IF-statements. END IF !Since the tests must all be passed END IF !Rather than say three out of four. END IF !For the given method. END SUBROUTINE INSPECT!That was weird. END SUBROUTINE ZST !But so it goes.
SUBROUTINE SHOW(A) !Display an image array on the standard output. INTEGER A(:,:) !Values are expected to be zero and one. CHARACTER*1 HIC(0:1) !But I don't want to look at wads of digits. PARAMETER (HIC = (/".","#"/)) !These offer better contrast. INTEGER I !A stepper. DO I = 1,UBOUND(A,DIM = 1) !Work down the given number of rows. WRITE (6,"(666A1)") HIC(A(I,:)) !Roll a translated line. END DO !Hopefully, no more than 666 to a line. END SUBROUTINE SHOW !That was straightforward. END MODULE ZhangSuenThinning
PROGRAM POKE !Just set up the example. USE ZhangSuenThinning INTEGER N,M !Parameters for the example. PARAMETER (N = 10,M = 32) !Rows and columns. CHARACTER*(M) CANVAS(N) !Rather than some monster DATA statement, PARAMETER (CANVAS = (/ !It is easier to prepare a worksheet. 1 " ", 2 " 111111111 11111111 ", 3 " 111 1111 1111 1111 ", 4 " 111 111 111 111 ", 5 " 111 1111 111 ", 6 " 111111111 111 ", 7 " 111 1111 111 111 ", 8 " 111 1111 111 1111 1111 111 ", 9 " 111 1111 111 11111111 111 ", o " "/)) INTEGER IMAGE(N,M) !The image array. Exactly the required size. INTEGER I !A stepper.
DO I = 1,N !Read the rows. READ (CANVAS(I),"(666I1)") IMAGE(I,:) !Presumably, 666 will suffice. END DO !A blank is taken as a zero with formatted input.
WRITE (6,*) "The initial image..." CALL SHOW(IMAGE) WRITE (6,*)
CALL ZST(IMAGE) WRITE (6,*) "And after 'thinning'..." CALL SHOW(IMAGE)
END PROGRAM POKE </lang>
Output:
The initial image... ................................ .#########.......########....... .###...####.....####..####...... .###....###.....###....###...... .###...####.....###............. .#########......###............. .###.####.......###....###...... .###..####..###.####..####.###.. .###...####.###..########..###.. ................................ And after 'thinning'... ................................ ..#######.........######........ ..#.....#........##............. ..#......#.......#.............. ..#.....#........#.............. ..#####.#........#.............. .......##........#.............. ........#....#...##....##...#... .........#.........####......... ................................
FreeBASIC
<lang freebasic>' version 08-10-2016 ' compile with: fbc -s console
Data "00000000000000000000000000000000" Data "01111111110000000111111110000000" Data "01110001111000001111001111000000" Data "01110000111000001110000111000000" Data "01110001111000001110000000000000" Data "01111111110000001110000000000000" Data "01110111100000001110000111000000" Data "01110011110011101111001111011100" Data "01110001111011100111111110011100" Data "00000000000000000000000000000000" Data "END"
' ------=< MAIN >=------
Dim As UInteger x, y, m, n Dim As String input_str
Do ' find out how big it is
Read input_str If input_str = "END" Then Exit Do If x < Len(input_str) Then x = Len(input_str) y = y + 1
Loop
m = x -1 : n = y -1 ReDim As UByte old(m, n), new_(m, n)
y = 0 Restore ' restore data pointer Do ' put data in array
Read input_str If input_str="END" Then Exit Do For x = 0 To Len(input_str) -1 old(x,y) = input_str[x] - Asc("0") ' print image If old(x, y) = 0 Then Print "."; Else Print "#"; Next Print y = y + 1
Loop
'corners and sides do not change For x = 0 To m
new_(x, 0) = old(x, 0) new_(x, n) = old(x, n)
Next
For y = 0 To n
new_(0, y) = old(0, y) new_(m, y) = old(m, y)
Next
Dim As UInteger tmp, change, stage = 1 Do
change = 0 For y = 1 To n -1 For x = 1 To m -1 ' -1- If old(x,y) = 0 Then ' first condition, p1 must be black new_(x,y) = 0 Continue For End If ' -2- tmp = old(x, y -1) + old(x +1, y -1) tmp = tmp + old(x +1, y) + old(x +1, y +1) + old(x, y +1) tmp = tmp + old(x -1, y +1) + old(x -1, y) + old(x -1, y -1) If tmp < 2 OrElse tmp > 6 Then ' 2 <= B(p1) <= 6 new_(x, y) = 1 Continue For End If ' -3- tmp = 0 If old(x , y ) = 0 And old(x , y -1) = 1 Then tmp += 1 ' p1 > p2 If old(x , y -1) = 0 And old(x +1, y -1) = 1 Then tmp += 1 ' p2 > p3 If old(x +1, y -1) = 0 And old(x +1, y ) = 1 Then tmp += 1 ' p3 > p4 If old(x +1, y ) = 0 And old(x +1, y +1) = 1 Then tmp += 1 ' p4 > p5 If old(x +1, y +1) = 0 And old(x , y +1) = 1 Then tmp += 1 ' p5 > p6 If old(x , y +1) = 0 And old(x -1, y +1) = 1 Then tmp += 1 ' p6 > p7 If old(x -1, y +1) = 0 And old(x -1, y ) = 1 Then tmp += 1 ' p7 > p8 If old(x -1, y ) = 0 And old(x -1, y -1) = 1 Then tmp += 1 ' p8 > p9 If old(x -1, y -1) = 0 And old(x , y -1) = 1 Then tmp += 1 ' p9 > p2 ' tmp = 1 ==> A(P1) = 1 If tmp <> 1 Then new_(x, y) = 1 Continue For End If If (stage And 1) = 1 Then ' step 1 -4- -5- If (old(x, y -1) + old(x +1, y) + old(x, y +1)) = 3 OrElse _ (old(x +1, y) + old(x, y +1) + old(x -1, y)) = 3 Then new_(x, y) = 1 Continue For End If Else ' step 2 -4- -5- If (old(x, y -1) + old(x +1, y) + old(x -1, y)) = 3 OrElse _ (old(x, y -1) + old(x, y +1) + old(x -1, y)) = 3 Then new_(x, y) = 1 Continue For End If End If ' all condition are met, make p1 white (0) new_(x, y) = 0 change = 1 ' flag change Next Next
' copy new_() into old() For y = 0 To n For x = 0 To m old(x, y) = new_(x, y) Next Next
stage += 1
Loop Until change = 0 ' stop when there are no changes made
Print ' print result Print "End result" For y = 0 To n
For x = 0 To m If old(x, y) = 0 Then Print "."; Else Print "#"; Next Print
Next
' empty keyboard buffer
While Inkey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End</lang>
- Output:
................................ .#########.......########....... .###...####.....####..####...... .###....###.....###....###...... .###...####.....###............. .#########......###............. .###.####.......###....###...... .###..####..###.####..####.###.. .###...####.###..########..###.. ................................ End result ................................ ..#######.........######........ ..#.....#........##............. ..#......#.......#.............. ..#.....#........#.............. ..#####.#........#.............. .......##........#.............. ........#....#...##....##...#... .........#.........####......... ................................
Go
<lang go>package main
import (
"bytes" "fmt" "strings"
)
var in = ` 00000000000000000000000000000000 01111111110000000111111110000000 01110001111000001111001111000000 01110000111000001110000111000000 01110001111000001110000000000000 01111111110000001110000000000000 01110111100000001110000111000000 01110011110011101111001111011100 01110001111011100111111110011100 00000000000000000000000000000000`
func main() {
b := wbFromString(in, '1') b.zhangSuen() fmt.Println(b)
}
const (
white = 0 black = 1
)
type wbArray [][]byte // elements are white or black.
// parameter blk is character to read as black. otherwise kinda rigid, // expects ascii, leading newline, no trailing newline, // takes color from low bit of character. func wbFromString(s string, blk byte) wbArray {
lines := strings.Split(s, "\n")[1:] b := make(wbArray, len(lines)) for i, sl := range lines { bl := make([]byte, len(sl)) for j := 0; j < len(sl); j++ { bl[j] = sl[j] & 1 } b[i] = bl } return b
}
// rigid again, hard coded to output space for white, # for black, // no leading or trailing newline. var sym = [2]byte{
white: ' ', black: '#',
}
func (b wbArray) String() string {
b2 := bytes.Join(b, []byte{'\n'}) for i, b1 := range b2 { if b1 > 1 { continue } b2[i] = sym[b1] } return string(b2)
}
// neighbor offsets var nb = [...][2]int{
2: {-1, 0}, // p2 offsets 3: {-1, 1}, // ... 4: {0, 1}, 5: {1, 1}, 6: {1, 0}, 7: {1, -1}, 8: {0, -1}, 9: {-1, -1}, // p9 offsets
}
func (b wbArray) reset(en []int) (rs bool) {
var r, c int var p [10]byte
readP := func() { for nx := 1; nx <= 9; nx++ { n := nb[nx] p[nx] = b[r+n[0]][c+n[1]] } }
shiftRead := func() { n := nb[3] p[9], p[2], p[3] = p[2], p[3], b[r+n[0]][c+n[1]] n = nb[4] p[8], p[1], p[4] = p[1], p[4], b[r+n[0]][c+n[1]] n = nb[5] p[7], p[6], p[5] = p[6], p[5], b[r+n[0]][c+n[1]] }
// returns "A", count of white->black transitions in circuit of neighbors // of an interior pixel b[r][c] countA := func() (ct byte) { bit := p[9] for nx := 2; nx <= 9; nx++ { last := bit bit = p[nx] if last == white { ct += bit } } return ct }
// returns "B", count of black pixels neighboring interior pixel b[r][c]. countB := func() (ct byte) { for nx := 2; nx <= 9; nx++ { ct += p[nx] } return ct }
lastRow := len(b) - 1 lastCol := len(b[0]) - 1
mark := make([][]bool, lastRow) for r = range mark { mark[r] = make([]bool, lastCol) }
for r = 1; r < lastRow; r++ { c = 1 readP() for { // column loop m := false // test for failure of any of the five conditions, if !(p[1] == black) { goto markDone } if b1 := countB(); !(2 <= b1 && b1 <= 6) { goto markDone } if !(countA() == 1) { goto markDone } { e1, e2 := p[en[1]], p[en[2]] if !(p[en[0]]&e1&e2 == 0) { goto markDone } if !(e1&e2&p[en[3]] == 0) { goto markDone } } // no conditions failed, mark this pixel for reset m = true rs = true // and mark that image changes markDone: mark[r][c] = m c++ if c == lastCol { break } shiftRead() } } if rs { for r = 1; r < lastRow; r++ { for c = 1; c < lastCol; c++ { if mark[r][c] { b[r][c] = white } } } } return rs
}
var step1 = []int{2, 4, 6, 8} var step2 = []int{4, 2, 8, 6}
func (b wbArray) zhangSuen() {
for { rs1 := b.reset(step1) rs2 := b.reset(step2) if !rs1 && !rs2 { break } }
}</lang>
- Output:
####### ###### # # ## # # # # # # ##### # # ## # # # ## ## # # ####
Groovy
<lang groovy>def zhangSuen(text) {
def image = text.split('\n').collect { line -> line.collect { it == '#' ? 1 : 0} } def p2, p3, p4, p5, p6, p7, p8, p9 def step1 = { (p2 * p4 * p6 == 0) && (p4 * p6 * p8 == 0) } def step2 = { (p2 * p4 * p8 == 0) && (p2 * p6 * p8 == 0) } def reduce = { step -> def toWhite = [] image.eachWithIndex{ line, y -> line.eachWithIndex{ pixel, x -> if (!pixel) return (p2, p3, p4, p5, p6, p7, p8, p9) = [image[y-1][x], image[y-1][x+1], image[y][x+1], image[y+1][x+1], image[y+1][x], image[y+1][x-1], image[y][x-1], image[y-1][x-1]] def a = [[p2,p3],[p3,p4],[p4,p5],[p5,p6],[p6,p7],[p7,p8],[p8,p9],[p9,p2]].collect { a1, a2 -> (a1 == 0 && a2 ==1) ? 1 : 0 }.sum() def b = [p2, p3, p4, p5, p6, p7, p8, p9].sum() if (a != 1 || b < 2 || b > 6) return
if (step.call()) toWhite << [y,x] } } toWhite.each { y, x -> image[y][x] = 0 } !toWhite.isEmpty() }
while (reduce(step1) | reduce(step2)); image.collect { line -> line.collect { it ? '#' : '.' }.join() }.join('\n')
}</lang> Testing: <lang groovy>def small = """\
................................ .#########.......########....... .###...####.....####..####...... .###....###.....###....###...... .###...####.....###............. .#########......###............. .###.####.......###....###...... .###..####..###.####..####.###.. .###...####.###..########..###.. ................................""".stripIndent()
def large = """\
........................................................... .#################...................#############......... .##################...............################......... .###################............##################......... .########.....#######..........###################......... ...######.....#######.........#######.......######......... ...######.....#######........#######....................... ...#################.........#######....................... ...################..........#######....................... ...#################.........#######....................... ...######.....#######........#######....................... ...######.....#######........#######....................... ...######.....#######.........#######.......######......... .########.....#######..........###################......... .########.....#######.######....##################.######.. .########.....#######.######......################.######.. .########.....#######.######.........#############.######.. ...........................................................""".stripIndent()
[small, large].each {
println "From:" println it println "To:" println zhangSuen(it) println()
}</lang> Output:
From: ................................ .#########.......########....... .###...####.....####..####...... .###....###.....###....###...... .###...####.....###............. .#########......###............. .###.####.......###....###...... .###..####..###.####..####.###.. .###...####.###..########..###.. ................................ To: ................................ ..#######.........######........ ..#.....#........##............. ..#......#.......#.............. ..#.....#........#.............. ..#####.#........#.............. .......##........#.............. ........#....#...##....##...#... .........#.........####......... ................................ From: ........................................................... .#################...................#############......... .##################...............################......... .###################............##################......... .########.....#######..........###################......... ...######.....#######.........#######.......######......... ...######.....#######........#######....................... ...#################.........#######....................... ...################..........#######....................... ...#################.........#######....................... ...######.....#######........#######....................... ...######.....#######........#######....................... ...######.....#######.........#######.......######......... .########.....#######..........###################......... .########.....#######.######....##################.######.. .########.....#######.######......################.######.. .########.....#######.######.........#############.######.. ........................................................... To: ........................................................... ........................................................... ....#.##########.......................#######............. .....##........#...................####.......#............ .....#..........#.................##....................... .....#..........#................#......................... .....#..........#................#......................... .....#..........#................#......................... .....############...............#.......................... .....#..........#...............#.......................... .....#..........#................#......................... .....#..........#................#......................... .....#..........#................#......................... .....#............................##....................... .....#.............................############............ .......................###..........................###.... ........................................................... ...........................................................
Haskell
<lang Haskell>import Data.Array import qualified Data.List as List
data BW = Black | White
deriving (Eq, Show)
type Index = (Int, Int) type BWArray = Array Index BW
toBW :: Char -> BW toBW '0' = White toBW '1' = Black toBW ' ' = White toBW '#' = Black toBW _ = error "toBW: illegal char"
toBWArray :: [String] -> BWArray toBWArray strings = arr
where height = length strings width = minimum $ map length strings arr = listArray ((0, 0), (width - 1, height - 1)) . map toBW . concat . List.transpose $ map (take width) strings
toChar :: BW -> Char toChar White = ' ' toChar Black = '#'
chunksOf :: Int -> [a] -> a chunksOf _ [] = [] chunksOf n xs = take n xs : (chunksOf n $ drop n xs)
showBWArray :: BWArray -> String showBWArray arr =
List.intercalate "\n" . List.transpose . chunksOf (height + 1) . map toChar $ elems arr where (_, (_, height)) = bounds arr
add :: Num a => (a, a) -> (a, a) -> (a, a) add (a, b) (x, y) = (a + x, b + y)
within :: Ord a => ((a, a), (a, a)) -> (a, a) -> Bool within ((a, b), (c, d)) (x, y) =
a <= x && x <= c && b <= y && y <= d
p2, p3, p4, p5, p6, p7, p8, p9 :: Index p2 = ( 0, -1) p3 = ( 1, -1) p4 = ( 1, 0) p5 = ( 1, 1) p6 = ( 0, 1) p7 = (-1, 1) p8 = (-1, 0) p9 = (-1, -1)
ixamap :: Ix i => ((i, a) -> b) -> Array i a -> Array i b ixamap f a = listArray (bounds a) $ map f $ assocs a
thin :: BWArray -> BWArray thin arr =
if pass2 == arr then pass2 else thin pass2 where (low, high) = bounds arr lowB = low `add` (1, 1) highB = high `add` (-1, -1) isInner = within (lowB, highB) offs p = map (add p) [p2, p3, p4, p5, p6, p7, p8, p9] trans c (a, b) = if a == White && b == Black then c + 1 else c zipshift xs = zip xs (drop 1 xs ++ xs) transitions a = (== (1 :: Int)) . foldl trans 0 . zipshift . map (a !) . offs within2to6 n = 2 <= n && n <= 6 blacks a p = within2to6 . length . filter ((== Black) . (a !)) $ offs p oneWhite xs a p = any ((== White) . (a !) . add p) xs oneRight = oneWhite [p2, p4, p6] oneDown = oneWhite [p4, p6, p8] oneUp = oneWhite [p2, p4, p8] oneLeft = oneWhite [p2, p6, p8] precond a p = (a ! p == Black) && isInner p && blacks a p && transitions a p stage1 a p = precond a p && oneRight a p && oneDown a p stage2 a p = precond a p && oneUp a p && oneLeft a p stager f (p, d) = if f p then White else d pass1 = ixamap (stager $ stage1 arr) arr pass2 = ixamap (stager $ stage2 pass1) pass1
sampleExA :: [String] sampleExA =
["00000000000000000000000000000000" ,"01111111110000000111111110000000" ,"01110001111000001111001111000000" ,"01110000111000001110000111000000" ,"01110001111000001110000000000000" ,"01111111110000001110000000000000" ,"01110111100000001110000111000000" ,"01110011110011101111001111011100" ,"01110001111011100111111110011100" ,"00000000000000000000000000000000"]
sampleExB :: [String] sampleExB =
[" " ," ################# ############# " ," ################## ################ " ," ################### ################## " ," ######## ####### ################### " ," ###### ####### ####### ###### " ," ###### ####### ####### " ," ################# ####### " ," ################ ####### " ," ################# ####### " ," ###### ####### ####### " ," ###### ####### ####### " ," ###### ####### ####### ###### " ," ######## ####### ################### " ," ######## ####### ###### ################## ###### " ," ######## ####### ###### ################ ###### " ," ######## ####### ###### ############# ###### " ," "]
main :: IO () main = mapM_ (putStrLn . showBWArray . thin . toBWArray) [sampleExA, sampleExB]</lang>
- Output:
####### ###### # # ## # # # # # # ##### # # ## # # # ## ## # # #### # ########## ####### ## # #### # # # ## # # # # # # # # # ############ # # # # # # # # # # # # # # ## # ############ ### ###
J
Solution: <lang j>isBlackPx=: '1'&=;._2 NB. boolean array of black pixels toImage=: [: , LF ,.~ '01' {~ ] NB. convert to original representation frameImg=: 0 ,. 0 , >:@$ {. ] NB. adds border of 0's to image
neighbrs=: 1 :'(1 1 ,: 3 3)&(u;._3)' NB. applies verb u to neighbourhoods
Bdry=: 1 2 5 8 7 6 3 0 1 NB. map pixel index to neighbour order getPx=: { , NB. get desired pixels from neighbourhood Ap1=: [: +/ 2 </\ Bdry&getPx NB. count 0->1 transitions Bp1=: [: +/ [: }. Bdry&getPx NB. count black neighbours
c11=: (2&<: *. <:&6)@Bp1 NB. step 1, condition 1 c12=: 1 = Ap1 NB. ... c13=: 0 e. 1 5 7&getPx c14=: 0 e. 5 7 3&getPx c23=: 0 e. 1 5 3&getPx NB. step2, condition 3 c24=: 0 e. 1 7 3&getPx
cond1=: c11 *. c12 *. c13 *. c14 NB. step1 conditions cond2=: c11 *. c12 *. c23 *. c24 NB. step2 conditions whiten=: [ * -.@:*. NB. make black pixels white step1=: whiten frameImg@(cond1 neighbrs) step2=: whiten frameImg@(cond2 neighbrs)
zhangSuen=: [: toImage [: step2@step1^:_ isBlackPx</lang> Alternative, explicit representation of last verb above <lang j>zhangSuenX=: verb define
img=. isBlackPx y whilst. 0 < +/ , msk1 +.&-. msk2 do. msk1=. (-.@:*. [: frameImg cond1 neighbrs) img img=. msk1 * img msk2=. (-.@:*. [: frameImg cond2 neighbrs) img img=. msk2 * img end. toImage img
)</lang> Example Use: <lang j>toASCII=: ' #' {~ '1'&=;._2 NB. convert to ASCII representation
ExampleImg=: noun define 00000000000000000000000000000000 01111111110000000111111110000000 01110001111000001111001111000000 01110000111000001110000111000000 01110001111000001110000000000000 01111111110000001110000000000000 01110111100000001110000111000000 01110011110011101111001111011100 01110001111011100111111110011100 00000000000000000000000000000000 )
toASCII zhangSuen ExampleImg ####### ###### # # ## # # # # # # ##### # # ## # # # ## ## # # #### </lang>
Java
<lang java>import java.awt.Point; import java.util.*;
public class ZhangSuen {
final static String[] image = { " ", " ################# ############# ", " ################## ################ ", " ################### ################## ", " ######## ####### ################### ", " ###### ####### ####### ###### ", " ###### ####### ####### ", " ################# ####### ", " ################ ####### ", " ################# ####### ", " ###### ####### ####### ", " ###### ####### ####### ", " ###### ####### ####### ###### ", " ######## ####### ################### ", " ######## ####### ###### ################## ###### ", " ######## ####### ###### ################ ###### ", " ######## ####### ###### ############# ###### ", " "};
final static int[][] nbrs = {{0, -1}, {1, -1}, {1, 0}, {1, 1}, {0, 1}, {-1, 1}, {-1, 0}, {-1, -1}, {0, -1}};
final static int[][][] nbrGroups = {{{0, 2, 4}, {2, 4, 6}}, {{0, 2, 6}, {0, 4, 6}}};
static List<Point> toWhite = new ArrayList<>(); static char[][] grid;
public static void main(String[] args) { grid = new char[image.length][]; for (int r = 0; r < image.length; r++) grid[r] = image[r].toCharArray();
thinImage(); }
static void thinImage() { boolean firstStep = false; boolean hasChanged;
do { hasChanged = false; firstStep = !firstStep;
for (int r = 1; r < grid.length - 1; r++) { for (int c = 1; c < grid[0].length - 1; c++) {
if (grid[r][c] != '#') continue;
int nn = numNeighbors(r, c); if (nn < 2 || nn > 6) continue;
if (numTransitions(r, c) != 1) continue;
if (!atLeastOneIsWhite(r, c, firstStep ? 0 : 1)) continue;
toWhite.add(new Point(c, r)); hasChanged = true; } }
for (Point p : toWhite) grid[p.y][p.x] = ' '; toWhite.clear();
} while (firstStep || hasChanged);
printResult(); }
static int numNeighbors(int r, int c) { int count = 0; for (int i = 0; i < nbrs.length - 1; i++) if (grid[r + nbrs[i][1]][c + nbrs[i][0]] == '#') count++; return count; }
static int numTransitions(int r, int c) { int count = 0; for (int i = 0; i < nbrs.length - 1; i++) if (grid[r + nbrs[i][1]][c + nbrs[i][0]] == ' ') { if (grid[r + nbrs[i + 1][1]][c + nbrs[i + 1][0]] == '#') count++; } return count; }
static boolean atLeastOneIsWhite(int r, int c, int step) { int count = 0; int[][] group = nbrGroups[step]; for (int i = 0; i < 2; i++) for (int j = 0; j < group[i].length; j++) { int[] nbr = nbrs[group[i][j]]; if (grid[r + nbr[1]][c + nbr[0]] == ' ') { count++; break; } } return count > 1; }
static void printResult() { for (char[] row : grid) System.out.println(row); }
}</lang>
Output:
# ########## ####### ## # #### # # # ## # # # # # # # # # ############ # # # # # # # # # # # # # # ## # ############ ### ###
JavaScript
<lang javascript>function Point(x, y) {
this.x = x; this.y = y;
} var ZhangSuen = (function () {
function ZhangSuen() { } ZhangSuen.image = [" ", " ################# ############# ", " ################## ################ ", " ################### ################## ", " ######## ####### ################### ", " ###### ####### ####### ###### ", " ###### ####### ####### ", " ################# ####### ", " ################ ####### ", " ################# ####### ", " ###### ####### ####### ", " ###### ####### ####### ", " ###### ####### ####### ###### ", " ######## ####### ################### ", " ######## ####### ###### ################## ###### ", " ######## ####### ###### ################ ###### ", " ######## ####### ###### ############# ###### ", " "];
ZhangSuen.nbrs = [[0, -1], [1, -1], [1, 0], [1, 1], [0, 1], [-1, 1], [-1, 0], [-1, -1], [0, -1]];
ZhangSuen.nbrGroups = [[[0, 2, 4], [2, 4, 6]], [[0, 2, 6], [0, 4, 6]]];
ZhangSuen.toWhite = new Array(); ; ZhangSuen.main = function (args) { ZhangSuen.grid = new Array(ZhangSuen.image.length); for (var r = 0; r < ZhangSuen.image.length; r++) ZhangSuen.grid[r] = (ZhangSuen.image[r]).split(); ZhangSuen.thinImage(); }; ZhangSuen.thinImage = function () { var firstStep = false; var hasChanged; do { hasChanged = false; firstStep = !firstStep; for (var r = 1; r < ZhangSuen.grid.length - 1; r++) { for (var c = 1; c < ZhangSuen.grid[0].length - 1; c++) { if (ZhangSuen.grid[r][c] !== '#') continue; var nn = ZhangSuen.numNeighbors(r, c); if (nn < 2 || nn > 6) continue; if (ZhangSuen.numTransitions(r, c) !== 1) continue; if (!ZhangSuen.atLeastOneIsWhite(r, c, firstStep ? 0 : 1)) continue; ZhangSuen.toWhite.push(new Point(c, r)); hasChanged = true; } } for (let i = 0; i < ZhangSuen.toWhite.length; i++) { var p = ZhangSuen.toWhite[i]; ZhangSuen.grid[p.y][p.x] = ' '; } ZhangSuen.toWhite = new Array(); } while ((firstStep || hasChanged)); ZhangSuen.printResult(); }; ZhangSuen.numNeighbors = function (r, c) { var count = 0; for (var i = 0; i < ZhangSuen.nbrs.length - 1; i++) if (ZhangSuen.grid[r + ZhangSuen.nbrs[i][1]][c + ZhangSuen.nbrs[i][0]] === '#') count++; return count; }; ZhangSuen.numTransitions = function (r, c) { var count = 0; for (var i = 0; i < ZhangSuen.nbrs.length - 1; i++) if (ZhangSuen.grid[r + ZhangSuen.nbrs[i][1]][c + ZhangSuen.nbrs[i][0]] === ' ') { if (ZhangSuen.grid[r + ZhangSuen.nbrs[i + 1][1]][c + ZhangSuen.nbrs[i + 1][0]] === '#') count++; } return count; }; ZhangSuen.atLeastOneIsWhite = function (r, c, step) { var count = 0; var group = ZhangSuen.nbrGroups[step]; for (var i = 0; i < 2; i++) for (var j = 0; j < group[i].length; j++) { var nbr = ZhangSuen.nbrs[group[i][j]]; if (ZhangSuen.grid[r + nbr[1]][c + nbr[0]] === ' ') { count++; break; } } return count > 1; }; ZhangSuen.printResult = function () { for (var i = 0; i < ZhangSuen.grid.length; i++) { var row = ZhangSuen.grid[i]; console.log(row.join()); } }; return ZhangSuen;
}()); ZhangSuen.main(null);</lang>
Output:
# ########## ####### ## # #### # # # ## # # # # # # # # # ############ # # # # # # # # # # # # # # ## # ############ ### ###
Julia
<lang julia> const pixelstring = "00000000000000000000000000000000" * "01111111110000000111111110000000" * "01110001111000001111001111000000" * "01110000111000001110000111000000" * "01110001111000001110000000000000" * "01111111110000001110000000000000" * "01110111100000001110000111000000" * "01110011110011101111001111011100" * "01110001111011100111111110011100" * "00000000000000000000000000000000" const pixels = reshape([UInt8(c- 48) for c in pixelstring], (32,10))'
function surroundtesting(px, i, j, step)
if px[i,j] == 0 return false end isize, jsize = size(px) if i < 1 || j < 1 || i == isize || j == jsize # criteria 0.both return false end s = Array{Int,1}(9) s[1] = s[9] = px[i-1,j]; s[2] = px[i-1,j+1]; s[3] = px[i,j+1]; s[4] = px[i+1,j+1] s[5] = px[i+1,j]; s[6] = px[i+1,j-1]; s[7] = px[i,j-1]; s[8] = px[i-1,j-1] b = sum(s[1:8]) if b < 2 || b > 6 # criteria 1.both return false end if sum([(s[i] == 0 && s[i+1] == 1) for i in 1:length(s)-1]) != 1 # criteria 2.both return false end if step == 1 rightwhite = s[1] == 0 || s[3] == 0 || s[5] == 0 # 1.3 downwhite = s[3] == 0 || s[5] == 0 || s[7] == 0 # 1.4 return rightwhite && downwhite end upwhite = s[1] == 0 || s[3] == 0 || s[7] == 0 # 2.3 leftwhite = s[1] == 0 || s[5] == 0 || s[7] == 0 # 2.4 return upwhite && leftwhite
end
function zsthinning(mat)
retmat = copy(mat) testmat = zeros(Int, size(mat)) isize, jsize = size(testmat) needredo = true loops = 0 while(needredo) loops += 1 println("loop number $loops") needredo = false for n in 1:2 for i in 1:isize, j in 1:jsize testmat[i,j] = surroundtesting(retmat, i, j, n) ? 1 : 0 end for i in 1:isize, j in 1:jsize if testmat[i,j] == 1 retmat[i,j] = 0 needredo = true end end end end retmat
end
function asciiprint(mat)
for i in 1:size(mat)[1] println(join(map(i -> i == 1 ? '#' : ' ', mat[i,:]))) end
end
asciiprint(zsthinning(pixels))</lang>
- Output:
loop number 1 loop number 2 loop number 3
####### ###### # # ## # # # # # # ##### # # ## # # # ## ## # # ####
Kotlin
<lang scala>// version 1.1.2
class Point(val x: Int, val y: Int)
val image = arrayOf(
" ", " ################# ############# ", " ################## ################ ", " ################### ################## ", " ######## ####### ################### ", " ###### ####### ####### ###### ", " ###### ####### ####### ", " ################# ####### ", " ################ ####### ", " ################# ####### ", " ###### ####### ####### ", " ###### ####### ####### ", " ###### ####### ####### ###### ", " ######## ####### ################### ", " ######## ####### ###### ################## ###### ", " ######## ####### ###### ################ ###### ", " ######## ####### ###### ############# ###### ", " "
)
val nbrs = arrayOf(
intArrayOf( 0, -1), intArrayOf( 1, -1), intArrayOf( 1, 0), intArrayOf( 1, 1), intArrayOf( 0, 1), intArrayOf(-1, 1), intArrayOf(-1, 0), intArrayOf(-1, -1), intArrayOf( 0, -1)
)
val nbrGroups = arrayOf(
arrayOf(intArrayOf(0, 2, 4), intArrayOf(2, 4, 6)), arrayOf(intArrayOf(0, 2, 6), intArrayOf(0, 4, 6))
)
val toWhite = mutableListOf<Point>() val grid = Array(image.size) { image[it].toCharArray() }
fun thinImage() {
var firstStep = false var hasChanged: Boolean do { hasChanged = false firstStep = !firstStep for (r in 1 until grid.size - 1) { for (c in 1 until grid[0].size - 1) { if (grid[r][c] != '#') continue val nn = numNeighbors(r, c) if (nn !in 2..6) continue if (numTransitions(r, c) != 1) continue val step = if (firstStep) 0 else 1 if (!atLeastOneIsWhite(r, c, step)) continue toWhite.add(Point(c, r)) hasChanged = true } } for (p in toWhite) grid[p.y][p.x] = ' ' toWhite.clear() } while (firstStep || hasChanged) for (row in grid) println(row)
}
fun numNeighbors(r: Int, c: Int): Int {
var count = 0 for (i in 0 until nbrs.size - 1) { if (grid[r + nbrs[i][1]][c + nbrs[i][0]] == '#') count++ } return count
}
fun numTransitions(r: Int, c: Int): Int {
var count = 0 for (i in 0 until nbrs.size - 1) { if (grid[r + nbrs[i][1]][c + nbrs[i][0]] == ' ') { if (grid[r + nbrs[i + 1][1]][c + nbrs[i + 1][0]] == '#') count++ } } return count
}
fun atLeastOneIsWhite(r: Int, c: Int, step: Int): Boolean {
var count = 0; val group = nbrGroups[step] for (i in 0..1) { for (j in 0 until group[i].size) { val nbr = nbrs[group[i][j]] if (grid[r + nbr[1]][c + nbr[0]] == ' ') { count++ break } } } return count > 1
}
fun main(args: Array<String>) {
thinImage()
}</lang>
- Output:
# ########## ####### ## # #### # # # ## # # # # # # # # # ############ # # # # # # # # # # # # # # ## # ############ ### ###
Lua
<lang lua>function zhangSuenThin(img)
local dirs={ { 0,-1}, { 1,-1}, { 1, 0}, { 1, 1}, { 0, 1}, {-1, 1}, {-1, 0}, {-1,-1}, { 0,-1}, }
local black=1 local white=0
function A(x, y) local c=0 local current=img[y+dirs[1][2]][x+dirs[1][1]] for i=2,#dirs do local to_compare=img[y+dirs[i][2]][x+dirs[i][1]] if current==white and to_compare==black then c=c+1 end current=to_compare end return c end
function B(x, y) local c=0 for i=2,#dirs do local value=img[y+dirs[i][2]][x+dirs[i][1]] if value==black then c=c+1 end end return c end
function common_step(x, y) if img[y][x]~=black or x<=1 or x>=#img[y] or y<=1 or y>=#img then return false end
local b_value=B(x, y) if b_value<2 or b_value>6 then return false end
local a_value=A(x, y) if a_value~=1 then return false end return true end
function step_one(x, y) if not common_step(x, y) then return false end local p2=img[y+dirs[1][2]][x+dirs[1][1]] local p4=img[y+dirs[3][2]][x+dirs[3][1]] local p6=img[y+dirs[5][2]][x+dirs[5][1]] local p8=img[y+dirs[7][2]][x+dirs[7][1]]
if p4==white or p6==white or p2==white and p8==white then return true end return false end
function step_two(x, y) if not common_step(x, y) then return false end local p2=img[y+dirs[1][2]][x+dirs[1][1]] local p4=img[y+dirs[3][2]][x+dirs[3][1]] local p6=img[y+dirs[5][2]][x+dirs[5][1]] local p8=img[y+dirs[7][2]][x+dirs[7][1]]
if p2==white or p8==white or p4==white and p6==white then return true end return false end
function convert(to_do) for k,v in pairs(to_do) do img[v[2]][v[1]]=white end end
function do_step_on_all(step) local to_convert={} for y=1,#img do for x=1,#img[y] do if step(x, y) then table.insert(to_convert, {x,y}) end end end convert(to_convert) return #to_convert>0 end
local continue=true while continue do continue=false if do_step_on_all(step_one) then continue=true end
if do_step_on_all(step_two) then continue=true end end
for y=1,#img do for x=1,#img[y] do io.write(img[y][x]==black and '#' or ' ') end io.write('\n') end
end
local image = {
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0}, {0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0}, {0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0}, {0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0}, {0,1,1,1,0,0,1,1,1,1,0,0,1,1,1,0,1,1,1,1,0,0,1,1,1,1,0,1,1,1,0,0}, {0,1,1,1,0,0,0,1,1,1,1,0,1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,1,1,1,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
}
zhangSuenThin(image) </lang>
Output:
####### ###### # # ## # # # # # # ##### # # ## # # # ## ## # # ####
Mathematica/Wolfram Language
Mathematica supports directly the Thinning methods "Morphological" and "MedialAxis". The Zhang-Suen algorithm implementation could be done with: <lang Mathematica>nB[mat_] := Delete[mat // Flatten, 5] // Total;
nA[mat_] := Module[{l},
l = Flatten[mat][[{2, 3, 6, 9, 8, 7, 4, 1, 2}]]; Total[Map[If[#1 == 0 && #2 == 1, 1, 0] &, Partition[l, 2, 1]]] ];
iW1[mat_] :=
Module[{l = Flatten[mat]}, If[Apply[Times, l[[{2, 6, 8}]]] + Apply[Times, l[[{4, 6, 8}]]] == 0, 0, 1]];
iW2[mat_] :=
Module[{l = Flatten[mat]}, If[Apply[Times, l[[{2, 6, 4}]]] + Apply[Times, l[[{4, 2, 8}]]] == 0, 0, 1]];
check[i_, j_, dat_, t_] := Module[{mat, d = Dimensions[dat], r, c},
r = d1; c = d2; If[i > 1 && i < r && j > 1 && j < c, mat = dati - 1 ;; i + 1, j - 1 ;; j + 1; If[dati, j == 1 && nA[mat] == 1 && 2 <= nB[mat] <= 6 && If[t == 1, iW1[mat], iW2[mat]] == 0, 0, dati, j], dati, j ]];
iter[dat_] :=
Module[{i = Flatten[Outer[List, Range[Dimensions[dat]1], Range[Dimensions[dat]2]], 1], tmp}, tmp = Partition[check[#1, #2, dat, 1] & /@ i, Dimensions[dat]2]; Partition[check[#1, #2, tmp, 2] & /@ i, Dimensions[tmp]2]];
FixedPoint[iter, dat]</lang>
Which results in: (printMat is only defined to print an text output - the natural Mathemaica way would be to use ArrayPlot function, which create a graphic object which we can't paste into this wiki)
printMat[mat_] := StringReplace[ Riffle[Map[StringJoin, Map[ToString, mat, {2}]], "\n"] // StringJoin, {"1" -> "#", "0" -> "."}]; dat1 = {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0}, {0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0}, {0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0}, {0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0}, {0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}; printMat[dat1] printMat[FixedPoint[iter, dat1]] ................................ .#########.......########....... .###...####.....####..####...... .###....###.....###....###...... .###...####.....###............. .#########......###............. .###.####.......###....###...... .###..####..###.####..####.###.. .###...####.###..########..###.. ................................ ................................ ..#######.........######........ ..#.....#........##............. ..#......#.......#.............. ..#.....#........#.............. ..#####.#........#.............. .......##........#.............. ........#....#...##....##...#... .........#.........####......... ................................ dat2 = {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0}, {0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0}, {0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}; printMat[dat2] printMat[FixedPoint[iter, dat2]] ........................................................... .#################...................#############......... .##################...............################......... .###################............##################......... .########.....#######..........###################......... ...######.....#######.........#######.......######......... ...######.....#######........#######....................... ...#################.........#######....................... ...################..........#######....................... ...#################.........#######....................... ...######.....#######........#######....................... ...######.....#######........#######....................... ...######.....#######.........#######.......######......... .########.....#######..........###################......... .########.....#######.######....##################.######.. .########.....#######.######......################.######.. .########.....#######.######.........#############.######.. ........................................................... ........................................................... ........................................................... ....#.##########.......................#######............. .....##........#...................####.......#............ .....#..........#.................##....................... .....#..........#................#......................... .....#..........#................#......................... .....#..........#................#......................... .....############...............#.......................... .....#..........#...............#.......................... .....#..........#................#......................... .....#..........#................#......................... .....#..........#................#......................... .....#............................##....................... .....#.............................############............ .......................###..........................###.... ........................................................... ...........................................................
Nim
<lang Nim>import math, sequtils, strutils
type
Bit = 0..1 BitMatrix = seq[seq[Bit]] # Two-dimensional array of 0/1. Neighbors = array[2..9, Bit] # Neighbor values.
const Symbols = [Bit(0): '.', Bit(1): '#']
func toBitMatrix(s: openArray[string]): BitMatrix =
## Convert an array of 01 strings into a BitMatrix. for row in s: assert row.allCharsInSet({'0', '1'}) result.add row.mapIt(Bit(ord(it) - ord('0')))
proc `$`(m: BitMatrix): string =
## Return the string representation of a BitMatrix. for row in m: echo row.mapIt(Symbols[it]).join()
- Templates to allow using double indexing.
template `[]`(m: BitMatrix; i, j: Natural): Bit = m[i][j] template `[]=`(m: var BitMatrix; i, j: Natural; val: Bit) = m[i][j] = val
func neighbors(m: BitMatrix; i, j: int): Neighbors =
## Return the array of neighbors. [m[i-1, j], m[i-1, j+1], m[i, j+1], m[i+1, j+1], m[i+1, j], m[i+1, j-1], m[i, j-1], m[i-1, j-1]]
func transitions(p: Neighbors): int =
## Return the numbers of transitions from P2 to P9. for (i, j) in [(2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (7, 8), (8, 9), (9, 2)]: result += ord(p[i] == 0 and p[j] == 1)
func thinned(m: BitMatrix): BitMatrix =
## Return a thinned version of "m". const Pair1 = [2, 8] const Pair2 = [4, 6] let rowMax = m.high let colMax = m[0].high result = m
while true: var changed = false
for step in 1..2: let (p1, p2) = if step == 1: (Pair1, Pair2) else: (Pair2, Pair1) var m = result for i in 1..<rowMax: for j in 1..<colMax:
# Check criteria. if m[i, j] == 0: # criterion 0. continue let p = m.neighbors(i, j) if sum(p) notin 2..6: # criterion 1. continue if transitions(p) != 1: # criterion 2. continue if p[p1[0]] + p[p2[0]] + p[p2[1]] == 3 or # criterion 3. p[p1[1]] + p[p2[0]] + p[p2[1]] == 3: # criterion 4. continue
# All criteria satisfied. Store a 0 in "result". result[i, j] = 0 changed = true
if not changed: break
when isMainModule:
const Input = ["00000000000000000000000000000000", "01111111110000000111111110000000", "01110001111000001111001111000000", "01110000111000001110000111000000", "01110001111000001110000000000000", "01111111110000001110000000000000", "01110111100000001110000111000000", "01110011110011101111001111011100", "01110001111011100111111110011100", "00000000000000000000000000000000"]
let input = Input.toBitMatrix() let output = input.thinned() echo "Input image:" echo input echo() echo "Output image:" echo output</lang>
- Output:
Input image: ................................ .#########.......########....... .###...####.....####..####...... .###....###.....###....###...... .###...####.....###............. .#########......###............. .###.####.......###....###...... .###..####..###.####..####.###.. .###...####.###..########..###.. ................................ Output image: ................................ ..#######.........######........ ..#.....#........##............. ..#......#.......#.............. ..#.....#........#.............. ..#####.#........#.............. .......##........#.............. ........#....#...##....##...#... .........#.........####......... ................................
Perl
<lang perl>use List::Util qw(sum min);
$source = <<'END'; ............................................................ ..#################...................#############......... ..##################...............################......... ..###################............##################......... ..########.....#######..........###################......... ....######.....#######.........#######.......######......... ....######.....#######........#######....................... ....#################.........#######....................... ....################..........#######....................... ....#################.........#######....................... ....######.....#######........#######....................... ....######.....#######........#######....................... ....######.....#######.........#######.......######......... ..########.....#######..........###################......... ..########.....#######.######....##################.######.. ..########.....#######.######......################.######.. ..########.....#######.######.........#############.######.. ............................................................ END
for $line (split "\n", $source) {
push @lines, [map { 1 & ord $_ } split , $line]
}
$v = @lines; $h = @{$lines[0]}; push @black, @$_ for @lines; @p8 = ((-$h-1), (-$h+0), (-$h+1), # flatland distances to 8 neighbors.
0-1, 0+1, $h-1, $h+0, $h+1)[1,2,4,7,6,5,3,0]; # (in cycle order)
- Candidates have 8 neighbors and are known black
@cand = grep { $black[$_] } map { my $x = $_; map $_*$h + $x, 1..$v-2 } 1..$h-2;
do {
sub seewhite { my($w1,$w2) = @_; my(@results); sub cycles { my(@neighbors)=@_; my $c; $c += $neighbors[$_] < $neighbors[($_+1)%8] for 0..$#neighbors; return $c } sub blacks { my(@neighbors)=@_; sum @neighbors }
@prior = @cand; @cand = (); for $p (@prior) { @n = @black[map { $_+$p } @p8]; if (cycles(@n) == 1 and 2 <= sum(blacks(@n)) and sum(blacks(@n)) <= 6 and min(@n[@$w1]) == 0 and min(@n[@$w2]) == 0) { push @results, $p; } else { push @cand, $p } } return @results; }
@goners1 = seewhite [0,2,4], [2,4,6]; @black[@goners1] = 0 x @goners1; @goners2 = seewhite [0,2,6], [0,4,6]; @black[@goners2] = 0 x @goners2;
} until @goners1 == 0 and @goners2 == 0;
while (@black) { push @thinned, join , qw<. #>[splice(@black,0,$h)] }
print join "\n", @thinned;</lang>
- Output:
............................................................ ............................................................ .....#.##########.......................#######............. ......##........#...................####.......#............ ......#..........#.................##....................... ......#..........#................#......................... ......#..........#................#......................... ......#..........#................#......................... ......############...............#.......................... ......#..........#...............#.......................... ......#..........#................#......................... ......#..........#................#......................... ......#..........#................#......................... ......#............................##....................... ......#.............................############............ ........................###..........................###.... ............................................................ ............................................................
Phix
with javascript_semantics constant n = {{-1,0},{-1,1},{0,1},{1,1},{1,0},{1,-1},{0,-1},{-1,-1},{-1,0}}; function AB(sequence text, integer y, x, step) integer wtb = 0, bn = 0 integer prev = '#', next string p2468 = "" for i=1 to length(n) do next = text[y+n[i][1]][x+n[i][2]] wtb += (prev='.' and next<='#') bn += (i>1 and next<='#') if and_bits(i,1)=0 then p2468 = append(p2468,prev) end if prev = next end for if step=2 then -- make it p6842 p2468 = p2468[3..4]&p2468[1..2] end if return {wtb,bn,p2468} end function procedure Zhang_Suen(sequence text) integer wtb, bn, changed, changes string p2468 -- (p6842 for step 2) text = split(text,'\n') while 1 do changed = 0 for step=1 to 2 do changes = 0 for y=2 to length(text)-1 do for x=2 to length(text[y])-1 do if text[y][x]='#' then {wtb,bn,p2468} = AB(text,y,x,step) if wtb=1 and bn>=2 and bn<=6 and find('.',p2468[1..3]) and find('.',p2468[2..4])then changes = 1 text[y][x] = '!' -- (logically still black) end if end if end for end for if changes then for y=2 to length(text)-1 do text[y] = substitute(text[y],"!",".") end for changed = 1 end if end for if not changed then exit end if end while puts(1,join(text,"\n")) end procedure string small_rc = """ ................................ .#########.......########....... .###...####.....####..####...... .###....###.....###....###...... .###...####.....###............. .#########......###............. .###.####.......###....###...... .###..####..###.####..####.###.. .###...####.###..########..###.. ................................""" Zhang_Suen(small_rc)
- Output:
................................ ..#######.........######........ ..#.....#........##............. ..#......#.......#.............. ..#.....#........#.............. ..#####.#........#.............. .......##........#.............. ........#....#...##....##...#... .........#.........####......... ................................
PL/I
<lang>zhang: procedure options (main); /* 8 July 2014 */
declare pic(10) bit(32) initial ( '00000000000000000000000000000000'b, '01111111110000000111111110000000'b, '01110001111000001111001111000000'b, '01110000111000001110000111000000'b, '01110001111000001110000000000000'b, '01111111110000001110000000000000'b, '01110111100000001110000111000000'b, '01110011110011101111001111011100'b, '01110001111011100111111110011100'b, '00000000000000000000000000000000'b ); declare image (10,32) bit(1) defined pic; declare status (10,32) fixed decimal (1); declare changes bit(1); declare (i, j, k, m, n) fixed binary;
m = hbound(image,1); n = hbound(image,2);
call display;
/* Pixel labelling for pixels surrounding P1, co-ordinates (i,j). */ /* P9 P2 P3 */ /* P8 P1 P4 */ /* P7 P6 P5 */
do k = 1 to 10 until (^changes); changes = '0'b; /* Set conditions as follows: */ /* (0) The pixel is black and has eight neighbours */ /* (1) 2 < = B(P1) < = 6 */ /* (2) A(P1) = 1 */ /* (3) At least one of P2 and P4 and P6 is white */ /* (4) At least one of P4 and P6 and P8 is white */ status = -1; do i = 2 to m-1; do j = 2 to n-1; if image(i,j) then if B(i,j) >= 2 & B(i,j) <= 6 then if A(i,j) = 1 then if ^image(i-1,j) | ^image(i,j+1) | ^image(i+1,j) then if ^image(i,j+1) | ^image(i+1,j) | ^image(i,j-1) then status(i,j) = 4; end; end; /* Having determined a status for every bit in the image, */ /* change those bits to white. */ do i = 2 to m-1; do j = 2 to n-1; if status(i,j) ^= -1 then do; image(i,j) = '0'b; changes = '1'b; end; end; end;
/* Set conditions as follows: */ /* (0) The pixel is black and has eight neighbours */ /* (1) 2 < = B(P1) < = 6 */ /* (2) A(P1) = 1 */ /* (3) At least one of P2 and P4 and P8 is white */ /* (4) At least one of P2 and P6 and P8 is white */ status = -1; do i = 2 to m-1; do j = 2 to n-1; if image(i,j) then if B(i,j) >= 2 & B(i,j) <= 6 then if A(i,j) = 1 then if ^image(i-1,j) | ^image(i,j+1) | ^image(i,j-1) then if ^image(i-1,j) | ^image(i+1,j) | ^image(i,j-1) then status(i,j) = 4; end; end; /* Having determined a status for every bit in the image, */ /* change those bits to white. */ do i = 2 to m-1; do j = 2 to n-1; if status(i,j) ^= -1 then do; image(i,j) = '0'b; changes = '1'b; end; end; end;
end; /* of the "until" loop */
put skip list ('Final image after ' || trim(k) || ' iterations:'); call display;
display: procedure;
declare (i, j) fixed binary; declare c character (1);
do i = 1 to m; put skip edit ('row:', i) (A, F(3)); do j = 1 to n; if image(i,j) then c = '.'; else c = ' '; put edit (c) (A); end; end; put skip;
end;
/* Returns the number of transitions from white to black from P2 through P9 and P2. */ A: procedure (i,j) returns (fixed binary);
declare (i,j) fixed binary nonassignable; declare n(2:10) bit(1);
n(2) = image(i-1,j); n(3) = image(i-1,j+1); n(4) = image(i, j+1); n(5) = image(i+1,j+1); n(6) = image(i+1,j); n(7) = image(i+1,j-1); n(8) = image(i,j-1); n(9) = image(i-1,j-1); n(10) = image(i-1,j); return ( tally(string(n), '01'b) );
end A;
/* Count the pixel neighbors of P1 that are black */ B: procedure (i, j) returns (fixed binary);
declare (i,j) fixed binary nonassignable; declare s fixed binary;
s = image(i-1,j-1) + image(i-1,j) + image(i-1,j+1); s = s + image(i,j-1) + image(i,j+1); return ( s + image(i+1,j-1) + image(i+1,j) + image(i+1,j+1) );
end B;
end zhang;</lang>
[Initial configuration:] row: 1 row: 2 ......... ........ row: 3 ... .... .... .... row: 4 ... ... ... ... row: 5 ... .... ... row: 6 ......... ... row: 7 ... .... ... ... row: 8 ... .... ... .... .... ... row: 9 ... .... ... ........ ... row: 10 [Intermeduiate "images" omitted] Final image after 3 iterations: row: 1 row: 2 ....... ...... row: 3 . . .. row: 4 . . . row: 5 . . . row: 6 ..... . . row: 7 .. . row: 8 . . .. .. . row: 9 . .... row: 10 Second image: Image to be thinned: row 1: row 2: ............... row 3: .................. row 4: .................. row 5: .... ..... row 6: .... ..... row 7: .... ..... row 8: .... ..... row 9: .... ...... row 10: .... ..... row 11: .... ..... row 12: .... ..... row 13: .... ..... row 14: ............. row 15: .............. row 16: ............... row 17: .... ...... row 18: .... ...... row 19: .... ..... row 20: .... ...... row 21: .... ..... row 22: .... ..... row 23: .... ...... row 24: .... ...... row 25: ................... row 26: ................... row 27: ................. row 28: Final image after 3 iterations: row 1: row 2: row 3: .............. row 4: . . row 5: . . row 6: . . row 7: . . row 8: . . row 9: . . row 10: . .. row 11: . . row 12: . . row 13: . . row 14: . . row 15: ........... row 16: . . row 17: . .. row 18: . . row 19: . . row 20: . . row 21: . . row 22: . . row 23: . . row 24: . .. row 25: . .. row 26: ... ........... row 27: row 28:
Python
Several input images are converted. <lang python># -*- coding: utf-8 -*-
- Example from this blog post.
beforeTxt = \ 1100111 1100111 1100111 1100111 1100110 1100110 1100110 1100110 1100110 1100110 1100110 1100110 1111110 0000000\
- Thanks to this site and vim for these next two examples
smallrc01 = \ 00000000000000000000000000000000 01111111110000000111111110000000 01110001111000001111001111000000 01110000111000001110000111000000 01110001111000001110000000000000 01111111110000001110000000000000 01110111100000001110000111000000 01110011110011101111001111011100 01110001111011100111111110011100 00000000000000000000000000000000\
rc01 = \ 00000000000000000000000000000000000000000000000000000000000 01111111111111111100000000000000000001111111111111000000000 01111111111111111110000000000000001111111111111111000000000 01111111111111111111000000000000111111111111111111000000000 01111111100000111111100000000001111111111111111111000000000 00011111100000111111100000000011111110000000111111000000000 00011111100000111111100000000111111100000000000000000000000 00011111111111111111000000000111111100000000000000000000000 00011111111111111110000000000111111100000000000000000000000 00011111111111111111000000000111111100000000000000000000000 00011111100000111111100000000111111100000000000000000000000 00011111100000111111100000000111111100000000000000000000000 00011111100000111111100000000011111110000000111111000000000 01111111100000111111100000000001111111111111111111000000000 01111111100000111111101111110000111111111111111111011111100 01111111100000111111101111110000001111111111111111011111100 01111111100000111111101111110000000001111111111111011111100 00000000000000000000000000000000000000000000000000000000000\
def intarray(binstring):
Change a 2D matrix of 01 chars into a list of lists of ints return [[1 if ch == '1' else 0 for ch in line] for line in binstring.strip().split()]
def chararray(intmatrix):
Change a 2d list of lists of 1/0 ints into lines of 1/0 chars return '\n'.join(.join(str(p) for p in row) for row in intmatrix)
def toTxt(intmatrix):
Change a 2d list of lists of 1/0 ints into lines of '#' and '.' chars return '\n'.join(.join(('#' if p else '.') for p in row) for row in intmatrix)
def neighbours(x, y, image):
Return 8-neighbours of point p1 of picture, in order i = image x1, y1, x_1, y_1 = x+1, y-1, x-1, y+1 #print ((x,y)) return [i[y1][x], i[y1][x1], i[y][x1], i[y_1][x1], # P2,P3,P4,P5 i[y_1][x], i[y_1][x_1], i[y][x_1], i[y1][x_1]] # P6,P7,P8,P9
def transitions(neighbours):
n = neighbours + neighbours[0:1] # P2, ... P9, P2 return sum((n1, n2) == (0, 1) for n1, n2 in zip(n, n[1:]))
def zhangSuen(image):
changing1 = changing2 = [(-1, -1)] while changing1 or changing2: # Step 1 changing1 = [] for y in range(1, len(image) - 1): for x in range(1, len(image[0]) - 1): P2,P3,P4,P5,P6,P7,P8,P9 = n = neighbours(x, y, image) if (image[y][x] == 1 and # (Condition 0) P4 * P6 * P8 == 0 and # Condition 4 P2 * P4 * P6 == 0 and # Condition 3 transitions(n) == 1 and # Condition 2 2 <= sum(n) <= 6): # Condition 1 changing1.append((x,y)) for x, y in changing1: image[y][x] = 0 # Step 2 changing2 = [] for y in range(1, len(image) - 1): for x in range(1, len(image[0]) - 1): P2,P3,P4,P5,P6,P7,P8,P9 = n = neighbours(x, y, image) if (image[y][x] == 1 and # (Condition 0) P2 * P6 * P8 == 0 and # Condition 4 P2 * P4 * P8 == 0 and # Condition 3 transitions(n) == 1 and # Condition 2 2 <= sum(n) <= 6): # Condition 1 changing2.append((x,y)) for x, y in changing2: image[y][x] = 0 #print changing1 #print changing2 return image
if __name__ == '__main__':
for picture in (beforeTxt, smallrc01, rc01): image = intarray(picture) print('\nFrom:\n%s' % toTxt(image)) after = zhangSuen(image) print('\nTo thinned:\n%s' % toTxt(after))</lang>
- Output:
Just the example asked for in the task:
From: ................................ .#########.......########....... .###...####.....####..####...... .###....###.....###....###...... .###...####.....###............. .#########......###............. .###.####.......###....###...... .###..####..###.####..####.###.. .###...####.###..########..###.. ................................ To thinned: ................................ ..#######.........######........ ..#.....#........##............. ..#......#.......#.............. ..#.....#........#.............. ..#####.#........#.............. .......##........#.............. ........#....#...##....##...#... .........#.........####......... ................................
Racket
<lang racket>#lang racket (define (img-01string->vector str)
(define lines (regexp-split "\n" str)) (define h (length lines)) (define w (if (zero? h) 0 (string-length (car lines)))) (define v (for*/vector #:length (* w h) ((l (in-list lines)) (p (in-string l))) (match p (#\0 0) (#\1 1) (#\# 1) (#\. 0)))) (values v h w))
- Task (2) asks for "or an ASCII-art image of space/non-space characters."
- Spaces don't really impress where the borders are, so we'll use a dot.
(define cell->display-char (match-lambda (0 ".") (1 "#") (else "?")))
(define (display-img v w)
(for ((p (in-vector v)) (col (in-naturals))) (printf "~a" (cell->display-char p)) (when (= (modulo col w) (sub1 w)) (newline))))
- returns vector of ([P1's idx] P1 P2 ... P9)
(define (Pns v w r c)
(define i (+ c (* r w))) (define-syntax-rule (vi+ x) (vector-ref v (+ i x))) (define-syntax-rule (vi- x) (vector-ref v (- i x))) (vector i (vi+ 0) (vi- w) (vi+ (- 1 w)) (vi+ 1) (vi+ (+ w 1)) (vi+ w) (vi+ (- w 1)) (vi- 1) (vi- (+ w 1))))
- Second argument to in-vector is the start offset;
- We skip offset 0 (idx) and 1 (P1)
(define (B Ps) (for/sum ((Pn (in-vector Ps 2))) Pn))
(define (A Ps)
(define P2 (vector-ref Ps 2)) (define-values (rv _) (for/fold ((acc 0) (Pn-1 P2)) ((Pn (in-sequences (in-vector Ps 3) (in-value P2)))) (values (+ acc (if (and (= 0 Pn-1) (= 1 Pn)) 1 0)) Pn))) rv)
(define-syntax-rule (not-all-black? Pa Pb Pc) (zero? (* Pa Pb Pc))) (define (z-s-thin v h w)
; return idx when thin necessary, #f otherwise (define (thin? Ps n/bour-check-1 n/bour-check-2) (match-define (vector idx P1 P2 _ P4 _ P6 _ P8 _) Ps) (and (= P1 1) (<= 2 (B Ps) 6) (= (A Ps) 1) (n/bour-check-1 P2 P4 P6 P8) (n/bour-check-2 P2 P4 P6 P8) idx)) (define (has-white?-246 P2 P4 P6 P8) (not-all-black? P2 P4 P6)) (define (has-white?-468 P2 P4 P6 P8) (not-all-black? P4 P6 P8)) (define (has-white?-248 P2 P4 P6 P8) (not-all-black? P2 P4 P8)) (define (has-white?-268 P2 P4 P6 P8) (not-all-black? P2 P6 P8)) (define (step-n even-Pn-check-1 even-Pn-check-2) (for*/list ((r (in-range 1 (- h 1))) (c (in-range 1 (- w 1))) (idx (in-value (thin? (Pns v w r c) even-Pn-check-1 even-Pn-check-2))) #:when idx) idx)) (define (step-1) (step-n has-white?-246 has-white?-468)) (define (step-2) (step-n has-white?-248 has-white?-268)) (define (inner-z-s-thin) (define changed-list-1 (step-1)) (for ((idx (in-list changed-list-1))) (vector-set! v idx 0)) (define changed-list-2 (step-2)) (for ((idx (in-list changed-list-2))) (vector-set! v idx 0)) (unless (and (null? changed-list-1) (null? changed-list-2)) (inner-z-s-thin))) (inner-z-s-thin))
(define (read-display-thin-display-image img-str)
(define-values (v h w) (img-01string->vector img-str)) (printf "Original image:~%") (display-img v w) (z-s-thin v h w) (printf "Thinned image:~%") (display-img v w))
(define e.g.-image #<<EOS 00000000000000000000000000000000 01111111110000000111111110000000 01110001111000001111001111000000 01110000111000001110000111000000 01110001111000001110000000000000 01111111110000001110000000000000 01110111100000001110000111000000 01110011110011101111001111011100 01110001111011100111111110011100 00000000000000000000000000000000 EOS
)
(define e.g.-image/2 #<<EOS
- ..###
- ..###
- ..###
- ..###
- ..##.
- ..##.
- ..##.
- ..##.
- ..##.
- ..##.
- ..##.
- ..##.
- .
....... EOS
)
(module+ main
; (read-display-thin-display-image e.g.-image/2) ; (newline) (read-display-thin-display-image e.g.-image))</lang>
- Output:
Only the requested image is output:
Original image: ................................ .#########.......########....... .###...####.....####..####...... .###....###.....###....###...... .###...####.....###............. .#########......###............. .###.####.......###....###...... .###..####..###.####..####.###.. .###...####.###..########..###.. ................................ Thinned image: ................................ ..#######.........######........ ..#.....#........##............. ..#......#.......#.............. ..#.....#........#.............. ..#####.#........#.............. .......##........#.............. ........#....#...##....##...#... .........#.........####......... ................................
Raku
(formerly Perl 6) Source image may be based on any characters whose low bits are 0 or 1 (which conveniently includes . and #). <lang perl6>my $source = qq:to/EOD/; ................................ .#########.......########....... .###...####.....####..####...... .###....###.....###....###...... .###...####.....###............. .#########......###............. .###.####.......###....###...... .###..####..###.####..####.###.. .###...####.###..########..###.. ................................ EOD
my @lines = ([.ords X+& 1] for $source.split("\n")); # The low bits Just Work. my \v = +@lines; my \h = +@lines[0]; my @black = flat @lines.map: *.values; # Flatten to 1-dimensional.
my \p8 = [-h-1, -h+0, -h+1, # Flatland distances to 8 neighbors.
0-1, 0+1, h-1, h+0, h+1].[1,2,4,7,6,5,3,0]; # (in cycle order)
- Candidates have 8 neighbors and are known black
my @cand = grep { @black[$_] }, do
for 1..v-2 X 1..h-2 -> (\y,\x) { y*h + x }
repeat while my @goners1 or my @goners2 {
sub seewhite (\w1,\w2) { sub cycles (@neighbors) { [+] @neighbors Z< @neighbors[].rotate } sub blacks (@neighbors) { [+] @neighbors }
my @prior = @cand; @cand = ();
gather for @prior -> \p { my \n = @black[p8 X+ p]; if cycles(n) == 1 and 2 <= blacks(n) <= 6 and n[w1].any == 0 and n[w2].any == 0 { take p } else { @cand.push: p } } }
@goners1 = seewhite (0,2,4), (2,4,6); @black[@goners1] = 0 xx *; say "Ping: {[+] @black} remaining after removing ", @goners1;
@goners2 = seewhite (0,2,6), (0,4,6); @black[@goners2] = 0 xx *; say "Pong: {[+] @black} remaining after removing ", @goners2;
}
say @black.splice(0,h).join.trans('01' => '.#') while @black;</lang>
- Output:
Ping: 66 remaining after removing 33 41 49 56 67 71 74 80 83 86 89 99 106 114 119 120 121 131 135 138 146 169 178 195 197 210 215 217 227 230 233 236 238 240 243 246 249 251 253 257 258 259 263 264 266 268 269 270 273 274 279 280 283 284 285 Pong: 47 remaining after removing 65 73 88 97 104 112 129 137 144 161 167 176 193 198 208 216 225 226 231 Ping: 45 remaining after removing 87 194 Pong: 45 remaining after removing Ping: 45 remaining after removing Pong: 45 remaining after removing ................................ ..#######.........######........ ..#.....#........##............. ..#......#.......#.............. ..#.....#........#.............. ..#####.#........#.............. .......##........#.............. ........#....#...##....##...#... .........#.........####......... ................................
REXX
<lang rexx>/*REXX program thins a NxM character grid using the Zhang-Suen thinning algorithm.*/ parse arg iFID .; if iFID== then iFID='ZHANG_SUEN.DAT' white=' '; @.=white /* [↓] read the input character grid. */
do row=1 while lines(iFID)\==0; _=linein(iFID) _=translate(_,,.0); cols.row=length(_) do col=1 for cols.row; @.row.col=substr(_,col,1) end /*col*/ /* [↑] assign whole row of characters.*/ end /*row*/
rows=row-1 /*adjust ROWS because of the DO loop. */ call show@ 'input file ' iFID " contents:" /*display show the input character grid*/
do until changed==0; changed=0 /*keep slimming until we're finished. */ do step=1 for 2 /*keep track of step one or step two.*/ do r=1 for rows /*process all the rows and columns. */ do c=1 for cols.r; !.r.c=@.r.c /*assign an alternate grid. */ if r==1|r==rows|c==1|c==cols.r then iterate /*is this an edge?*/ if @.r.c==white then iterate /*Is the character white? Then skip it*/ call Ps; b=b() /*define Ps and also "b". */ if b<2 | b>6 then iterate /*is B within the range ? */ if a()\==1 then iterate /*count the number of transitions. */ /* ╔══╦══╦══╗ */ if step==1 then if (p2 & p4 & p6) | p4 & p6 & p8 then iterate /* ║p9║p2║p3║ */ if step==2 then if (p2 & p4 & p8) | p2 & p6 & p8 then iterate /* ╠══╬══╬══╣ */ !.r.c=white /*set a grid character to white. */ /* ║p8║p1║p4║ */ changed=1 /*indicate a character was changed. */ /* ╠══╬══╬══╣ */ end /*c*/ /* ║p7║p6║p5║ */ end /*r*/ /* ╚══╩══╩══╝ */ call copy! /*copy the alternate to working grid. */ end /*step*/ end /*until changed==0*/
call show@ 'slimmed output:' /*display the slimmed character grid. */ exit /*stick a fork in it, we're all done. */ /*─────────────────────────────────────────────────────────────────────────────────────────────────────────────*/ a: return (\p2==p3&p3)+(\p3==p4&p4)+(\p4==p5&p5)+(\p5==p6&p6)+(\p6==p7&p7)+(\p7==p8&p8)+(\p8==p9&p9)+(\p9==p2&p2) b: return p2 + p3 + p4 + p5 + p6 + p7 + p8 + p9 copy!: do r=1 for rows; do c=1 for cols.r; @.r.c=!.r.c; end; end; return show@: say; say arg(1); say; do r=1 for rows; _=; do c=1 for cols.r; _=_ || @.r.c; end; say _; end; return /*──────────────────────────────────────────────────────────────────────────────────────*/ Ps: rm=r-1; rp=r+1; cm=c-1; cp=c+1 /*calculate some shortcuts.*/
p2=@.rm.c\==white; p3=@.rm.cp\==white; p4=@.r.cp\==white; p5=@.rp.cp\==white p6=@.rp.c\==white; p7=@.rp.cm\==white; p8=@.r.cm\==white; p9=@.rm.cm\==white; return</lang>
output when using the default input:
input file ZHANG_SUEN.DAT contents: ################# ############# ################## ################ ################### ################## ######## ####### ################### ###### ####### ####### ###### ###### ####### ####### ################# ####### ################ ####### ################# ####### ###### ####### ####### ###### ####### ####### ###### ####### ####### ###### ######## ####### ################### ######## ####### ###### ################## ###### ######## ####### ###### ################ ###### ######## ####### ###### ############# ###### slimmed output: # ########## ####### ## # #### # # # ## # # # # # # # # # ############ # # # # # # # # # # # # # # ## # ############ ### ###
output when using the default input: zhang_suen2.dat
input file zhang_suen2.dat contents: 111111111 11111111 111 1111 1111 1111 111 111 111 111 111 1111 111 111111111 111 111 1111 111 111 111 1111 111 1111 1111 111 111 1111 111 11111111 111 slimmed output: 1111111 111111 1 1 11 1 1 1 1 1 1 11111 1 1 11 1 1 1 11 11 1 1 1111
Ruby
First I define a function zs which given a point and its eight neighbours returns 1 if the point may be culled, 0 otherwise. g indicates if this is step 1 or step 2 in the task description. zs may be changed to remember the step independently if the reader does not wish to explore the algorithm.
<lang ruby>class ZhangSuen
NEIGHBOUR8 = [[-1,0],[-1,1],[0,1],[1,1],[1,0],[1,-1],[0,-1],[-1,-1]] # 8 neighbors CIRCULARS = NEIGHBOUR8 + [NEIGHBOUR8.first] # P2, ... P9, P2 def initialize(str, black="#") s1 = str.each_line.map{|line| line.chomp.each_char.map{|c| c==black ? 1 : 0}} s2 = s1.map{|line| line.map{0}} xrange = 1 ... s1.size-1 yrange = 1 ... s1[0].size-1 printout(s1) begin @r = 0 xrange.each{|x| yrange.each{|y| s2[x][y] = s1[x][y] - zs(s1,x,y,1)}} # Step 1 xrange.each{|x| yrange.each{|y| s1[x][y] = s2[x][y] - zs(s2,x,y,0)}} # Step 2 end until @r == 0 printout(s1) end def zs(ng,x,y,g) return 0 if ng[x][y] == 0 or # P1 (ng[x-1][y] + ng[x][y+1] + ng[x+g][y-1+g]) == 3 or # P2, P4, P6/P8 (ng[x-1+g][y+g] + ng[x+1][y] + ng[x][y-1]) == 3 # P4/P2, P6, P8 bp1 = NEIGHBOUR8.inject(0){|res,(i,j)| res += ng[x+i][y+j]} # B(P1) return 0 if bp1 < 2 or 6 < bp1 ap1 = CIRCULARS.map{|i,j| ng[x+i][y+j]}.each_cons(2).count{|a,b| a<b} # A(P1) return 0 if ap1 != 1 @r = 1 end def printout(image) puts image.map{|row| row.map{|col| " #"[col]}.join} end
end
str = <<EOS ........................................................... .#################...................#############......... .##################...............################......... .###################............##################......... .########.....#######..........###################......... ...######.....#######.........#######.......######......... ...######.....#######........#######....................... ...#################.........#######....................... ...################..........#######....................... ...#################.........#######....................... ...######.....#######........#######....................... ...######.....#######........#######....................... ...######.....#######.........#######.......######......... .########.....#######..........###################......... .########.....#######.######....##################.######.. .########.....#######.######......################.######.. .########.....#######.######.........#############.######.. ........................................................... EOS
ZhangSuen.new(str)
task_example = <<EOS 00000000000000000000000000000000 01111111110000000111111110000000 01110001111000001111001111000000 01110000111000001110000111000000 01110001111000001110000000000000 01111111110000001110000000000000 01110111100000001110000111000000 01110011110011101111001111011100 01110001111011100111111110011100 00000000000000000000000000000000 EOS
ZhangSuen.new(task_example, "1")</lang>
- Output:
(only the requested result is shown here)
####### ###### # # ## # # # # # # ##### # # ## # # # ## ## # # ####
Sidef
<lang ruby>class ZhangSuen(str, black="1") {
const NEIGHBOURS = [[-1,0],[-1,1],[0,1],[1,1],[1,0],[1,-1],[0,-1],[-1,-1]] # 8 neighbors const CIRCULARS = (NEIGHBOURS + [NEIGHBOURS.first]) # P2, ... P9, P2
has r = 0 has image = [[]]
method init { var s1 = str.lines.map{|line| line.chars.map{|c| c==black ? 1 : 0 }} var s2 = s1.len.of { s1[0].len.of(0) } var xr = range(1, s1.end-1) var yr = range(1, s1[0].end-1) do { r = 0 xr.each{|x| yr.each{|y| s2[x][y] = (s1[x][y] - self.zs(s1,x,y,1)) }} # Step 1 xr.each{|x| yr.each{|y| s1[x][y] = (s2[x][y] - self.zs(s2,x,y,0)) }} # Step 2 } while !r.is_zero image = s1 }
method zs(ng,x,y,g) { (ng[x][y] == 0) -> || (ng[x-1][y] + ng[x][y+1] + ng[x+g][y+g - 1] == 3) -> || (ng[x+g - 1][y+g] + ng[x+1][y] + ng[x][y-1] == 3) -> && return 0
var bp1 = NEIGHBOURS.map {|p| ng[x+p[0]][y+p[1]] }.sum # B(P1) return 0 if ((bp1 < 2) || (6 < bp1))
var ap1 = 0 CIRCULARS.map {|p| ng[x+p[0]][y+p[1]] }.each_cons(2, {|a,b| ++ap1 if (a < b) # A(P1) })
return 0 if (ap1 != 1) r = 1 }
method display { image.each{|row| say row.map{|col| col ? '#' : ' ' }.join } }
}
var text = <<EOS 00000000000000000000000000000000 01111111110000000111111110000000 01110001111000001111001111000000 01110000111000001110000111000000 01110001111000001110000000000000 01111111110000001110000000000000 01110111100000001110000111000000 01110011110011101111001111011100 01110001111011100111111110011100 00000000000000000000000000000000 EOS
ZhangSuen.new(text, black: "1").display</lang>
- Output:
####### ###### # # ## # # # # # # ##### # # ## # # # ## ## # # ####
Tcl
Only the single image is converted. <lang tcl># -*- coding: utf-8 -*-
set data { 00000000000000000000000000000000 01111111110000000111111110000000 01110001111000001111001111000000 01110000111000001110000111000000 01110001111000001110000000000000 01111111110000001110000000000000 01110111100000001110000111000000 01110011110011101111001111011100 01110001111011100111111110011100 00000000000000000000000000000000 } proc zhang-suen data {
set data [string trim $data] while 1 {
set n 0 incr n [step 1 data] incr n [step 2 data] if !$n break
} return $data
} proc step {number _data} {
upvar 1 $_data data set xmax [string length [lindex $data 0]] set ymax [llength $data] switch -- $number {
1 {set cond {(!$P2 || !$P4 || !$P6) && (!$P4 || !$P6 || !$P8)}} 2 {set cond {(!$P2 || !$P4 || !$P8) && (!$P2 || !$P6 || !$P8)}}
} set hits {} for {set x 1} {$x < $xmax-1} {incr x} {
for {set y 1} {$y < $ymax-1} {incr y} { if {[getpix $data $x $y] == 1} { set b [B $data $x $y] if {2 <= $b && $b <= 6} { if {[A $data $x $y] == 1} { set P2 [getpix $data $x [expr $y-1]] set P4 [getpix $data [expr $x+1] $y] set P6 [getpix $data $x [expr $y+1]] set P8 [getpix $data [expr $x-1] $y] if $cond {lappend hits $x $y} } } } }
} foreach {x y} $hits {set data [setpix $data $x $y 0]} return [llength $hits]
} proc A {data x y} {
set res 0 set last [getpix $data $x [expr $y-1]] foreach {dx dy} {1 -1 1 0 1 1 0 1 -1 1 -1 0 -1 -1 0 -1} {
set this [getpix $data [expr $x+$dx] [expr $y+$dy]] if {$this > $last} {incr res} set last $this
} return $res
} proc B {data x y} {
set res 0 foreach {dx dy} {1 -1 1 0 1 1 0 1 -1 1 -1 0 -1 -1 0 -1} {
incr res [getpix $data [expr $x+$dx] [expr $y+$dy]]
} return $res
} proc getpix {data x y} {
string index [lindex $data $y] $x
} proc setpix {data x y val} {
set row [lindex $data $y] lset data $y [string replace $row $x $x $val] return $data
} puts [string map {1 @ 0 .} [join [zhang-suen $data] \n]]</lang>
- Output:
................................ ..@@@@@@@.........@@@@@@........ ..@.....@........@@............. ..@......@.......@.............. ..@.....@........@.............. ..@@@@@.@........@.............. .......@@........@.............. ........@....@...@@....@@...@... .........@.........@@@@......... ................................
VBA
<lang vb>Public n As Variant Private Sub init()
n = [{-1,0;-1,1;0,1;1,1;1,0;1,-1;0,-1;-1,-1;-1,0}]
End Sub
Private Function AB(text As Variant, y As Integer, x As Integer, step As Integer) As Variant
Dim wtb As Integer Dim bn As Integer Dim prev As String: prev = "#" Dim next_ As String Dim p2468 As String For i = 1 To UBound(n) next_ = Mid(text(y + n(i, 1)), x + n(i, 2), 1) wtb = wtb - (prev = "." And next_ <= "#") bn = bn - (i > 1 And next_ <= "#") If (i And 1) = 0 Then p2468 = p2468 & prev prev = next_ Next i If step = 2 Then '-- make it p6842 p2468 = Mid(p2468, 3, 2) & Mid(p2468, 1, 2) 'p2468 = p2468(3..4)&p2468(1..2) End If Dim ret(2) As Variant ret(0) = wtb ret(1) = bn ret(2) = p2468 AB = ret
End Function
Private Sub Zhang_Suen(text As Variant)
Dim wtb As Integer Dim bn As Integer Dim changed As Boolean, changes As Boolean Dim p2468 As String '-- (p6842 for step 2) Dim x As Integer, y As Integer, step As Integer Do While True changed = False For step = 1 To 2 changes = False For y = 1 To UBound(text) - 1 For x = 2 To Len(text(y)) - 1 If Mid(text(y), x, 1) = "#" Then ret = AB(text, y, x, step) wtb = ret(0) bn = ret(1) p2468 = ret(2) If wtb = 1 _ And bn >= 2 And bn <= 6 _ And InStr(1, Mid(p2468, 1, 3), ".") _ And InStr(1, Mid(p2468, 2, 3), ".") Then changes = True text(y) = Left(text(y), x - 1) & "!" & Right(text(y), Len(text(y)) - x) End If End If Next x Next y If changes Then For y = 1 To UBound(text) - 1 text(y) = Replace(text(y), "!", ".") Next y changed = True End If Next step If Not changed Then Exit Do Loop Debug.Print Join(text, vbCrLf)
End Sub
Public Sub main()
init Dim Small_rc(9) As String Small_rc(0) = "................................" Small_rc(1) = ".#########.......########......." Small_rc(2) = ".###...####.....####..####......" Small_rc(3) = ".###....###.....###....###......" Small_rc(4) = ".###...####.....###............." Small_rc(5) = ".#########......###............." Small_rc(6) = ".###.####.......###....###......" Small_rc(7) = ".###..####..###.####..####.###.." Small_rc(8) = ".###...####.###..########..###.." Small_rc(9) = "................................" Zhang_Suen (Small_rc)
End Sub</lang>
- Output:
................................ ...######.........######........ ...#....#.........#....##....... ...#....#.........#......#...... ...#....#.........#............. ...####.#.........#............. .......##.........#............. ........#....#....#....##...#... .........#....#....####......#.. ................................
Wren
<lang ecmascript>class Point {
construct new(x, y) { _x = x _y = y } x { _x } y { _y }
}
var image = [ " ", " ################# ############# ", " ################## ################ ", " ################### ################## ", " ######## ####### ################### ", " ###### ####### ####### ###### ", " ###### ####### ####### ", " ################# ####### ", " ################ ####### ", " ################# ####### ", " ###### ####### ####### ", " ###### ####### ####### ", " ###### ####### ####### ###### ", " ######## ####### ################### ", " ######## ####### ###### ################## ###### ", " ######## ####### ###### ################ ###### ", " ######## ####### ###### ############# ###### ", " "
]
var nbrs = [
[ 0, -1], [ 1, -1], [ 1, 0], [ 1, 1], [ 0, 1], [-1, 1], [-1, 0], [-1, -1], [ 0, -1]
]
var nbrGroups = [
[ [0, 2, 4], [2, 4, 6] ], [ [0, 2, 6], [0, 4, 6] ]
]
var toWhite = [] var grid = List.filled(image.count, null) for (i in 0...grid.count) grid[i] = image[i].toList
var numNeighbors = Fn.new { |r, c|
var count = 0 for (i in 0...nbrs.count - 1) { if (grid[r + nbrs[i][1]][c + nbrs[i][0]] == "#") count = count + 1 } return count
}
var numTransitions = Fn.new { |r, c|
var count = 0 for (i in 0...nbrs.count - 1) { if (grid[r + nbrs[i][1]][c + nbrs[i][0]] == " ") { if (grid[r + nbrs[i + 1][1]][c + nbrs[i + 1][0]] == "#") count = count + 1 } } return count
}
var atLeastOneIsWhite = Fn.new { |r, c, step|
var count = 0 var group = nbrGroups[step] for (i in 0..1) { for (j in 0...group[i].count) { var nbr = nbrs[group[i][j]] if (grid[r + nbr[1]][c + nbr[0]] == " ") { count = count + 1 break } } } return count > 1
}
var thinImage = Fn.new {
var firstStep = false var hasChanged while (true) { hasChanged = false firstStep = !firstStep for (r in 1...grid.count - 1) { for (c in 1...grid[0].count - 1) { if (grid[r][c] == "#") { var nn = numNeighbors.call(r, c) if ((2..6).contains(nn)) { if (numTransitions.call(r, c) == 1) { var step = firstStep ? 0 : 1 if (atLeastOneIsWhite.call(r, c, step)) { toWhite.add(Point.new(c, r)) hasChanged = true } } } } } } for (p in toWhite) grid[p.y][p.x] = " " toWhite.clear() if (!firstStep && !hasChanged) break } for (row in grid) System.print(row.join())
}
thinImage.call()</lang>
- Output:
# ########## ####### ## # #### # # # ## # # # # # # # # # ############ # # # # # # # # # # # # # # ## # ############ ### ###