Zhang-Suen thinning algorithm: Difference between revisions
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def zs(ng,g) |
def zs(ng,g) |
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# The following line cannot be correct; each of the 4 directions must be ignored in |
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# one of the triples, and [1][2], [0][1], [2][1], and [1][0] are never ignored. |
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return 0 if ng[1][1] == 0 or (ng[1][2] + ng[0][1] + ng[1+g][g]) == 3 or (ng[g][1+g] + ng[2][1] + ng[1][0]) == 3 |
return 0 if ng[1][1] == 0 or (ng[1][2] + ng[0][1] + ng[1+g][g]) == 3 or (ng[g][1+g] + ng[2][1] + ng[1][0]) == 3 |
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t = -1; ng.each{|n| n.each{|g| t+=g}}; return 0 unless (2 <= t and t <= 6) |
t = -1; ng.each{|n| n.each{|g| t+=g}}; return 0 unless (2 <= t and t <= 6) |
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Revision as of 09:26, 21 October 2013
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 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
D
This uses the module from the Bitmap Task. <lang d>import std.stdio, std.algorithm, std.string, std.functional,
std.typecons, std.typetuple, bitmap;
alias sum = curry!(reduce!q{a + b}, 0); //
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) pure /*nothrow*/ in {
assert(image1.image.all!(x => x == Img.black || x == Img.white));
} 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 {
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 {
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)
return image1;
auto image2 = Img.fromData(image1.image.dup, image1.nx, image1.ny);
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 && // 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.textualShow(/*bl=*/ '.', /*wh=*/ '#');
writeln;
}
}</lang>
- Output:
From: ##..### ##..### ##..### ##..### ##..##. ##..##. ##..##. ##..##. ##..##. ##..##. ##..##. ##..##. ######. ....... To thinned: ##..### #.....# #.....# #...### #...#.. #...#.. #...#.. #...#.. #...#.. #...#.. #...#.. #...#.. #####.. ....... From: ................................ .#########.......########....... .###...####.....####..####...... .###....###.....###....###...... .###...####.....###............. .#########......###............. .###.####.......###....###...... .###..####..###.####..####.###.. .###...####.###..########..###.. ................................ To thinned: ................................ ..#######.........######........ ..#.....#........##............. ..#......#.......#.............. ..#.....#........#.............. ..#####.#........#.............. .......##........#.............. ........#....#...##....##...#... .........#.........####......... ................................ From: ........................................................... .#################...................#############......... .##################...............################......... .###################............##################......... .########.....#######..........###################......... ...######.....#######.........#######.......######......... ...######.....#######........#######....................... ...#################.........#######....................... ...################..........#######....................... ...#################.........#######....................... ...######.....#######........#######....................... ...######.....#######........#######....................... ...######.....#######.........#######.......######......... .########.....#######..........###################......... .########.....#######.######....##################.######.. .########.....#######.######......################.######.. .########.....#######.######.........#############.######.. ........................................................... To thinned: ........................................................... ........................................................... ....#.##########.......................#######............. .....##........#...................####.......#............ .....#..........#.................##....................... .....#..........#................#......................... .....#..........#................#......................... .....#..........#................#......................... .....############...............#.......................... .....#..........#...............#.......................... .....#..........#................#......................... .....#..........#................#......................... .....#..........#................#......................... .....#............................##....................... .....#.............................############............ .......................###..........................###.... ........................................................... ...........................................................
Perl 6
Takes the original image from a file that may be based on any characters whose low bits are 0 or 1 (which conveniently includes . and #). <lang perl6>constant DEBUG = 1;
my @lines = ([.ords X+& 1] for lines); # The low bits Just Work. my \v = +@lines; my \h = +@lines[0]; my @black = @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 if DEBUG;
@goners2 = seewhite (0,2,6), (0,4,6);
@black[@goners2] = 0 xx *;
say "Pong: {[+] @black} remaining after removing ", @goners2 if DEBUG;
}
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 ................................ ..#######.........######........ ..#.....#........##............. ..#......#.......#.............. ..#.....#........#.............. ..#####.#........#.............. .......##........#.............. ........#....#...##....##...#... .........#.........####......... ................................
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: ................................ ..#######.........######........ ..#.....#........##............. ..#......#.......#.............. ..#.....#........#.............. ..#####.#........#.............. .......##........#.............. ........#....#...##....##...#... .........#.........####......... ................................
Ruby
See Zhang-Suen thinning algorithm/smallRC.csv for the input file contents. <lang ruby>
- Thinning RC
- Nigel_Galloway: October 18th., 2013.
require 'csv' s2 = CSV.read("smallRC.csv", converters: :numeric) @r = 1 s1 = Array.new(s2.length){Array.new(s2[0].length,0)}
def zs(ng,g)
return 0 if ng[1][1] == 0 or (ng[1][2] + ng[0][1] + ng[1+g][g]) == 3 or (ng[g][1+g] + ng[2][1] + ng[1][0]) == 3
t = -1; ng.each{|n| n.each{|g| t+=g}}; return 0 unless (2 <= t and t <= 6)
t=-1;[ng[0][1],ng[0][2],ng[1][2],ng[2][2],ng[2][1],ng[2][0],ng[1][0],ng[0][0],ng[0][1]].each{|n| t+=(t==0 or t==2)? n : 1-n}
return 0 unless t==1 or t==2
@r=1
end
s2.each{|row| row.each{|col| print(col==1? "#": " ")}; print("\n")} while @r == 1
@r = 0
(1...s2.length-1).each{|n| (1...s2[0].length-1).each{|g| s1[n][g] = s2[n][g] - zs(s2[n-1..n+1].collect{|n| n[g-1..g+1]},0)}}
(1...s2.length-1).each{|n| (1...s2[0].length-1).each{|g| s2[n][g] = s1[n][g] - zs(s1[n-1..n+1].collect{|n| n[g-1..g+1]},1)}}
end s2.each{|row| row.each{|col| print(col==1? "#": " ")}; print("\n")} </lang>
- Output:
######### ########
### #### #### ####
### ### ### ###
### #### ###
######### ###
### #### ### ###
### #### ### #### #### ###
### #### ### ######## ###
##### ####
# # # ##
# # #
# # #
#### # #
# ## #
# # #
# # ###### #