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Zhang-Suen thinning algorithm: Difference between revisions

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Zhang-Suen thinning algorithm (view source)

Revision as of 21:34, 23 July 2014

6,622 bytes added ,  9 years ago
→‎{{header|Mathematica}}
mNo edit summary
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=={{header|Mathematica}}==
{{incomplete|Mathematica|Although good to see, output is not that of Zhang-Suen algorithm. (Would be good to know what algo. this is)?}}
Mathematica has a built in Thinning function which can be applied to images or data. Here is the result of applying it to data...
 
<lang Mathematica> supports directly the Thinning[{ methods "Morphological" and "MedialAxis".
The Zhang-Suen algorithm implementation could be done with:
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
<lang Mathematica>nB[mat_] := Delete[mat // Flatten, 5] // Total;
{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},
nA[mat_] := Module[{l, ct = 0, f},
{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},
f[a_, b_] := If[a == 0 && b == 1, ct++; b, b];
{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,l 1,= 1Flatten[mat][[{2, 13, 16, 19, 18, 07, 0, 0, 0, 0, 04, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 02}, ]];
Fold[f, l[[1]], l[[2 ;;]]];
{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},
ct];
{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},
iW1[mat_] :=
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}]</lang>
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 = d[[1]];
c = d[[2]];
If[i > 1 && i < r && j > 1 && j < c,
mat = dat[[i - 1 ;; i + 1, j - 1 ;; j + 1]];
If[dat[[i, j]] == 1 && nA[mat] == 1 && 2 <= nB[mat] <= 6 &&
If[t == 1, iW1[mat], iW2[mat]] == 0, 0, dat[[i, j]]],
dat[[i, 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]]]];
 
printMat[mat_] :=
StringReplace[
Riffle[Map[StringJoin, Map[ToString, mat, {2}]], "\n"] //
StringJoin, {"1" -> "#", "0" -> "."}];
 
FixedPoint[iter, dat]</lang>
 
Which returns
 
<pre>
<lang Mathematica>{
{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, 0, 1, 1, 1, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 1, 1, 01, 01, 01, 01, 0, 0, 0, 0, 0, 0}1,
{0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 01, 01, 01, 1, 0, 0, 01, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0},
{0, 0, 1, 0, 0}, {0, 01, 01, 1, 0, 0, 0, 01, 01, 0, 0, 01, 1, 0, 0, 0, 0, 0, 01, 01, 01, 0, 0, 0, 0, 0, 0}1,
{0, 0, 1, 0, 0, 0, 01, 01, 1, 01, 0, 0, 0, 0, 0, 0}, {0, 1, 01, 01, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}1,
{0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 01, 0, 0, 01, 1, 0, 0, 0, 0, 01, 01, 01, 0, 0, 0, 0, 0, 0, 0},
{0, 0, 1, 0}, {0, 1, 1, 1, 0, 0, 0, 01, 01, 0, 0, 0, 01, 1, 0, 0, 0, 0, 0, 01, 01, 01, 0, 0, 0, 0, 0, 0},
{0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 01, 01, 01, 01, 1, 1, 0, 0, 0, 0, 0, 0, 0}1,
{0, 0, 0 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0},
{0, 0, 0, 0, 0}, {0, 01, 01, 01, 0, 01, 01, 01, 01, 0, 0, 0, 0, 0, 0, 0, 01, 01, 01, 0, 0, 0, 0, 0, 0, 0, 0}}</lang>
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]]
 
...........................................................
.#################...................#############.........
.##################...............################.........
.###################............##################.........
.########.....#######..........###################.........
...######.....#######.........#######.......######.........
...######.....#######........#######.......................
...#################.........#######.......................
...################..........#######.......................
...#################.........#######.......................
...######.....#######........#######.......................
...######.....#######........#######.......................
...######.....#######.........#######.......######.........
.########.....#######..........###################.........
.########.....#######.######....##################.######..
.########.....#######.######......################.######..
.########.....#######.######.........#############.######..
...........................................................
...........................................................
...........................................................
....#.##########.......................#######.............
.....##........#...................####.......#............
.....#..........#.................##.......................
.....#..........#................#.........................
.....#..........#................#.........................
.....#..........#................#.........................
.....############...............#..........................
.....#..........#...............#..........................
.....#..........#................#.........................
.....#..........#................#.........................
.....#..........#................#.........................
.....#............................##.......................
.....#.............................############............
.......................###..........................###....
...........................................................
...........................................................</pre>
 
=={{header|Perl 6}}==
Anonymous user
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