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Zhang-Suen thinning algorithm: Difference between revisions
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changed table to be not so compacted, added other whitespace.
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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.
<table border="1">▼
The neighbours are, in order, arranged as:
<tr><td>P9</td><td>P2</td><td>P3</td></tr>▼
<tr><td>P8</td><td><b>P1</b></td><td>P4</td></tr>▼
<tr><td>P7</td><td>P6</td><td>P5</td></tr>▼
▲ <tr><td> P9 </td><td> P2 </td><td> P3 </td></tr>
▲ <tr><td> P8 </td><td><b> P1 </b></td><td> P4 </td></tr>
▲ <tr><td> P7 </td><td> P6 </td><td> P5 </td></tr>
</table>
Obviously the boundary pixels of the image cannot have the full eight neighbours.
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* Define <math>A(P1)</math> = 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 <math>B(P1)</math> = The number of black pixel neighbours of P1. ( = sum(P2 .. P9) )
;Step 1:
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* (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:
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* (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.
01111111110000000111111110000000
01110001111000001111001111000000
01110000111000001110000111000000
01110001111000001110000000000000
01111111110000001110000000000000
01110111100000001110000111000000
01110011110011101111001111011100
01110001111011100111111110011100
00000000000000000000000000000000
;Reference:
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