311 lines
11 KiB
Markdown
311 lines
11 KiB
Markdown
---
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title: Zhang-Suen thinning algorithm
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id: 594810f028c0303b75339ad7
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challengeType: 5
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---
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## Description
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<section id='description'>
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This is an algorithm used to thin a black and white i.e. one bit per pixel images.
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For example, with an input image of:
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<pre>
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################# #############
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################## ################
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################### ##################
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######## ####### ###################
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###### ####### ####### ######
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###### ####### #######
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################# #######
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################ #######
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################# #######
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###### ####### #######
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###### ####### #######
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###### ####### ####### ######
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######## ####### ###################
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######## ####### ###### ################## ######
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######## ####### ###### ################ ######
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######## ####### ###### ############# ######
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</pre>
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It produces the thinned output:
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<pre>
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# ########## #######
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## # #### #
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# # ##
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# # #
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# # #
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# # #
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############ #
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# # #
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# # #
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# # #
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# # #
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# ##
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# ############
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### ###
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</pre>
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<h2>Algorithm</h2>
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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.
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The algorithm operates on all black pixels P1 that can have eight neighbours. The neighbours are, in order, arranged as:
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<table border="1">
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<tr><td>P9</td><td>P2</td><td>P3</td></tr>
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<tr><td>P8</td><td><b>P1</b></td><td>P4</td></tr>
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<tr><td>P7</td><td>P6</td><td>P5</td></tr>
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</table>
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Obviously the boundary pixels of the image cannot have the full eight neighbours.
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Define $A(P1)$ = 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).
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Define $B(P1)$ = the number of black pixel neighbours of P1. ( = sum(P2 .. P9) )
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<h3>Step 1:</h3>
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All pixels are tested and pixels satisfying all the following conditions (simultaneously) are just noted at this stage.
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(0) The pixel is black and has eight neighbours
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(1) $2 <= B(P1) <= 6$
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(2) $A(P1) = 1$
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(3) At least one of P2 and P4 and P6 is white
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(4) At least one of P4 and P6 and P8 is white
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After iterating over the image and collecting all the pixels satisfying all step 1 conditions, all these condition satisfying pixels are set to white.
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<h3>Step 2:</h3>
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All pixels are again tested and pixels satisfying all the following conditions are just noted at this stage.
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(0) The pixel is black and has eight neighbours
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(1) $2 <= B(P1) <= 6$
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(2) $A(P1) = 1$
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(3) At least one of P2 and P4 and '''P8''' is white
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(4) At least one of '''P2''' and P6 and P8 is white
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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.
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Iteration:
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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.
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<p>
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Task:
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Write a routine to perform Zhang-Suen thinning on an image matrix of ones and zeroes.
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</p>
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>thinImage</code> must be a function
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testString: assert.equal(typeof thinImage, 'function', '<code>thinImage</code> must be a function');
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- text: <code>thinImage</code> must return an array
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testString: assert(Array.isArray(result), '<code>thinImage</code> must return an array');
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- text: <code>thinImage</code> must return an array of strings
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testString: assert.equal(typeof result[0], 'string', '<code>thinImage</code> must return an array of strings');
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- text: <code>thinImage</code> must return an array of strings
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testString: assert.deepEqual(result, expected, '<code>thinImage</code> must return an array of strings');
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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const testImage = [
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' ',
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' ################# ############# ',
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' ################## ################ ',
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' ################### ################## ',
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' ######## ####### ################### ',
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' ###### ####### ####### ###### ',
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' ###### ####### ####### ',
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' ################# ####### ',
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' ################ ####### ',
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' ################# ####### ',
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' ###### ####### ####### ',
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' ###### ####### ####### ',
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' ###### ####### ####### ###### ',
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' ######## ####### ################### ',
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' ######## ####### ###### ################## ###### ',
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' ######## ####### ###### ################ ###### ',
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' ######## ####### ###### ############# ###### ',
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' '];
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function thinImage(image) {
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// Good luck!
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}
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```
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</div>
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### After Test
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<div id='js-teardown'>
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```js
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const imageForTests = [
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' ',
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' ################# ############# ',
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' ################## ################ ',
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' ################### ################## ',
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' ######## ####### ################### ',
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' ###### ####### ####### ###### ',
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' ###### ####### ####### ',
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' ################# ####### ',
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' ################ ####### ',
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' ################# ####### ',
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' ###### ####### ####### ',
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' ###### ####### ####### ',
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' ###### ####### ####### ###### ',
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' ######## ####### ################### ',
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' ######## ####### ###### ################## ###### ',
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' ######## ####### ###### ################ ###### ',
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' ######## ####### ###### ############# ###### ',
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' '];
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const expected = [
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' ',
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' ',
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' # ########## ####### ',
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' ## # #### # ',
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' # # ## ',
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' # # # ',
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' # # # ',
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' # # # ',
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' ############ # ',
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' # # # ',
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' # # # ',
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' # # # ',
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' # # # ',
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' # ## ',
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' # ############ ',
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' ### ### ',
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' ',
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' '
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];
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const result = thinImage(imageForTests);
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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function Point(x, y) {
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this.x = x;
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this.y = y;
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}
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const ZhangSuen = (function () {
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function ZhangSuen() {
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}
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ZhangSuen.nbrs = [[0, -1], [1, -1], [1, 0], [1, 1], [0, 1], [-1, 1], [-1, 0], [-1, -1], [0, -1]];
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ZhangSuen.nbrGroups = [[[0, 2, 4], [2, 4, 6]], [[0, 2, 6], [0, 4, 6]]];
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ZhangSuen.toWhite = [];
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ZhangSuen.main = function (image) {
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ZhangSuen.grid = new Array(image);
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for (let r = 0; r < image.length; r++) {
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ZhangSuen.grid[r] = image[r].split('');
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}
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ZhangSuen.thinImage();
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return ZhangSuen.getResult();
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};
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ZhangSuen.thinImage = function () {
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let firstStep = false;
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let hasChanged;
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do {
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hasChanged = false;
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firstStep = !firstStep;
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for (let r = 1; r < ZhangSuen.grid.length - 1; r++) {
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for (let c = 1; c < ZhangSuen.grid[0].length - 1; c++) {
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if (ZhangSuen.grid[r][c] !== '#') {
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continue;
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}
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const nn = ZhangSuen.numNeighbors(r, c);
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if (nn < 2 || nn > 6) {
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continue;
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}
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if (ZhangSuen.numTransitions(r, c) !== 1) {
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continue;
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}
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if (!ZhangSuen.atLeastOneIsWhite(r, c, firstStep ? 0 : 1)) {
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continue;
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}
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ZhangSuen.toWhite.push(new Point(c, r));
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hasChanged = true;
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}
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}
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for (let i = 0; i < ZhangSuen.toWhite.length; i++) {
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const p = ZhangSuen.toWhite[i];
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ZhangSuen.grid[p.y][p.x] = ' ';
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}
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ZhangSuen.toWhite = [];
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} while ((firstStep || hasChanged));
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};
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ZhangSuen.numNeighbors = function (r, c) {
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let count = 0;
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for (let i = 0; i < ZhangSuen.nbrs.length - 1; i++) {
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if (ZhangSuen.grid[r + ZhangSuen.nbrs[i][1]][c + ZhangSuen.nbrs[i][0]] === '#') {
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count++;
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}
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}
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return count;
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};
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ZhangSuen.numTransitions = function (r, c) {
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let count = 0;
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for (let i = 0; i < ZhangSuen.nbrs.length - 1; i++) {
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if (ZhangSuen.grid[r + ZhangSuen.nbrs[i][1]][c + ZhangSuen.nbrs[i][0]] === ' ') {
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if (ZhangSuen.grid[r + ZhangSuen.nbrs[i + 1][1]][c + ZhangSuen.nbrs[i + 1][0]] === '#') {
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count++;
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}
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}
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}
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return count;
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};
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ZhangSuen.atLeastOneIsWhite = function (r, c, step) {
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let count = 0;
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const group = ZhangSuen.nbrGroups[step];
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for (let i = 0; i < 2; i++) {
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for (let j = 0; j < group[i].length; j++) {
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const nbr = ZhangSuen.nbrs[group[i][j]];
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if (ZhangSuen.grid[r + nbr[1]][c + nbr[0]] === ' ') {
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count++;
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break;
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}
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}
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}
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return count > 1;
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};
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ZhangSuen.getResult = function () {
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const result = [];
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for (let i = 0; i < ZhangSuen.grid.length; i++) {
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const row = ZhangSuen.grid[i].join('');
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result.push(row);
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}
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return result;
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};
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return ZhangSuen;
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}());
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function thinImage(image) {
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return ZhangSuen.main(image);
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}
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```
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</section>
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