ee1e8abd87
* feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
322 lines
11 KiB
Markdown
322 lines
11 KiB
Markdown
---
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id: 594810f028c0303b75339ad7
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title: Zhang-Suen 细化算法
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challengeType: 5
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forumTopicId: 302347
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dashedName: zhang-suen-thinning-algorithm
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---
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# --description--
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这是一个黑白图像（二值图像）的细化算法。 例如，输入图像如下：
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<!-- TODO write fully in markdown>
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<!-- markdownlint-disable -->
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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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细化后的输出图像为：
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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>算法</h2>
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假设黑像素点为 1，白像素点为 0；则输入图像可以用一个 N \* M 的矩阵（或数组）来表示，其中，矩阵中的元素只能为 0 或 1。这个算法对所有黑像素点 P1 进行操作。每个点 P1 都可以有 8 个相邻的点，分别是：
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<table border="3">
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<tr><td style="text-align: center;">P9</td><td style="text-align: center;">P2</td><td style="text-align: center;">P3</td></tr>
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<tr><td style="text-align: center;">P8</td><td style="text-align: center;"><strong>P1</strong></td><td style="text-align: center;">P4</td></tr>
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<tr><td style="text-align: center;">P7</td><td style="text-align: center;">P6</td><td style="text-align: center;">P5</td></tr>
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</table>
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显然，对于图像边框上的像素点，与它们相邻的点的数量是小于 8 的。
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<ul>
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<li>令 $A(P1)$ 为需要变为黑点的白点数量，即在 P2, P3, P4, P5, P6, P7, P8, P9, P2 这一序列中，(0 -> 1) 的操作次数（注意：为了表示循环/闭环，我们在序列的结尾特地多加了一个 P2）</li>
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<li>令 $B(P1)$ 为与 P1 相邻的点中，黑点的数量（即 sum(P2 .. P9)）</li>
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</ul>
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<h3>步骤一：</h3>
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选出同时满足以下列出条件的所有像素点：
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<ol>
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<li>像素点为黑色，且有 8 个点与之相邻</li>
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<li>$2 <= B(P1) <= 6$</li>
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<li>$A(P1) = 1$</li>
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<li><strong>P2, P4 and P6</strong> 中至少有一个是白点</li>
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<li><strong>P4, P6 and P8</strong> 中至少有一个是白点</li>
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</ol>
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在对图像进行迭代并选出所有符合这一步所述条件的点后，把这些点都设置为白色。
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<h3>步骤二：</h3>
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选出同时满足以下列出条件的所有像素点：
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<ol>
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<li>像素点为黑色，且有 8 个点与之相邻</li>
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<li>$2 <= B(P1) <= 6$</li>
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<li>$A(P1) = 1$</li>
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<li><strong>P2, P4 and P6</strong> 中至少有一个是白点</li>
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<li><strong>P2, P6 and P8</strong> 中至少有一个是白点</li>
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</ol>
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在对图像进行迭代并选出所有符合这一步所述条件的点后，把这些点都设置为白色。
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<h3>迭代：</h3>
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只要在步骤一或步骤二，有黑色点被选出并设置成了白色，则继续重复步骤一和步骤二，直到没有黑色点被选出并更改为止。
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# --instructions--
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基于输入图像（以矩阵的形式给出），实现 Zhang-suen 细化算法。
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# --hints--
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`thinImage` 应为函数。
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```js
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assert.equal(typeof thinImage, 'function');
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```
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`thinImage` 应返回数组。
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```js
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assert(Array.isArray(result));
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```
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`thinImage` 应返回字符串数组。
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```js
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assert.equal(typeof result[0], 'string');
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```
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`thinImage` 应返回预计的结果。
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```js
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assert.deepEqual(result, expected);
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```
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# --seed--
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## --after-user-code--
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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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## --seed-contents--
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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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}
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```
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# --solutions--
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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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