图像处理之霍夫变换

图像处理之霍夫变换（直线检测算法）霍夫变换是图像变换中的经典手段之一，主要用来从图像中分离出具有某种相同特征的几何形状（如，直线，圆等）。

霍夫变换寻找直线与圆的方法相比与其它方法可以更好的减少噪声干扰。

经典的霍夫变换常用来检测直线，圆，椭圆等。

霍夫变换算法思想：以直线检测为例，每个像素坐标点经过变换都变成都直线特质有贡献的统一度量，一个简单的例子如下：一条直线在图像中是一系列离散点的集合，通过一个直线的离散极坐标公式，可以表达出直线的离散点几何等式如下：X *cos(theta) + y * sin(theta) = r 其中角度theta指r与X轴之间的夹角，r为到直线几何垂直距离。

任何在直线上点，x, y都可以表达，其中r，theta是常量。

该公式图形表示如下：然而在实现的图像处理领域，图像的像素坐标P(x, y)是已知的，而r, theta则是我们要寻找的变量。

如果我们能绘制每个(r, theta)值根据像素点坐标P(x, y)值的话，那么就从图像笛卡尔坐标系统转换到极坐标霍夫空间系统，这种从点到曲线的变换称为直线的霍夫变换。

变换通过量化霍夫参数空间为有限个值间隔等分或者累加格子。

当霍夫变换算法开始，每个像素坐标点P(x, y)被转换到(r, theta)的曲线点上面，累加到对应的格子数据点，当一个波峰出现时候，说明有直线存在。

同样的原理，我们可以用来检测圆，只是对于圆的参数方程变为如下等式：(x –a ) ^2 + (y-b) ^ 2 = r^2其中(a, b)为圆的中心点坐标，r圆的半径。

这样霍夫的参数空间就变成一个三维参数空间。

给定圆半径转为二维霍夫参数空间，变换相对简单，也比较常用。

编程思路解析：1. 读取一幅带处理二值图像，最好背景为黑色。

2. 取得源像素数据3. 根据直线的霍夫变换公式完成霍夫变换，预览霍夫空间结果4. 寻找最大霍夫值，设置阈值，反变换到图像RGB值空间(程序难点之一)5. 越界处理，显示霍夫变换处理以后的图像关键代码解析：直线的变换角度为[0 ~ PI]之间，设置等份为500为PI/500，同时根据参数直线参数方程的取值范围为[-r, r]有如下霍夫参数定义：[java]view plaincopy1.// prepare for hough transform2.int centerX = width / 2;3.int centerY = height / 2;4.double hough_interval = PI_VALUE/(double)hough_space;5.6.int max = Math.max(width, height);7.int max_length = (int)(Math.sqrt(2.0D) * max);8.hough_1d = new int[2 * hough_space * max_length];实现从像素RGB空间到霍夫空间变换的代码为：[java]view plaincopy1.// start hough transform now....2.int[][] image_2d = convert1Dto2D(inPixels);3.for (int row = 0; row < height; row++) {4.for (int col = 0; col < width; col++) {5.int p = image_2d[row][col] & 0xff;6.if(p == 0) continue; // which means background color7.8.// since we does not know the theta angle and r value,9.// we have to calculate all hough space for each pixel point10.// then we got the max possible theta and r pair.11.// r = x * cos(theta) + y * sin(theta)12.for(int cell=0; cell < hough_space; cell++ ) {13. max = (int)((col - centerX) * Math.cos(cell * hough_interval) +(row - centerY) * Math.sin(cell * hough_interval));14. max += max_length; // start from zero, not (-max_length)15.if (max < 0 || (max >= 2 * max_length)) {// make sure r did notout of scope[0, 2*max_lenght]16.continue;17. }18. hough_2d[cell][max] +=1;19. }20. }21.}寻找最大霍夫值计算霍夫阈值的代码如下：[java]view plaincopy1.// find the max hough value2.int max_hough = 0;3.for(int i=0; i<hough_space; i++) {4.for(int j=0; j<2*max_length; j++) {5. hough_1d[(i + j * hough_space)] = hough_2d[i][j];6.if(hough_2d[i][j] > max_hough) {7. max_hough = hough_2d[i][j];8. }9. }10.}11.System.out.println("MAX HOUGH VALUE = " + max_hough);12.13.// transfer back to image pixels space from hough parameter space14.int hough_threshold = (int)(threshold * max_hough);从霍夫空间反变换回像素数据空间代码如下：[java]view plaincopy1.// transfer back to image pixels space from hough parameter space2.int hough_threshold = (int)(threshold * max_hough);3.for(int row = 0; row < hough_space; row++) {4.for(int col = 0; col < 2*max_length; col++) {5.if(hough_2d[row][col] < hough_threshold) // discard it6.continue;7.int hough_value = hough_2d[row][col];8.boolean isLine = true;9.for(int i=-1; i<2; i++) {10.for(int j=-1; j<2; j++) {11.if(i != 0 || j != 0) {12.int yf = row + i;13.int xf = col + j;14.if(xf < 0) continue;15.if(xf < 2*max_length) {16.if (yf < 0) {17. yf += hough_space;18. }19.if (yf >= hough_space) {20. yf -= hough_space;21. }22.if(hough_2d[yf][xf] <= hough_value) {23.continue;24. }25. isLine = false;26.break;27. }28. }29. }30. }31.if(!isLine) continue;32.33.// transform back to pixel data now...34.double dy = Math.sin(row * hough_interval);35.double dx = Math.cos(row * hough_interval);36.if ((row <= hough_space / 4) || (row >= 3 * hough_space / 4)) {37.for (int subrow = 0; subrow < height; ++subrow) {38.int subcol = (int)((col - max_length - ((subrow - centerY) * dy)) / dx) + centerX;39.if ((subcol < width) && (subcol >= 0)) {40. image_2d[subrow][subcol] = -16776961;41. }42. }43. } else {44.for (int subcol = 0; subcol < width; ++subcol) {45.int subrow = (int)((col - max_length - ((subcol - centerX) * dx)) / dy) + centerY;46.if ((subrow < height) && (subrow >= 0)) {47. image_2d[subrow][subcol] = -16776961;48. }49. }50. }51. }52.}霍夫变换源图如下：霍夫变换以后，在霍夫空间显示如下：（白色表示已经找到直线信号）最终反变换回到像素空间效果如下：一个更好的运行监测直线的结果(输入为二值图像)：完整的霍夫变换源代码如下：[java]view plaincopy1.package com.gloomyfish.image.transform;2.3.import java.awt.image.BufferedImage;4.5.import com.process.blur.study.AbstractBufferedImageOp;6.7.public class HoughLineFilter extends AbstractBufferedImageOp {8.public final static double PI_VALUE = Math.PI;9.private int hough_space = 500;10.private int[] hough_1d;11.private int[][] hough_2d;12.private int width;13.private int height;14.15.private float threshold;16.private float scale;17.private float offset;18.19.public HoughLineFilter() {20.// default hough transform parameters21.// scale = 1.0f;22.// offset = 0.0f;23. threshold = 0.5f;24. scale = 1.0f;25. offset = 0.0f;26. }27.28.public void setHoughSpace(int space) {29.this.hough_space = space;30. }31.32.public float getThreshold() {33.return threshold;34. }35.36.public void setThreshold(float threshold) {37.this.threshold = threshold;38. }39.40.public float getScale() {41.return scale;42. }43.44.public void setScale(float scale) {45.this.scale = scale;46. }47.48.public float getOffset() {49.return offset;50. }51.52.public void setOffset(float offset) {53.this.offset = offset;54. }55.56.@Override57.public BufferedImage filter(BufferedImage src, BufferedImage dest) {58. width = src.getWidth();59. height = src.getHeight();60.61.if ( dest == null )62. dest = createCompatibleDestImage( src, null );63.64.int[] inPixels = new int[width*height];65.int[] outPixels = new int[width*height];66. getRGB( src, 0, 0, width, height, inPixels );67. houghTransform(inPixels, outPixels);68. setRGB( dest, 0, 0, width, height, outPixels );69.return dest;70. }71.72.private void houghTransform(int[] inPixels, int[] outPixels) {73.// prepare for hough transform74.int centerX = width / 2;75.int centerY = height / 2;76.double hough_interval = PI_VALUE/(double)hough_space;77.78.int max = Math.max(width, height);79.int max_length = (int)(Math.sqrt(2.0D) * max);80. hough_1d = new int[2 * hough_space * max_length];81.82.// define temp hough 2D array and initialize the hough 2D83. hough_2d = new int[hough_space][2*max_length];84.for(int i=0; i<hough_space; i++) {85.for(int j=0; j<2*max_length; j++) {86. hough_2d[i][j] = 0;87. }88. }89.90.// start hough transform now....91.int[][] image_2d = convert1Dto2D(inPixels);92.for (int row = 0; row < height; row++) {93.for (int col = 0; col < width; col++) {94.int p = image_2d[row][col] & 0xff;95.if(p == 0) continue; // which means background color96.97.// since we does not know the theta angle and r value,98.// we have to calculate all hough space for each pixel point99.// then we got the max possible theta and r pair.100.// r = x * cos(theta) + y * sin(theta)101.for(int cell=0; cell < hough_space; cell++ ) {102. max = (int)((col - centerX) * Math.cos(cell * hough_int erval) + (row - centerY) * Math.sin(cell * hough_interval));103. max += max_length; // start from zero, not (-max_length )104.if (max < 0 || (max >= 2 * max_length)) {// make sure r did not out of scope[0, 2*max_lenght]105.continue;106. }107. hough_2d[cell][max] +=1;108. }109. }110. }111.112.// find the max hough value113.int max_hough = 0;114.for(int i=0; i<hough_space; i++) {115.for(int j=0; j<2*max_length; j++) {116. hough_1d[(i + j * hough_space)] = hough_2d[i][j];117.if(hough_2d[i][j] > max_hough) {118. max_hough = hough_2d[i][j];119. }120. }121. }122. System.out.println("MAX HOUGH VALUE = " + max_hough);123.124.// transfer back to image pixels space from hough parameter space 125.int hough_threshold = (int)(threshold * max_hough);126.for(int row = 0; row < hough_space; row++) {127.for(int col = 0; col < 2*max_length; col++) {128.if(hough_2d[row][col] < hough_threshold) // discard it 129.continue;130.int hough_value = hough_2d[row][col];131.boolean isLine = true;132.for(int i=-1; i<2; i++) {133.for(int j=-1; j<2; j++) {134.if(i != 0 || j != 0) {135.int yf = row + i;136.int xf = col + j;137.if(xf < 0) continue;138.if(xf < 2*max_length) {139.if (yf < 0) {140. yf += hough_space;141. }142.if (yf >= hough_space) {143. yf -= hough_space;144. }145.if(hough_2d[yf][xf] <= hough_value) {146.continue;147. }148. isLine = false;149.break;150. }151. }152. }153. }154.if(!isLine) continue;155.156.// transform back to pixel data now...157.double dy = Math.sin(row * hough_interval);158.double dx = Math.cos(row * hough_interval);159.if ((row <= hough_space / 4) || (row >= 3 * hough_space / 4 )) {160.for (int subrow = 0; subrow < height; ++subrow) { 161.int subcol = (int)((col - max_length - ((subrow - cen terY) * dy)) / dx) + centerX;162.if ((subcol < width) && (subcol >= 0)) {163. image_2d[subrow][subcol] = -16776961;164. }165. }166. } else {167.for (int subcol = 0; subcol < width; ++subcol) { 168.int subrow = (int)((col - max_length - ((subcol - cen terX) * dx)) / dy) + centerY;169.if ((subrow < height) && (subrow >= 0)) {170. image_2d[subrow][subcol] = -16776961;171. }172. }173. }174. }175. }176.177.// convert to hough 1D and return result178.for (int i = 0; i < this.hough_1d.length; i++)179. {180.int value = clamp((int)(scale * this.hough_1d[i] + offset)); // s cale always equals 1181.this.hough_1d[i] = (0xFF000000 | value + (value << 16) + (value < < 8));182. }183.184.// convert to image 1D and return185.for (int row = 0; row < height; row++) {186.for (int col = 0; col < width; col++) {187. outPixels[(col + row * width)] = image_2d[row][col]; 188. }189. }190. }191.192.public BufferedImage getHoughImage() {193. BufferedImage houghImage = new BufferedImage(hough_2d[0].length, ho ugh_space, BufferedImage.TYPE_4BYTE_ABGR);194. setRGB(houghImage, 0, 0, hough_2d[0].length, hough_space, hough_1d) ;195.return houghImage;196. }197.198.public static int clamp(int value) {199.if (value < 0)200. value = 0;201.else if (value > 255) {202. value = 255;203. }204.return value;205. }206.207.private int[][] convert1Dto2D(int[] pixels) {208.int[][] image_2d = new int[height][width];209.int index = 0;210.for(int row = 0; row < height; row++) {211.for(int col = 0; col < width; col++) {212. index = row * width + col;213. image_2d[row][col] = pixels[index];214. }215. }216.return image_2d;217. }218.219.}。