图像处理之霍夫变换圆检测算法一:霍夫变换检测圆的数学原理根据极坐标,圆上任意一点的坐标可以表示为如上形式, 所以对于任意一个圆, 假设中心像素点p(x0, y0)像素点已知, 圆半径已知,则旋转360由极坐标方程可以得到每个点上得坐标同样,如果只是知道图像上像素点, 圆半径,旋转360°则中心点处的坐标值必定最强.这正是霍夫变换检测圆的数学原理.二:算法流程该算法大致可以分为以下几个步骤三:运行效果图像从空间坐标变换到极坐标效果, 最亮一点为圆心.图像从极坐标变换回到空间坐标,检测结果显示:四:关键代码解析个人觉得这次注释已经是非常的详细啦,而且我写的还是中文注释[java]view plaincopy1./**2. * 霍夫变换处理 - 检测半径大小符合的圆的个数3. * 1. 将图像像素从2D空间坐标转换到极坐标空间4. * 2. 在极坐标空间中归一化各个点强度，使之在0〜255之间5. * 3. 根据极坐标的R值与输入参数(圆的半径)相等，寻找2D空间的像素点6. * 4. 对找出的空间像素点赋予结果颜色(红色)7. * 5. 返回结果2D空间像素集合8. * @return int []9. */10.public int[] process() {11.12.// 对于圆的极坐标变换来说，我们需要360度的空间梯度叠加值13. acc = new int[width * height];14.for (int y = 0; y < height; y++) {15.for (int x = 0; x < width; x++) {16. acc[y * width + x] = 0;17. }18. }19.int x0, y0;20.double t;21.for (int x = 0; x < width; x++) {22.for (int y = 0; y < height; y++) {23.24.if ((input[y * width + x] & 0xff) == 255) {25.26.for (int theta = 0; theta < 360; theta++) {27. t = (theta * 3.14159265) / 180; // 角度值0 ~ 2*PI28. x0 = (int) Math.round(x - r * Math.cos(t));29. y0 = (int) Math.round(y - r * Math.sin(t));30.if (x0 < width && x0 > 0 && y0 < height && y0 > 0) {31. acc[x0 + (y0 * width)] += 1;32. }33. }34. }35. }36. }37.38.// now normalise to 255 and put in format for a pixel array39.int max = 0;40.41.// Find max acc value42.for (int x = 0; x < width; x++) {43.for (int y = 0; y < height; y++) {44.45.if (acc[x + (y * width)] > max) {46. max = acc[x + (y * width)];47. }48. }49. }50.51.// 根据最大值，实现极坐标空间的灰度值归一化处理52.int value;53.for (int x = 0; x < width; x++) {54.for (int y = 0; y < height; y++) {55. value = (int) (((double) acc[x + (y * width)] / (double) max) *255.0);56. acc[x + (y * width)] = 0xff000000 | (value << 16 | value << 8 |value);57. }58. }59.60.// 绘制发现的圆61. findMaxima();62. System.out.println("done");63.return output;64.}完整的算法源代码, 已经全部的加上注释[java]view plaincopy1.package com.gloomyfish.image.transform.hough;2./***3. *4. * 传入的图像为二值图像，背景为黑色，目标前景颜色为为白色5. * @author gloomyfish6. *7. */8.public class CircleHough {9.10.private int[] input;11.private int[] output;12.private int width;13.private int height;14.private int[] acc;15.private int accSize = 1;16.private int[] results;17.private int r; // 圆周的半径大小18.19.public CircleHough() {20. System.out.println("Hough Circle Detection...");21. }22.23.public void init(int[] inputIn, int widthIn, int heightIn, int radius) {24. r = radius;25. width = widthIn;26. height = heightIn;27. input = new int[width * height];28. output = new int[width * height];29. input = inputIn;30.for (int y = 0; y < height; y++) {31.for (int x = 0; x < width; x++) {32. output[x + (width * y)] = 0xff000000; //默认图像背景颜色为黑色33. }34. }35. }36.37.public void setCircles(int circles) {38. accSize = circles; // 检测的个数39. }40.41./**42. * 霍夫变换处理 - 检测半径大小符合的圆的个数43. * 1. 将图像像素从2D空间坐标转换到极坐标空间44. * 2. 在极坐标空间中归一化各个点强度，使之在0〜255之间45. * 3. 根据极坐标的R值与输入参数(圆的半径)相等，寻找2D空间的像素点46. * 4. 对找出的空间像素点赋予结果颜色(红色)47. * 5. 返回结果2D空间像素集合48. * @return int []49. */50.public int[] process() {51.52.// 对于圆的极坐标变换来说，我们需要360度的空间梯度叠加值53. acc = new int[width * height];54.for (int y = 0; y < height; y++) {55.for (int x = 0; x < width; x++) {56. acc[y * width + x] = 0;57. }58. }59.int x0, y0;60.double t;61.for (int x = 0; x < width; x++) {62.for (int y = 0; y < height; y++) {63.64.if ((input[y * width + x] & 0xff) == 255) {65.66.for (int theta = 0; theta < 360; theta++) {67. t = (theta * 3.14159265) / 180; // 角度值0 ~ 2*PI68. x0 = (int) Math.round(x - r * Math.cos(t));69. y0 = (int) Math.round(y - r * Math.sin(t));70.if (x0 < width && x0 > 0 && y0 < height && y0 > 0) {71. acc[x0 + (y0 * width)] += 1;72. }73. }74. }75. }76. }77.78.// now normalise to 255 and put in format for a pixel array79.int max = 0;80.81.// Find max acc value82.for (int x = 0; x < width; x++) {83.for (int y = 0; y < height; y++) {84.85.if (acc[x + (y * width)] > max) {86. max = acc[x + (y * width)];87. }88. }89. }90.91.// 根据最大值，实现极坐标空间的灰度值归一化处理92.int value;93.for (int x = 0; x < width; x++) {94.for (int y = 0; y < height; y++) {95. value = (int) (((double) acc[x + (y * width)] / (double) max) * 255.0);96. acc[x + (y * width)] = 0xff000000 | (value << 16 | value <<8 | value);97. }98. }99.100.// 绘制发现的圆101. findMaxima();102. System.out.println("done");103.return output;104. }105.106.private int[] findMaxima() {107. results = new int[accSize * 3];108.int[] output = new int[width * height];109.110.// 获取最大的前accSize个值111.for (int x = 0; x < width; x++) {112.for (int y = 0; y < height; y++) {113.int value = (acc[x + (y * width)] & 0xff);114.115.// if its higher than lowest value add it and then sort 116.if (value > results[(accSize - 1) * 3]) {117.118.// add to bottom of array119. results[(accSize - 1) * 3] = value; //像素值120. results[(accSize - 1) * 3 + 1] = x; // 坐标X121. results[(accSize - 1) * 3 + 2] = y; // 坐标Y122.123.// shift up until its in right place124.int i = (accSize - 2) * 3;125.while ((i >= 0) && (results[i + 3] > results[i])) { 126.for (int j = 0; j < 3; j++) {127.int temp = results[i + j];128. results[i + j] = results[i + 3 + j];129. results[i + 3 + j] = temp;130. }131. i = i - 3;132.if (i < 0)133.break;134. }135. }136. }137. }138.139.// 根据找到的半径R，中心点像素坐标p(x, y)，绘制圆在原图像上140. System.out.println("top " + accSize + " matches:");141.for (int i = accSize - 1; i >= 0; i--) {142. drawCircle(results[i * 3], results[i * 3 + 1], results[i * 3 + 2]);143. }144.return output;145. }146.147.private void setPixel(int value, int xPos, int yPos) {148./// output[(yPos * width) + xPos] = 0xff000000 | (value << 16 | val ue << 8 | value);149. output[(yPos * width) + xPos] = 0xffff0000;150. }151.152.// draw circle at x y153.private void drawCircle(int pix, int xCenter, int yCenter) { 154. pix = 250; // 颜色值，默认为白色155.156.int x, y, r2;157.int radius = r;158. r2 = r * r;159.160.// 绘制圆的上下左右四个点161. setPixel(pix, xCenter, yCenter + radius);162. setPixel(pix, xCenter, yCenter - radius);163. setPixel(pix, xCenter + radius, yCenter);164. setPixel(pix, xCenter - radius, yCenter);165.166. y = radius;167. x = 1;168. y = (int) (Math.sqrt(r2 - 1) + 0.5);169.170.// 边缘填充算法，其实可以直接对循环所有像素，计算到做中心点距离来做171.// 这个方法是别人写的，发现超赞，超好！172.while (x < y) {173. setPixel(pix, xCenter + x, yCenter + y);174. setPixel(pix, xCenter + x, yCenter - y);175. setPixel(pix, xCenter - x, yCenter + y);176. setPixel(pix, xCenter - x, yCenter - y);177. setPixel(pix, xCenter + y, yCenter + x);178. setPixel(pix, xCenter + y, yCenter - x);179. setPixel(pix, xCenter - y, yCenter + x);180. setPixel(pix, xCenter - y, yCenter - x);181. x += 1;182. y = (int) (Math.sqrt(r2 - x * x) + 0.5);183. }184.if (x == y) {185. setPixel(pix, xCenter + x, yCenter + y);186. setPixel(pix, xCenter + x, yCenter - y);187. setPixel(pix, xCenter - x, yCenter + y);188. setPixel(pix, xCenter - x, yCenter - y);189. }190. }191.192.public int[] getAcc() {193.return acc;194. }195.196.}测试的UI类:[java]view plaincopy1.package com.gloomyfish.image.transform.hough;2.3.import java.awt.BorderLayout;4.import java.awt.Color;5.import java.awt.Dimension;6.import java.awt.FlowLayout;7.import java.awt.Graphics;8.import java.awt.Graphics2D;9.import java.awt.GridLayout;10.import java.awt.event.ActionEvent;11.import java.awt.event.ActionListener;12.import java.awt.image.BufferedImage;13.import java.io.File;14.15.import javax.imageio.ImageIO;16.import javax.swing.BorderFactory;17.import javax.swing.JButton;18.import javax.swing.JFrame;19.import javax.swing.JPanel;20.import javax.swing.JSlider;21.import javax.swing.event.ChangeEvent;22.import javax.swing.event.ChangeListener;23.24.public class HoughUI extends JFrame implements ActionListener, ChangeListener {25./**26. *27. */28.public static final String CMD_LINE = "Line Detection";29.public static final String CMD_CIRCLE = "Circle Detection";30.private static final long serialVersionUID = 1L;31.private BufferedImage sourceImage;32.// private BufferedImage houghImage;33.private BufferedImage resultImage;34.private JButton lineBtn;35.private JButton circleBtn;36.private JSlider radiusSlider;37.private JSlider numberSlider;38.public HoughUI(String imagePath)39. {40.super("GloomyFish-Image Process Demo");41.try{42. File file = new File(imagePath);43. sourceImage = ImageIO.read(file);44. } catch(Exception e){45. e.printStackTrace();46. }47. initComponent();48. }49.50.private void initComponent() {51.int RADIUS_MIN = 1;52.int RADIUS_INIT = 1;53.int RADIUS_MAX = 51;54. lineBtn = new JButton(CMD_LINE);55. circleBtn = new JButton(CMD_CIRCLE);56. radiusSlider = new JSlider(JSlider.HORIZONTAL, RADIUS_MIN, RADIUS_MAX, RADIUS_INIT);57. radiusSlider.setMajorTickSpacing(10);58. radiusSlider.setMinorTickSpacing(1);59. radiusSlider.setPaintTicks(true);60. radiusSlider.setPaintLabels(true);61. numberSlider = new JSlider(JSlider.HORIZONTAL, RADIUS_MIN, RADIUS_MAX, RADIUS_INIT);62. numberSlider.setMajorTickSpacing(10);63. numberSlider.setMinorTickSpacing(1);64. numberSlider.setPaintTicks(true);65. numberSlider.setPaintLabels(true);66.67. JPanel sliderPanel = new JPanel();68. sliderPanel.setLayout(new GridLayout(1, 2));69. sliderPanel.setBorder(BorderFactory.createTitledBorder("Settings:"));70. sliderPanel.add(radiusSlider);71. sliderPanel.add(numberSlider);72. JPanel btnPanel = new JPanel();73. btnPanel.setLayout(new FlowLayout(FlowLayout.RIGHT));74. btnPanel.add(lineBtn);75. btnPanel.add(circleBtn);76.77.78. JPanel imagePanel = new JPanel(){79.80.private static final long serialVersionUID = 1L;81.82.protected void paintComponent(Graphics g) {83.if(sourceImage != null)84. {85. Graphics2D g2 = (Graphics2D) g;86. g2.drawImage(sourceImage, 10, 10, sourceImage.getWidth(), sourceImage.getHeight(),null);87. g2.setPaint(Color.BLUE);88. g2.drawString("原图", 10, sourceImage.getHeight() + 30);89.if(resultImage != null)90. {91. g2.drawImage(resultImage, resultImage.getWidth() + 20, 10, resultImage.getWidth(), resultImage.getHeight(), null);92. g2.drawString("最终结果,红色是检测结果", resultImage.getWidth() + 40, sourceImage.getHeight() + 30);93. }94. }95. }96.97. };98.this.getContentPane().setLayout(new BorderLayout());99.this.getContentPane().add(sliderPanel, BorderLayout.NORTH);100.this.getContentPane().add(btnPanel, BorderLayout.SOUTH);101.this.getContentPane().add(imagePanel, BorderLayout.CENTER);102.103.// setup listener104.this.lineBtn.addActionListener(this);105.this.circleBtn.addActionListener(this);106.this.numberSlider.addChangeListener(this);107.this.radiusSlider.addChangeListener(this);108. }109.110.public static void main(String[] args)111. {112. String filePath = System.getProperty ("user.home") + "/Desktop/" + "zhigang/hough-test.png";113. HoughUI frame = new HoughUI(filePath);114.// HoughUI frame = new HoughUI("D:\\image-test\\lines.png");115. frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);116. frame.setPreferredSize(new Dimension(800, 600));117. frame.pack();118. frame.setVisible(true);119. }120.121.@Override122.public void actionPerformed(ActionEvent e) {123.if(e.getActionCommand().equals(CMD_LINE))124. {125. HoughFilter filter = new HoughFilter(HoughFilter.LINE_TYPE);126. resultImage = filter.filter(sourceImage, null);127.this.repaint();128. }129.else if(e.getActionCommand().equals(CMD_CIRCLE))130. {131. HoughFilter filter = new HoughFilter(HoughFilter.CIRCLE_TYPE);132. resultImage = filter.filter(sourceImage, null);133.// resultImage = filter.getHoughSpaceImage(sourceImage, null);134.this.repaint();135. }136.137. }138.139.@Override140.public void stateChanged(ChangeEvent e) {141.// TODO Auto-generated method stub142.143. }144.}五:霍夫变换检测圆与直线的图像预处理使用霍夫变换检测圆与直线时候,一定要对图像进行预处理,灰度化以后,提取图像的边缘使用非最大信号压制得到一个像素宽的边缘, 这个步骤对霍夫变换非常重要.否则可能导致霍夫变换检测的严重失真。