图像处理之霍夫变换圆检测算法
之前写过一篇文章讲述霍夫变换原理与利用霍夫变换检测直线, 结果发现访问量还是蛮
多,有点超出我的意料,很多人都留言说代码写得不好,没有注释,结构也不是很清晰,所以
我萌发了再写一篇,介绍霍夫变换圆检测算法,同时也尽量的加上详细的注释,介绍代码
结构.让更多的人能够读懂与理解.
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
/** * 霍夫变换处理 - 检测半径大小符合的圆的个数 * 1. 将图像像素从2D空间坐标转换到极坐标空间 * 2. 在极坐标空间中归一化各个点强度，使之在0〜255之间 * 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 * 4. 对找出的空间像素点赋予结果颜色(红色) * 5. 返回结果2D空间像素集合 * @return int [] */ public int[] process() { // 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 acc = new int[width * height]; for (int y = 0; y < height; y++) { for (int x = 0; x < width; x++) { acc[y * width + x] = 0; } } int x0, y0; double t; for (int x = 0; x < width; x++) { for (int y = 0; y < height; y++) { if ((input[y * width + x] & 0xff) == 255) { for (int theta = 0; theta < 360; theta++) { t = (theta * 3.14159265) / 180; // 角度值0 ~ 2*PI x0 = (int) Math.round(x - r * Math.cos(t)); y0 = (int) Math.round(y - r * Math.sin(t)); if (x0 < width && x0 > 0 && y0 < height && y0 > 0) { acc[x0 + (y0 * width)] += 1; } } } } } // now normalise to 255 and put in format for a pixel array int max = 0; // Find max acc value for (int x = 0; x < width; x++) { for (int y = 0; y < height; y++) { if (acc[x + (y * width)] > max) { max = acc[x + (y * width)]; } } } // 根据最大值，实现极坐标空间的灰度值归一化处理 int value; for (int x = 0; x < width; x++) { for (int y = 0; y < height; y++) { value = (int) (((double) acc[x + (y * width)] / (double) max) * 255.0); acc[x + (y * width)] = 0xff000000 | (value << 16 | value << 8 | value); } } // 绘制发现的圆 findMaxima(); System.out.println("done"); return output; }
完整的算法源代码, 已经全部的加上注释
package com.gloomyfish.image.transform.hough; /*** * * 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 * @author gloomyfish * */ public class CircleHough { private int[] input; private int[] output; private int width; private int height; private int[] acc; private int accSize = 1; private int[] results; private int r; // 圆周的半径大小 public CircleHough() { System.out.println("Hough Circle Detection..."); } public void init(int[] inputIn, int widthIn, int heightIn, int radius) { r = radius; width = widthIn; height = heightIn; input = new int[width * height]; output = new int[width * height]; input = inputIn; for (int y = 0; y < height; y++) { for (int x = 0; x < width; x++) { output[x + (width * y)] = 0xff000000; //默认图像背景颜色为黑色 } } } public void setCircles(int circles) { accSize = circles; // 检测的个数 } /** * 霍夫变换处理 - 检测半径大小符合的圆的个数 * 1. 将图像像素从2D空间坐标转换到极坐标空间 * 2. 在极坐标空间中归一化各个点强度，使之在0〜255之间 * 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 * 4. 对找出的空间像素点赋予结果颜色(红色) * 5. 返回结果2D空间像素集合 * @return int [] */ public int[] process() { // 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 acc = new int[width * height]; for (int y = 0; y < height; y++) { for (int x = 0; x < width; x++) { acc[y * width + x] = 0; } } int x0, y0; double t; for (int x = 0; x < width; x++) { for (int y = 0; y < height; y++) { if ((input[y * width + x] & 0xff) == 255) { for (int theta = 0; theta < 360; theta++) { t = (theta * 3.14159265) / 180; // 角度值0 ~ 2*PI x0 = (int) Math.round(x - r * Math.cos(t)); y0 = (int) Math.round(y - r * Math.sin(t)); if (x0 < width && x0 > 0 && y0 < height && y0 > 0) { acc[x0 + (y0 * width)] += 1; } } } } } // now normalise to 255 and put in format for a pixel array int max = 0; // Find max acc value for (int x = 0; x < width; x++) { for (int y = 0; y < height; y++) { if (acc[x + (y * width)] > max) { max = acc[x + (y * width)]; } } } // 根据最大值，实现极坐标空间的灰度值归一化处理 int value; for (int x = 0; x < width; x++) { for (int y = 0; y < height; y++) { value = (int) (((double) acc[x + (y * width)] / (double) max) * 255.0); acc[x + (y * width)] = 0xff000000 | (value << 16 | value << 8 | value); } } // 绘制发现的圆 findMaxima(); System.out.println("done"); return output; } private int[] findMaxima() { results = new int[accSize * 3]; int[] output = new int[width * height]; // 获取最大的前accSize个值 for (int x = 0; x < width; x++) { for (int y = 0; y < height; y++) { int value = (acc[x + (y * width)] & 0xff); // if its higher than lowest value add it and then sort if (value > results[(accSize - 1) * 3]) { // add to bottom of array results[(accSize - 1) * 3] = value; //像素值 results[(accSize - 1) * 3 + 1] = x; // 坐标X results[(accSize - 1) * 3 + 2] = y; // 坐标Y // shift up until its in right place int i = (accSize - 2) * 3; while ((i >= 0) && (results[i + 3] > results[i])) { for (int j = 0; j < 3; j++) { int temp = results[i + j]; results[i + j] = results[i + 3 + j]; results[i + 3 + j] = temp; } i = i - 3; if (i < 0) break; } } } } // 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 System.out.println("top " + accSize + " matches:"); for (int i = accSize - 1; i >= 0; i--) { drawCircle(results[i * 3], results[i * 3 + 1], results[i * 3 + 2]); } return output; } private void setPixel(int value, int xPos, int yPos) { /// output[(yPos * width) + xPos] = 0xff000000 | (value << 16 | value << 8 | value); output[(yPos * width) + xPos] = 0xffff0000; } // draw circle at x y private void drawCircle(int pix, int xCenter, int yCenter) { pix = 250; // 颜色值，默认为白色 int x, y, r2; int radius = r; r2 = r * r; // 绘制圆的上下左右四个点 setPixel(pix, xCenter, yCenter + radius); setPixel(pix, xCenter, yCenter - radius); setPixel(pix, xCenter + radius, yCenter); setPixel(pix, xCenter - radius, yCenter); y = radius; x = 1; y = (int) (Math.sqrt(r2 - 1) + 0.5); // 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 // 这个方法是别人写的，发现超赞，超好！ while (x < y) { setPixel(pix, xCenter + x, yCenter + y); setPixel(pix, xCenter + x, yCenter - y); setPixel(pix, xCenter - x, yCenter + y); setPixel(pix, xCenter - x, yCenter - y); setPixel(pix, xCenter + y, yCenter + x); setPixel(pix, xCenter + y, yCenter - x); setPixel(pix, xCenter - y, yCenter + x); setPixel(pix, xCenter - y, yCenter - x); x += 1; y = (int) (Math.sqrt(r2 - x * x) + 0.5); } if (x == y) { setPixel(pix, xCenter + x, yCenter + y); setPixel(pix, xCenter + x, yCenter - y); setPixel(pix, xCenter - x, yCenter + y); setPixel(pix, xCenter - x, yCenter - y); } } public int[] getAcc() { return acc; } }
测试的UI类:
package com.gloomyfish.image.transform.hough; import java.awt.BorderLayout; import java.awt.Color; import java.awt.Dimension; import java.awt.FlowLayout; import java.awt.Graphics; import java.awt.Graphics2D; import java.awt.GridLayout; import java.awt.event.ActionEvent; import java.awt.event.ActionListener; import java.awt.image.BufferedImage; import java.io.File; import javax.imageio.ImageIO; import javax.swing.BorderFactory; import javax.swing.JButton; import javax.swing.JFrame; import javax.swing.JPanel; import javax.swing.JSlider; import javax.swing.event.ChangeEvent; import javax.swing.event.ChangeListener; public class HoughUI extends JFrame implements ActionListener, ChangeListener { /** * */ public static final String CMD_LINE = "Line Detection"; public static final String CMD_CIRCLE = "Circle Detection"; private static final long serialVersionUID = 1L; private BufferedImage sourceImage; // private BufferedImage houghImage; private BufferedImage resultImage; private JButton lineBtn; private JButton circleBtn; private JSlider radiusSlider; private JSlider numberSlider; public HoughUI(String imagePath) { super("GloomyFish-Image Process Demo"); try{ File file = new File(imagePath); sourceImage = ImageIO.read(file); } catch(Exception e){ e.printStackTrace(); } initComponent(); } private void initComponent() { int RADIUS_MIN = 1; int RADIUS_INIT = 1; int RADIUS_MAX = 51; lineBtn = new JButton(CMD_LINE); circleBtn = new JButton(CMD_CIRCLE); radiusSlider = new JSlider(JSlider.HORIZONTAL, RADIUS_MIN, RADIUS_MAX, RADIUS_INIT); radiusSlider.setMajorTickSpacing(10); radiusSlider.setMinorTickSpacing(1); radiusSlider.setPaintTicks(true); radiusSlider.setPaintLabels(true); numberSlider = new JSlider(JSlider.HORIZONTAL, RADIUS_MIN, RADIUS_MAX, RADIUS_INIT); numberSlider.setMajorTickSpacing(10); numberSlider.setMinorTickSpacing(1); numberSlider.setPaintTicks(true); numberSlider.setPaintLabels(true); JPanel sliderPanel = new JPanel(); sliderPanel.setLayout(new GridLayout(1, 2)); sliderPanel.setBorder(BorderFactory.createTitledBorder("Settings:")); sliderPanel.add(radiusSlider); sliderPanel.add(numberSlider); JPanel btnPanel = new JPanel(); btnPanel.setLayout(new FlowLayout(FlowLayout.RIGHT)); btnPanel.add(lineBtn); btnPanel.add(circleBtn); JPanel imagePanel = new JPanel(){ private static final long serialVersionUID = 1L; protected void paintComponent(Graphics g) { if(sourceImage != null) { Graphics2D g2 = (Graphics2D) g; g2.drawImage(sourceImage, 10, 10, sourceImage.getWidth(), sourceImage.getHeight(),null); g2.setPaint(Color.BLUE); g2.drawString("原图", 10, sourceImage.getHeight() + 30); if(resultImage != null) { g2.drawImage(resultImage, resultImage.getWidth() + 20, 10, resultImage.getWidth(), resultImage.getHeight(), null); g2.drawString("最终结果,红色是检测结果", resultImage.getWidth() + 40, sourceImage.getHeight() + 30); } } } }; this.getContentPane().setLayout(new BorderLayout()); this.getContentPane().add(sliderPanel, BorderLayout.NORTH); this.getContentPane().add(btnPanel, BorderLayout.SOUTH); this.getContentPane().add(imagePanel, BorderLayout.CENTER); // setup listener this.lineBtn.addActionListener(this); this.circleBtn.addActionListener(this); this.numberSlider.addChangeListener(this); this.radiusSlider.addChangeListener(this); } public static void main(String[] args) { String filePath = System.getProperty ("user.home") + "/Desktop/" + "zhigang/hough-test.png"; HoughUI frame = new HoughUI(filePath); // HoughUI frame = new HoughUI("D:\\image-test\\lines.png"); frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE); frame.setPreferredSize(new Dimension(800, 600)); frame.pack(); frame.setVisible(true); } @Override public void actionPerformed(ActionEvent e) { if(e.getActionCommand().equals(CMD_LINE)) { HoughFilter filter = new HoughFilter(HoughFilter.LINE_TYPE); resultImage = filter.filter(sourceImage, null); this.repaint(); } else if(e.getActionCommand().equals(CMD_CIRCLE)) { HoughFilter filter = new HoughFilter(HoughFilter.CIRCLE_TYPE); resultImage = filter.filter(sourceImage, null); // resultImage = filter.getHoughSpaceImage(sourceImage, null); this.repaint(); } } @Override public void stateChanged(ChangeEvent e) { // TODO Auto-generated method stub } }
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.
第一次用Mac发博文,编辑不好请见谅!
