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：

// prepare for hough transform  int centerX = width / 2;  int centerY = height / 2;  double hough_interval = PI_VALUE/(double)hough_space; 	      int max = Math.max(width, height);  int max_length = (int)(Math.sqrt(2.0D) * max);  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：

// start hough transform now.... int[][] image_2d = convert1Dto2D(inPixels); for (int row = 0; row < height; row++) { 	for (int col = 0; col < width; col++) {     	int p = image_2d[row][col] & 0xff;     	if(p == 0) continue; // which means background color     	     	// since we does not know the theta angle and r value,      	// we have to calculate all hough space for each pixel point     	// then we got the max possible theta and r pair.     	// r = x * cos(theta) + y * sin(theta)     	for(int cell=0; cell < hough_space; cell++ ) {     		max = (int)((col - centerX) * Math.cos(cell * hough_interval) + (row - centerY) * Math.sin(cell * hough_interval));     		max += max_length; // start from zero, not (-max_length)     		if (max < 0 || (max >= 2 * max_length)) {// make sure r did not out of scope[0, 2*max_lenght]                 continue;             }     		hough_2d[cell][max] +=1;     	}     } }

寻找最大霍夫值计算霍夫阈值的代码如下：

// find the max hough value int max_hough = 0; for(int i=0; i
     
       max_hough) { 			max_hough = hough_2d[i][j]; 		} 	} } System.out.println("MAX HOUGH VALUE = " + max_hough);  // transfer back to image pixels space from hough parameter space 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：

// transfer back to image pixels space from hough parameter space 	    int hough_threshold = (int)(threshold * max_hough); 	    for(int row = 0; row < hough_space; row++) { 	    	for(int col = 0; col < 2*max_length; col++) { 	    		if(hough_2d[row][col] < hough_threshold) // discard it 	    			continue; 	    		int hough_value = hough_2d[row][col]; 	    		boolean isLine = true; 	    		for(int i=-1; i<2; i++) { 	    			for(int j=-1; j<2; j++) { 	    				if(i != 0 || j != 0) {     		              int yf = row + i;     		              int xf = col + j;     		              if(xf < 0) continue;     		              if(xf < 2*max_length) {     		            	  if (yf < 0) {     		            		  yf += hough_space;     		            	  }     		                  if (yf >= hough_space) {     		                	  yf -= hough_space;     		                  }     		                  if(hough_2d[yf][xf] <= hough_value) {     		                	  continue;     		                  }     		                  isLine = false;     		                  break;     		              } 	    				} 	    			} 	    		} 	    		if(!isLine) continue; 	    		 	    		// transform back to pixel data now... 	            double dy = Math.sin(row * hough_interval); 	            double dx = Math.cos(row * hough_interval); 	            if ((row <= hough_space / 4) || (row >= 3 * hough_space / 4)) { 	                for (int subrow = 0; subrow < height; ++subrow) { 	                  int subcol = (int)((col - max_length - ((subrow - centerY) * dy)) / dx) + centerX; 	                  if ((subcol < width) && (subcol >= 0)) { 	                	  image_2d[subrow][subcol] = -16776961; 	                  } 	                } 	              } else { 	                for (int subcol = 0; subcol < width; ++subcol) { 	                  int subrow = (int)((col - max_length - ((subcol - centerX) * dx)) / dy) + centerY; 	                  if ((subrow < height) && (subrow >= 0)) { 	                	  image_2d[subrow][subcol] = -16776961; 	                  } 	                } 	              } 	    	} 	    }

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：

package com.gloomyfish.image.transform;  import java.awt.image.BufferedImage;  import com.process.blur.study.AbstractBufferedImageOp;  public class HoughLineFilter extends AbstractBufferedImageOp { 	public final static double PI_VALUE = Math.PI; 	private int hough_space = 500; 	private int[] hough_1d; 	private int[][] hough_2d; 	private int width; 	private int height; 	 	private float threshold; 	private float scale; 	private float offset; 	 	public HoughLineFilter() { 		// default hough transform parameters 		//	scale = 1.0f; 		//	offset = 0.0f; 		threshold = 0.5f; 		scale = 1.0f; 		offset = 0.0f; 	} 	 	public void setHoughSpace(int space) { 		this.hough_space = space; 	} 	 	public float getThreshold() { 		return threshold; 	}  	public void setThreshold(float threshold) { 		this.threshold = threshold; 	}  	public float getScale() { 		return scale; 	}  	public void setScale(float scale) { 		this.scale = scale; 	}  	public float getOffset() { 		return offset; 	}  	public void setOffset(float offset) { 		this.offset = offset; 	}  	@Override 	public BufferedImage filter(BufferedImage src, BufferedImage dest) { 		width = src.getWidth();         height = src.getHeight();          if ( dest == null )             dest = createCompatibleDestImage( src, null );          int[] inPixels = new int[width*height];         int[] outPixels = new int[width*height];         getRGB( src, 0, 0, width, height, inPixels );         houghTransform(inPixels, outPixels);         setRGB( dest, 0, 0, width, height, outPixels );         return dest; 	}  	private void houghTransform(int[] inPixels, int[] outPixels) {         // prepare for hough transform 	    int centerX = width / 2; 	    int centerY = height / 2; 	    double hough_interval = PI_VALUE/(double)hough_space; 	     	    int max = Math.max(width, height); 	    int max_length = (int)(Math.sqrt(2.0D) * max); 	    hough_1d = new int[2 * hough_space * max_length]; 	     	    // define temp hough 2D array and initialize the hough 2D 	    hough_2d = new int[hough_space][2*max_length]; 	    for(int i=0; i
     
      = 2 * max_length)) {// make sure r did not out of scope[0, 2*max_lenght] 	                    continue; 	                } 	        		hough_2d[cell][max] +=1; 	        	} 	        } 	    } 	     		// find the max hough value 		int max_hough = 0; 		for(int i=0; i
      
        max_hough) { 					max_hough = hough_2d[i][j]; 				} 			} 		} 		System.out.println("MAX HOUGH VALUE = " + max_hough); 		 		// transfer back to image pixels space from hough parameter space 		int hough_threshold = (int)(threshold * max_hough); 	    for(int row = 0; row < hough_space; row++) { 	    	for(int col = 0; col < 2*max_length; col++) { 	    		if(hough_2d[row][col] < hough_threshold) // discard it 	    			continue; 	    		int hough_value = hough_2d[row][col]; 	    		boolean isLine = true; 	    		for(int i=-1; i<2; i++) { 	    			for(int j=-1; j<2; j++) { 	    				if(i != 0 || j != 0) {     		              int yf = row + i;     		              int xf = col + j;     		              if(xf < 0) continue;     		              if(xf < 2*max_length) {     		            	  if (yf < 0) {     		            		  yf += hough_space;     		            	  }     		                  if (yf >= hough_space) {     		                	  yf -= hough_space;     		                  }     		                  if(hough_2d[yf][xf] <= hough_value) {     		                	  continue;     		                  }     		                  isLine = false;     		                  break;     		              } 	    				} 	    			} 	    		} 	    		if(!isLine) continue; 	    		 	    		// transform back to pixel data now... 	            double dy = Math.sin(row * hough_interval); 	            double dx = Math.cos(row * hough_interval); 	            if ((row <= hough_space / 4) || (row >= 3 * hough_space / 4)) { 	                for (int subrow = 0; subrow < height; ++subrow) { 	                  int subcol = (int)((col - max_length - ((subrow - centerY) * dy)) / dx) + centerX; 	                  if ((subcol < width) && (subcol >= 0)) { 	                	  image_2d[subrow][subcol] = -16776961; 	                  } 	                } 	              } else { 	                for (int subcol = 0; subcol < width; ++subcol) { 	                  int subrow = (int)((col - max_length - ((subcol - centerX) * dx)) / dy) + centerY; 	                  if ((subrow < height) && (subrow >= 0)) { 	                	  image_2d[subrow][subcol] = -16776961; 	                  } 	                } 	              } 	    	} 	    } 	     	    // convert to hough 1D and return result 	    for (int i = 0; i < this.hough_1d.length; i++) 	    { 	      int value = clamp((int)(scale * this.hough_1d[i] + offset)); // scale always equals 1 	      this.hough_1d[i] = (0xFF000000 | value + (value << 16) + (value << 8)); 	    } 	     	    // convert to image 1D and return 	    for (int row = 0; row < height; row++) { 	    	for (int col = 0; col < width; col++) { 	        	outPixels[(col + row * width)] = image_2d[row][col]; 	        } 	    } 	} 	 	public BufferedImage getHoughImage() { 		BufferedImage houghImage = new BufferedImage(hough_2d[0].length, hough_space, BufferedImage.TYPE_4BYTE_ABGR); 		setRGB(houghImage, 0, 0, hough_2d[0].length, hough_space, hough_1d); 		return houghImage; 	} 	 	public static int clamp(int value) { 	      if (value < 0) 	    	  value = 0; 	      else if (value > 255) { 	    	  value = 255; 	      } 	      return value; 	} 	 	private int[][] convert1Dto2D(int[] pixels) { 		int[][] image_2d = new int[height][width]; 		int index = 0; 		for(int row = 0; row < height; row++) { 			for(int col = 0; col < width; col++) { 				index = row * width + col; 				image_2d[row][col] = pixels[index]; 			} 		} 		return image_2d; 	}  }
      
     

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