图像处理之霍夫变换（直线检測算法）

图像处理之霍夫变换（直线检測算法）

霍夫变换是图像变换中的经典手段之中的一个，主要用来从图像中分离出具有某种同样特征的几何

形状（如，直线，圆等）。霍夫变换寻找直线与圆的方法相比与其他方法能够更好的降低噪

声干扰。经典的霍夫变换经常使用来检測直线，圆，椭圆等。

霍夫变换算法思想：

以直线检測为例，每一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

的样例例如以下：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，

能够表达出直线的离散点几何等式例如以下：

X *cos(theta) + y * sin(theta)  = r 当中角度theta指r与X轴之间的夹角，r为到直线几何垂

直距离。不论什么在直线上点，x, y都能够表达，当中 r， theta是常量。该公式图形表演示样例如以下：

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。假设我们能绘制每一个(r, theta)值依据像素点坐标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，这样的从点到曲线的变换称为直线的霍夫变换。变换

通过量化霍夫參数空间为有限个值间隔等分或者累加格子。当霍夫变换算法開始，每一个像素

坐标点P(x, y)被转换到(r, theta)的曲线点上面，累加到相应的格子数据点，当一个波峰出现

时候，说明有直线存在。相同的原理，我们能够用来检測圆，仅仅是对于圆的參数方程变为如

下等式：

(x –a ) ^2 + (y-b) ^ 2 = r^2当中(a, b)为圆的中心点坐标，r圆的半径。这样霍夫的參数空间就

变成一个三维參数空间。给定圆半径转为二维霍夫參数空间，变换相对简单，也比較经常使用。

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.      依据直线的霍夫变换公式完毕霍夫变换，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(程序难点之中的一个)

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，同一时候依据參数直线參数方程的取值

范围为[-r, r]有例如以下霍夫參数定义：

 // 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例如以下：

// find the max hough value
int max_hough = 0;
for(int i=0; i<hough_space; i++) {
	for(int j=0; j<2*max_length; j++) {
		hough_1d[(i + j * hough_space)] = hough_2d[i][j];
		if(hough_2d[i][j] > 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例如以下：

	    // 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;
	                  }
	                }
	              }
	    	}
	    }

霍夫变换以后，在霍夫空间显演示样例如以下：（白色表示已经找到直线信号）

终于反变换回到像素空间效果例如以下：

一个更好的执行监測直线的结果(输入为二值图像)：

完整的霍夫变换源码例如以下：

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<hough_space; i++) {
	    	for(int j=0; j<2*max_length; j++) {
	    		hough_2d[i][j] = 0;
	    	}
	    }
	    
	    // 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;
	        	}
	        }
	    }
	    
		// find the max hough value
		int max_hough = 0;
		for(int i=0; i<hough_space; i++) {
			for(int j=0; j<2*max_length; j++) {
				hough_1d[(i + j * hough_space)] = hough_2d[i][j];
				if(hough_2d[i][j] > 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;
	}

}