图像处理之霍夫变换（直线检测算法）

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
    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：

[java] view plain copy

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
            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
            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;
    }

}

转载自： 这里