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 transformint 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 spaceint 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 itcontinue;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;}}}}}

霍夫变换源图例如以下：

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;}@Overridepublic 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 transformint 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 2Dhough_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 valueint 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 spaceint 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 itcontinue;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 resultfor (int i = 0; i < this.hough_1d.length; i++){int value = clamp((int)(scale * this.hough_1d[i] + offset)); // scale always equals 1this.hough_1d[i] = (0xFF000000 | value + (value << 16) + (value << 8));}// convert to image 1D and returnfor (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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