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) +
4000
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：

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// 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：

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// 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：

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// 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如下：

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// 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：

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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;

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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;

}

}

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