图像处理之角点检测算法(Harris Corner Detection)
Harris角点检测是通过数学计算在图像上发现角点特征的一种算法，而且其具有旋转不
变性的特质。OpenCV中的Shi-Tomasi角点检测就是基于Harris角点检测改进算法。
基本原理：
角点是一幅图像上最明显与重要的特征，对于一阶导数而言，角点在各个方向的变化是
最大的，而边缘区域在只是某一方向有明显变化。一个直观的图示如下：
数学原理：
基本数学公式如下：
其中W(x, y)表示移动窗口，I(x, y)表示像素灰度值强度，范围为0～255。根据泰勒级数
计算一阶到N阶的偏导数，最终得到一个Harris矩阵公式：
根据Harris的矩阵计算矩阵特征值 
,然后计算Harris角点响应值：
其中K为系数值，通常取值范围为0.04 ~ 0.06之间。
算法详细步骤
第一步：计算图像X方向与Y方向的一阶高斯偏导数Ix与Iy
第二步：根据第一步结果得到Ix^2 , Iy^2与Ix*Iy值
第三步：高斯模糊第二步三个值得到Sxx, Syy, Sxy
第四部：定义每个像素的Harris矩阵，计算出矩阵的两个特质值
第五步：计算出每个像素的R值
第六步：使用3X3或者5X5的窗口，实现非最大值压制
第七步：根据角点检测结果计算，最提取到的关键点以绿色标记，显示在原图上。
程序关键代码解读：
第一步计算一阶高斯偏导数的Ix与Iy值代码如下：
filter.setDirectionType(GaussianDerivativeFilter.X_DIRECTION); BufferedImage xImage = filter.filter(grayImage, null); getRGB( xImage, 0, 0, width, height, inPixels ); extractPixelData(inPixels, GaussianDerivativeFilter.X_DIRECTION, height, width); filter.setDirectionType(GaussianDerivativeFilter.Y_DIRECTION); BufferedImage yImage = filter.filter(grayImage, null); getRGB( yImage, 0, 0, width, height, inPixels ); extractPixelData(inPixels, GaussianDerivativeFilter.Y_DIRECTION, height, width);
关于如何计算高斯一阶与二阶偏导数请看这里：
http://blog.csdn.net/jia20003/article/details/16369143
http://blog.csdn.net/jia20003/article/details/7664777
第三步：分别对第二步计算出来的三个值，单独进行高斯
模糊计算，代码如下：
private void calculateGaussianBlur(int width, int height) { int index = 0; int radius = (int)window_radius; double[][] gw = get2DKernalData(radius, sigma); double sumxx = 0, sumyy = 0, sumxy = 0; for(int row=0; row<height; row++) { for(int col=0; col<width; col++) { for(int subrow =-radius; subrow<=radius; subrow++) { for(int subcol=-radius; subcol<=radius; subcol++) { int nrow = row + subrow; int ncol = col + subcol; if(nrow >= height || nrow < 0) { nrow = 0; } if(ncol >= width || ncol < 0) { ncol = 0; } int index2 = nrow * width + ncol; HarrisMatrix whm = harrisMatrixList.get(index2); sumxx += (gw[subrow + radius][subcol + radius] * whm.getXGradient()); sumyy += (gw[subrow + radius][subcol + radius] * whm.getYGradient()); sumxy += (gw[subrow + radius][subcol + radius] * whm.getIxIy()); } } index = row * width + col; HarrisMatrix hm = harrisMatrixList.get(index); hm.setXGradient(sumxx); hm.setYGradient(sumyy); hm.setIxIy(sumxy); // clean up for next loop sumxx = 0; sumyy = 0; sumxy = 0; } } }
第六步：非最大信号压制(non-max value suppression)
这个在边源检测中是为了得到一个像素宽的边缘，在这里则
是为了得到准确的一个角点像素，去掉非角点值。代码如下：
/*** * we still use the 3*3 windows to complete the non-max response value suppression */ private void nonMaxValueSuppression(int width, int height) { int index = 0; int radius = (int)window_radius; for(int row=0; row<height; row++) { for(int col=0; col<width; col++) { index = row * width + col; HarrisMatrix hm = harrisMatrixList.get(index); double maxR = hm.getR(); boolean isMaxR = true; for(int subrow =-radius; subrow<=radius; subrow++) { for(int subcol=-radius; subcol<=radius; subcol++) { int nrow = row + subrow; int ncol = col + subcol; if(nrow >= height || nrow < 0) { nrow = 0; } if(ncol >= width || ncol < 0) { ncol = 0; } int index2 = nrow * width + ncol; HarrisMatrix hmr = harrisMatrixList.get(index2); if(hmr.getR() > maxR) { isMaxR = false; } } } if(isMaxR) { hm.setMax(maxR); } } } }
运行效果：
程序完整源代码：
package com.gloomyfish.image.harris.corner; import java.awt.image.BufferedImage; import java.util.ArrayList; import java.util.List; import com.gloomyfish.filter.study.GrayFilter; public class HarrisCornerDetector extends GrayFilter { private GaussianDerivativeFilter filter; private List<HarrisMatrix> harrisMatrixList; private double lambda = 0.04; // scope : 0.04 ~ 0.06 // i hard code the window size just keep it' size is same as // first order derivation Gaussian window size private double sigma = 1; // always private double window_radius = 1; // always public HarrisCornerDetector() { filter = new GaussianDerivativeFilter(); harrisMatrixList = new ArrayList<HarrisMatrix>(); } @Override public BufferedImage filter(BufferedImage src, BufferedImage dest) { int width = src.getWidth(); int height = src.getHeight(); initSettings(height, width); if ( dest == null ) dest = createCompatibleDestImage( src, null ); BufferedImage grayImage = super.filter(src, null); int[] inPixels = new int[width*height]; // first step - Gaussian first-order Derivatives (3 × 3) - X - gradient, (3 × 3) - Y - gradient filter.setDirectionType(GaussianDerivativeFilter.X_DIRECTION); BufferedImage xImage = filter.filter(grayImage, null); getRGB( xImage, 0, 0, width, height, inPixels ); extractPixelData(inPixels, GaussianDerivativeFilter.X_DIRECTION, height, width); filter.setDirectionType(GaussianDerivativeFilter.Y_DIRECTION); BufferedImage yImage = filter.filter(grayImage, null); getRGB( yImage, 0, 0, width, height, inPixels ); extractPixelData(inPixels, GaussianDerivativeFilter.Y_DIRECTION, height, width); // second step - calculate the Ix^2, Iy^2 and Ix^Iy for(HarrisMatrix hm : harrisMatrixList) { double Ix = hm.getXGradient(); double Iy = hm.getYGradient(); hm.setIxIy(Ix * Iy); hm.setXGradient(Ix*Ix); hm.setYGradient(Iy*Iy); } // 基于高斯方法，中心点化窗口计算一阶导数和，关键一步 SumIx2, SumIy2 and SumIxIy, 高斯模糊 calculateGaussianBlur(width, height); // 求取Harris Matrix 特征值 // 计算角度相应值R R= Det(H) - lambda * (Trace(H))^2 harrisResponse(width, height); // based on R, compute non-max suppression nonMaxValueSuppression(width, height); // match result to original image and highlight the key points int[] outPixels = matchToImage(width, height, src); // return result image setRGB( dest, 0, 0, width, height, outPixels ); return dest; } private int[] matchToImage(int width, int height, BufferedImage src) { int[] inPixels = new int[width*height]; int[] outPixels = new int[width*height]; getRGB( src, 0, 0, width, height, inPixels ); int index = 0; for(int row=0; row<height; row++) { int ta = 0, tr = 0, tg = 0, tb = 0; for(int col=0; col<width; col++) { index = row * width + col; ta = (inPixels[index] >> 24) & 0xff; tr = (inPixels[index] >> 16) & 0xff; tg = (inPixels[index] >> 8) & 0xff; tb = inPixels[index] & 0xff; HarrisMatrix hm = harrisMatrixList.get(index); if(hm.getMax() > 0) { tr = 0; tg = 255; // make it as green for corner key pointers tb = 0; outPixels[index] = (ta << 24) | (tr << 16) | (tg << 8) | tb; } else { outPixels[index] = (ta << 24) | (tr << 16) | (tg << 8) | tb; } } } return outPixels; } /*** * we still use the 3*3 windows to complete the non-max response value suppression */ private void nonMaxValueSuppression(int width, int height) { int index = 0; int radius = (int)window_radius; for(int row=0; row<height; row++) { for(int col=0; col<width; col++) { index = row * width + col; HarrisMatrix hm = harrisMatrixList.get(index); double maxR = hm.getR(); boolean isMaxR = true; for(int subrow =-radius; subrow<=radius; subrow++) { for(int subcol=-radius; subcol<=radius; subcol++) { int nrow = row + subrow; int ncol = col + subcol; if(nrow >= height || nrow < 0) { nrow = 0; } if(ncol >= width || ncol < 0) { ncol = 0; } int index2 = nrow * width + ncol; HarrisMatrix hmr = harrisMatrixList.get(index2); if(hmr.getR() > maxR) { isMaxR = false; } } } if(isMaxR) { hm.setMax(maxR); } } } } /*** * 计算两个特征值，然后得到R，公式如下，可以自己推导，关于怎么计算矩阵特征值，请看这里： * http://www.sosmath.com/matrix/eigen1/eigen1.html * * A = Sxx; * B = Syy; * C = Sxy*Sxy*4; * lambda = 0.04; * H = (A*B - C) - lambda*(A+B)^2; * * @param width * @param height */ private void harrisResponse(int width, int height) { int index = 0; for(int row=0; row<height; row++) { for(int col=0; col<width; col++) { index = row * width + col; HarrisMatrix hm = harrisMatrixList.get(index); double c = hm.getIxIy() * hm.getIxIy(); double ab = hm.getXGradient() * hm.getYGradient(); double aplusb = hm.getXGradient() + hm.getYGradient(); double response = (ab -c) - lambda * Math.pow(aplusb, 2); hm.setR(response); } } } private void calculateGaussianBlur(int width, int height) { int index = 0; int radius = (int)window_radius; double[][] gw = get2DKernalData(radius, sigma); double sumxx = 0, sumyy = 0, sumxy = 0; for(int row=0; row<height; row++) { for(int col=0; col<width; col++) { for(int subrow =-radius; subrow<=radius; subrow++) { for(int subcol=-radius; subcol<=radius; subcol++) { int nrow = row + subrow; int ncol = col + subcol; if(nrow >= height || nrow < 0) { nrow = 0; } if(ncol >= width || ncol < 0) { ncol = 0; } int index2 = nrow * width + ncol; HarrisMatrix whm = harrisMatrixList.get(index2); sumxx += (gw[subrow + radius][subcol + radius] * whm.getXGradient()); sumyy += (gw[subrow + radius][subcol + radius] * whm.getYGradient()); sumxy += (gw[subrow + radius][subcol + radius] * whm.getIxIy()); } } index = row * width + col; HarrisMatrix hm = harrisMatrixList.get(index); hm.setXGradient(sumxx); hm.setYGradient(sumyy); hm.setIxIy(sumxy); // clean up for next loop sumxx = 0; sumyy = 0; sumxy = 0; } } } public double[][] get2DKernalData(int n, double sigma) { int size = 2*n +1; double sigma22 = 2*sigma*sigma; double sigma22PI = Math.PI * sigma22; double[][] kernalData = new double[size][size]; int row = 0; for(int i=-n; i<=n; i++) { int column = 0; for(int j=-n; j<=n; j++) { double xDistance = i*i; double yDistance = j*j; kernalData[row][column] = Math.exp(-(xDistance + yDistance)/sigma22)/sigma22PI; column++; } row++; } // for(int i=0; i<size; i++) { // for(int j=0; j<size; j++) { // System.out.print("\t" + kernalData[i][j]); // } // System.out.println(); // System.out.println("\t ---------------------------"); // } return kernalData; } private void extractPixelData(int[] pixels, int type, int height, int width) { int index = 0; for(int row=0; row<height; row++) { int ta = 0, tr = 0, tg = 0, tb = 0; for(int col=0; col<width; col++) { index = row * width + col; ta = (pixels[index] >> 24) & 0xff; tr = (pixels[index] >> 16) & 0xff; tg = (pixels[index] >> 8) & 0xff; tb = pixels[index] & 0xff; HarrisMatrix matrix = harrisMatrixList.get(index); if(type == GaussianDerivativeFilter.X_DIRECTION) { matrix.setXGradient(tr); } if(type == GaussianDerivativeFilter.Y_DIRECTION) { matrix.setYGradient(tr); } } } } private void initSettings(int height, int width) { int index = 0; for(int row=0; row<height; row++) { for(int col=0; col<width; col++) { index = row * width + col; HarrisMatrix matrix = new HarrisMatrix(); harrisMatrixList.add(index, matrix); } } } }
最后注意：
我是把彩色图像变为灰度图像来计算，这个计算量小点
处理容易点，此外很多图像处理软件都会用标记来显示
关键点像素，我没有，只是将关键点像素改为绿色。
所以可以从这些方面有很大的提高空间。
