1、思想：算子使用两个3*3的矩阵算子分别和原始图片作卷积，分别得到横向Gx和纵向Ｇy的梯度值，如果梯度值大于某一个阈值，则认为该点为边缘点；
2、矩阵转换：事实上卷积矩阵也可以由两个一维矩阵卷积而成，在opencv源码中就是用两个一维矩阵卷积生成一个卷积矩阵：
3、梯度值：图像的梯度值由以下公式计算：图像近似梯度值如下：对于原始图像，P5的梯度值为：
4、OpenCV2410，sobel算子函数原型：void Sobel(InputArray src,OutputArray dst,int ddepth,int dx,int dy,int ksize=3,double scale=1,double delta=0,int borderType=BORDER_DEFAULT )函数参数解释：InputArray src：输入的原图像，Mat类型OutputArray dst：输出的边缘检测结果图像，Mat类型，大小与原图像相同。int ddepth：输出图像的深度，针对不同的输入图像，输出目标图像有不同的深度，具体组合如下：- 若src.depth() = CV_8U, 取ddepth =-1/CV_16S/CV_32F/CV_64F- 若src.depth() = CV_16U/CV_16S, 取ddepth =-1/CV_32F/CV_64F- 若src.depth() = CV_32F, 取ddepth =-1/CV_32F/CV_64F- 若src.depth() = CV_64F, 取ddepth = -1/CV_64F注：ddepth =-1时，代表输出图像与输入图像相同的深度。int dx：int类型dx，x 方向上的差分阶数，1或0int dy：int类型dy，y 方向上的差分阶数，1或0其中，dx=1，dy=0，表示计算X方向的导数，检测出的是垂直方向上的边缘；dx=0，dy=1，表示计算Y方向的导数，检测出的是水平方向上的边缘。int ksize：为进行边缘检测时的模板大小为ksize*ksize，取值为1、3、5和7，其中默认值为3。特殊情况：ksize=1时，采用的模板为3*1或1*3。当ksize=3时，Sobel内核可能产生比较明显的误差；double scale：默认1。double delta：默认0。int borderType：默认值为BORDER_DEFAULT。
5、Sobel调用格式：sobel算法代码实现过程为：// 求 X方向梯度Sobel( src_gray, grad_x, ddepth, 1, 0, 3, scale, delta, BORDER_DEFAULT );// 求 Y方向梯度Sobel( src_gray, grad_y, ddepth, 0, 1, 3, scale, delta, BORDER_DEFAULT );convertScaleAbs( grad_x, abs_grad_x );convertScaleAbs( grad_y, abs_grad_y );addWeighted( dst_x, 0.5, dst_y, 0.5, 0, dst); //一种近似的估计
6、Sobel算子实现：#include <opencv2\openc箪滹埘麽v.hpp>using namespace std;using 荏鱿胫协namespace cv;int main( int argc, char** argv ){ Mat in_img = imread("raw.jpg",0); if (!in_img.data) { return -1; } Mat out_img_dx = Mat::zeros(in_img.size(),CV_16SC1); Mat out_img_dy = Mat::zeros(in_img.size(),CV_16SC1); Mat out_img_dxy = Mat::zeros(in_img.size(),CV_16SC1); GaussianBlur(in_img,in_img,Size(3,3),0); unsigned char* p_data = (unsigned char*)in_img.data; unsigned char* p_data_dx = (unsigned char*)out_img_dx.data; unsigned char* p_data_dy = (unsigned char*)out_img_dy.data; int step = in_img.step; for (int i=1;i<in_img.rows-1;i++) { for (int j=1;j<in_img.cols-1;j++) { //通过指针遍历图像上每一个像素 p_data_dx[i*out_img_dx.step+j*(out_img_dx.step/in_img.step)]=abs(p_data[(i-1)*in_img.step+j+1]+2*p_data[i*in_img.step+j+1]+p_data[(i+1)*in_img.step+j+1] -p_data[(i-1)*in_img.step+j-1]-2*p_data[i*in_img.step+j-1]-p_data[(i+1)*in_img.step+j-1]); p_data_dy[i*out_img_dy.step+j*(out_img_dy.step/in_img.step)]=abs(p_data[i*in_img.step+j-1]+2*p_data[i*in_img.step+j]+p_data[i*in_img.step+j+1] -p_data[(i+1)*in_img.step+j-1]-2*p_data[(i+1)*in_img.step+j]-p_data[(i+1)*in_img.step+j+1]); } } addWeighted(out_img_dx,0.5,out_img_dy,0.5,0,out_img_dxy); Mat img_dx,img_dy,img_dxy; convertScaleAbs(out_img_dx,img_dx); convertScaleAbs(out_img_dy,img_dy); convertScaleAbs(out_img_dxy,img_dxy); imshow("raw img",in_img); imshow("x direction",img_dx); imshow("y direction",img_dy); imshow("xy direction",img_dxy); Mat sobel_img; Sobel(in_img,sobel_img,CV_8UC1,1,1,3); imshow("opencv sobel",sobel_img); waitKey( 0 ); return 0;}
7、OpenCV内源码：static void getSobelKe筠续师诈rnels( OutputArray _kx, OutputArray _ky, int dx, int dy, int _ksize, bool normalize, int ktype ){ int i, j, ksizeX = _ksize, ksizeY = _ksize; if( ksizeX == 1 && dx > 0 ) ksizeX = 3; if( ksizeY == 1 && dy > 0 ) ksizeY = 3; CV_Assert( ktype == CV_32F || ktype == CV_64F ); _kx.create(ksizeX, 1, ktype, -1, true); _ky.create(ksizeY, 1, ktype, -1, true); Mat kx = _kx.getMat(); Mat ky = _ky.getMat(); if( _ksize % 2 == 0 || _ksize > 31 ) CV_Error( CV_StsOutOfRange, "The kernel size must be odd and not larger than 31" ); std::vector<int> kerI(std::max(ksizeX, ksizeY) + 1); CV_Assert( dx >= 0 && dy >= 0 && dx+dy > 0 ); for( int k = 0; k < 2; k++ ) { Mat* kernel = k == 0 ? &kx : &ky; int order = k == 0 ? dx : dy; int ksize = k == 0 ? ksizeX : ksizeY; CV_Assert( ksize > order ); if( ksize == 1 ) kerI[0] = 1; else if( ksize == 3 ) { if( order == 0 ) kerI[0] = 1, kerI[1] = 2, kerI[2] = 1; else if( order == 1 ) kerI[0] = -1, kerI[1] = 0, kerI[2] = 1; else kerI[0] = 1, kerI[1] = -2, kerI[2] = 1; } else { int oldval, newval; kerI[0] = 1; for( i = 0; i < ksize; i++ ) kerI[i+1] = 0; for( i = 0; i < ksize - order - 1; i++ ) { oldval = kerI[0]; for( j = 1; j <= ksize; j++ ) { newval = kerI[j]+kerI[j-1]; kerI[j-1] = oldval; oldval = newval; } } for( i = 0; i < order; i++ ) { oldval = -kerI[0]; for( j = 1; j <= ksize; j++ ) { newval = kerI[j-1] - kerI[j]; kerI[j-1] = oldval; oldval = newval; } } } Mat temp(kernel->rows, kernel->cols, CV_32S, &kerI[0]); double scale = !normalize ? 1. : 1./(1 << (ksize-order-1)); temp.convertTo(*kernel, ktype, scale); }}