我对sobel算子的理解
索贝尔算子（Sobeloperator）主要用作边缘检测，在技术上，它是一离散性差分算子，用来运算图像亮度函数的灰度之近似值。在图像的任何一点使用此算子，将会产生对应的灰度矢量或是其法矢量
Sobel卷积因子为：
该算子包含两组3x3的矩阵，分别为横向及纵向，将之与图像作平面卷积，即可分别得出横向及纵向的亮度差分近似值。如果以A代表原始图像，Gx及Gy分别代表经横向及纵向边缘检测的图像灰度值，其公式如下：
具体计算如下：
图像的每一个像素的横向及纵向灰度值通过以下公式结合，来计算该点灰度的大小：
通常，为了提高效率使用不开平方的近似值：
然后可用以下公式计算梯度方向：
若图像为：
则使用近似公式的计算的结果为：
Sobel算子另一种形式是各向同性Sobel(Isotropic Sobel)算子，也有两个，一个是检测水平边沿的，另一个是检测垂直边沿的 。各向同性Sobel算子和普通Sobel算子相比，它的位置加权系数更为准确，在检测不同方向的边沿时梯度的幅度一致。将Sobel算子矩阵中的所有2改为根号2，就能得到各向同性Sobel的矩阵。
由于Sobel算子是滤波算子的形式，用于提取边缘，可以利用快速卷积函数， 简单有效，因此应用广泛。美中不足的是，Sobel算子并没有将图像的主体与背景严格地区分开来，即Sobel算子没有严格地模拟人的视觉生理特征，所以提取的图像轮廓有时并不能令人满意。
参考：http://homepages.inf.ed.ac.uk/rbf/HIPR2/sobel.htm
http://blog.csdn.net/tianhai110/article/details/5663756
除此之外：由于基础核具有关于0，0，0所在的中轴正负对称，所以通过对基础核的旋转，和图像做卷积，可以获得灰度图的边缘图，同时消去旋转角方向+180°上的边缘，迭代多个方向即可消去多个方向的边缘，但是为消去的边缘会加倍。
基础核：
0°
| -1 |
0 |
1 |
| -2 |
0 |
2 |
| -1 |
0 |
1 |
旋转后的核（顺时针为正）
45°
| -2 |
-1 |
0 |
| -1 |
0 |
1 |
| 0 |
1 |
2 |
90°
| -1 |
-2 |
-1 |
| 0 |
0 |
0 |
| 1 |
2 |
1 |
135°
| 0 |
-1 |
-2 |
| 1 |
0 |
-1 |
| 2 |
1 |
0 |
180°
| 1 |
0 |
-1 |
| 2 |
0 |
-2 |
| 1 |
0 |
-1 |
225°
| 2 |
1 |
0 |
| 1 |
0 |
-1 |
| 0 |
-1 |
-2 |
270°
| 1 |
2 |
1 |
| 0 |
0 |
0 |
| -1 |
-2 |
-1 |
原图：
结果图如下，按0°，45°，90°，135°，180°，225°，270°排序
代码如下：
#include "cv.h"
#include "cxmisc.h"
#include "highgui.h"
#include <vector>
#include <string>
#include <algorithm>
#include <stdio.h>
#include <ctype.h>
#pragma comment(lib, "G:\\OpenCV-2.1.0\\vc2008\\lib\\cxcore210d.lib")
#pragma comment(lib, "G:\\OpenCV-2.1.0\\vc2008\\lib\\cv210d.lib")
#pragma comment(lib, "G:\\OpenCV-2.1.0\\vc2008\\lib\\highgui210d.lib")
//对不同深度图片和较大的图片进行放缩，以至于可以在显示器上完全显示
void ShowConvertImage(char name[200],IplImage* Image)
{
cvNamedWindow(name,1);
char savename[350];
sprintf(savename,"%s.jpg",name);
cvSaveImage(savename,Image);
if(Image->width<1280)
{
if(Image->depth!=IPL_DEPTH_8U)
{
IplImage* NormalizeImage=NULL;
NormalizeImage=cvCreateImage(cvGetSize(Image),IPL_DEPTH_8U,1);
cvConvertScale(Image,NormalizeImage,1,0);//将图转为0-256，用于图片显示，
cvShowImage(name,NormalizeImage);
cvReleaseImage(&NormalizeImage);
}
else
{
cvShowImage(name,Image);
}
}
else
{
IplImage* ImageResize=cvCreateImage(cvSize(1280,Image->height/(Image->width/1280)),Image->depth ,Image->nChannels);
cvResize(Image,ImageResize,1);
if(ImageResize->depth!=IPL_DEPTH_8U)
{
IplImage* NormalizeImage=NULL;
NormalizeImage=cvCreateImage(cvGetSize(ImageResize),IPL_DEPTH_8U,1);
cvConvertScale(Image,NormalizeImage,1,0);//将图转为0-256，用于图片显示，
cvShowImage(name,NormalizeImage);
cvReleaseImage(&NormalizeImage);
}
else
{
cvShowImage(name,ImageResize);
}
cvReleaseImage(&ImageResize);
}
}
//对较大的图片缩放，不然显示器分辨率不支持，只能部分显示,具体见http://blog.csdn.net/yanmy2012/article/details/8110516
int MaxImageWidth=2650;
float Scale=1;
int MinPicWidth=640;
int MinPicHeight=428*MinPicWidth/640;
int Maxradius_self=68*MinPicWidth/640;
int Minradius_self=50*MinPicWidth/640;
int Radius_dist=20*MinPicWidth/640;
int MaxPicWidth=MinPicWidth*Scale;
int MaxPicHeight=MinPicHeight*Scale;
void main()
{
IplImage * pictemp=NULL;
IplImage * pic=NULL;
char *imgpath="12.jpg";
pictemp=cvLoadImage(imgpath,-1);///获取图片，原色获取
//pictemp=cvLoadImage("IMG_02071.jpg",-1);///获取图片，原色获取
/////////////////改变图片的像素大小
if(pic!=NULL)
{
cvReleaseImage(&pic);
}
if(pictemp->width>MaxImageWidth)
{
pic=cvCreateImage(cvSize(MaxPicWidth,MaxPicHeight),pictemp->depth ,3);
cvResize(pictemp,pic,CV_INTER_AREA );
}
else
{
pic=cvCloneImage(pictemp);
}
ShowConvertImage("pic",pic);
cvReleaseImage(&pictemp);
IplImage * Gray_pic=cvCreateImage(cvGetSize(pic),pic->depth ,1);
cvCvtColor(pic,Gray_pic, CV_BGR2GRAY ); //////将Image变成灰度图片保存在gray中
cvCanny(Gray_pic,Gray_pic,50,150,3);
IplImage * Result_pic=cvCreateImage(cvGetSize(pic),IPL_DEPTH_16S ,1);
// IplImage * Result_pic=cvCreateImage(cvGetSize(pic),IPL_DEPTH_8U ,1);
CvMat *kernel=cvCreateMat(3,3,CV_32FC1);
///卷积核的初始化
////90度模板卷积核
{
cvSetReal2D(kernel,0,0, 1); cvSetReal2D(kernel,0,1, 2); cvSetReal2D(kernel,0,2, 1);
cvSetReal2D(kernel,1,0, 0); cvSetReal2D(kernel,1,1, 0); cvSetReal2D(kernel,1,2, 0);
cvSetReal2D(kernel,2,0,-1); cvSetReal2D(kernel,2,1,-2); cvSetReal2D(kernel,2,2,-1);
}
////////////进行卷积核计算
cvFilter2D(Gray_pic,Result_pic,kernel,cvPoint(1,1));
ShowConvertImage("卷积结果90°",Result_pic);
////225度模板卷积核
{
cvSetReal2D(kernel,0,0, 2); cvSetReal2D(kernel,0,1, 1); cvSetReal2D(kernel,0,2, 0);
cvSetReal2D(kernel,1,0, 1); cvSetReal2D(kernel,1,1, 0); cvSetReal2D(kernel,1,2,-1);
cvSetReal2D(kernel,2,0, 0); cvSetReal2D(kernel,2,1,-1); cvSetReal2D(kernel,2,2,-2);
}
////////////进行卷积核计算
cvFilter2D(Gray_pic,Result_pic,kernel,cvPoint(1,1));
ShowConvertImage("卷积结果225°",Result_pic);
////180度模板卷积核
{
cvSetReal2D(kernel,0,0, 1); cvSetReal2D(kernel,0,1, 0); cvSetReal2D(kernel,0,2,-1);
cvSetReal2D(kernel,1,0, 2); cvSetReal2D(kernel,1,1, 0); cvSetReal2D(kernel,1,2,-2);
cvSetReal2D(kernel,2,0, 1); cvSetReal2D(kernel,2,1, 0); cvSetReal2D(kernel,2,2,-1);
}
////////////进行卷积核计算
cvFilter2D(Gray_pic,Result_pic,kernel,cvPoint(1,1));
ShowConvertImage("卷积结果180°",Result_pic);
////135度模板卷积核
{
cvSetReal2D(kernel,0,0, 0); cvSetReal2D(kernel,0,1,-1); cvSetReal2D(kernel,0,2,-2);
cvSetReal2D(kernel,1,0, 1); cvSetReal2D(kernel,1,1, 0); cvSetReal2D(kernel,1,2,-1);
cvSetReal2D(kernel,2,0, 2); cvSetReal2D(kernel,2,1, 1); cvSetReal2D(kernel,2,2, 0);
}
////////////进行卷积核计算
cvFilter2D(Gray_pic,Result_pic,kernel,cvPoint(1,1));
ShowConvertImage("卷积结果135°",Result_pic);
//90度模板卷积核
{
cvSetReal2D(kernel,0,0,-1); cvSetReal2D(kernel,0,1,-2); cvSetReal2D(kernel,0,2,-1);
cvSetReal2D(kernel,1,0, 0); cvSetReal2D(kernel,1,1, 0); cvSetReal2D(kernel,1,2, 0);
cvSetReal2D(kernel,2,0, 1); cvSetReal2D(kernel,2,1, 2); cvSetReal2D(kernel,2,2, 1);
}
////////////进行卷积核计算
cvFilter2D(Gray_pic,Result_pic,kernel,cvPoint(1,1));
ShowConvertImage("卷积结果90°",Result_pic);
////45度模板卷积核
{
cvSetReal2D(kernel,0,0,-2); cvSetReal2D(kernel,0,1,-1); cvSetReal2D(kernel,0,2, 0);
cvSetReal2D(kernel,1,0,-1); cvSetReal2D(kernel,1,1, 0); cvSetReal2D(kernel,1,2, 1);
cvSetReal2D(kernel,2,0, 0); cvSetReal2D(kernel,2,1, 1); cvSetReal2D(kernel,2,2, 2);
}
////////////进行卷积核计算
cvFilter2D(Gray_pic,Result_pic,kernel,cvPoint(1,1));
ShowConvertImage("卷积结果45°",Result_pic);
////0度模板卷积核
{
cvSetReal2D(kernel,0,0,-1); cvSetReal2D(kernel,0,1, 0); cvSetReal2D(kernel,0,2, 1);
cvSetReal2D(kernel,1,0,-2); cvSetReal2D(kernel,1,1, 0); cvSetReal2D(kernel,1,2, 2);
cvSetReal2D(kernel,2,0,-1); cvSetReal2D(kernel,2,1, 0); cvSetReal2D(kernel,2,2, 1);
}
////////////进行卷积核计算
cvFilter2D(Gray_pic,Result_pic,kernel,cvPoint(1,1));
ShowConvertImage("卷积结果0°",Result_pic);
//315度模板卷积核
{
cvSetReal2D(kernel,0,0, 0); cvSetReal2D(kernel,0,1, 1); cvSetReal2D(kernel,0,2, 2);
cvSetReal2D(kernel,1,0,-1); cvSetReal2D(kernel,1,1, 0); cvSetReal2D(kernel,1,2, 1);
cvSetReal2D(kernel,2,0,-2); cvSetReal2D(kernel,2,1,-1); cvSetReal2D(kernel,2,2, 0);
}
////////////进行卷积核计算
cvFilter2D(Gray_pic,Result_pic,kernel,cvPoint(-1,-1));
ShowConvertImage("卷积结果315",Result_pic);
cvSobel(Gray_pic,Result_pic,0,1,3);
ShowConvertImage("Sobel结果X=0,Y=1",Result_pic);
cvSobel(Gray_pic,Result_pic,0,2,3);
ShowConvertImage("Sobel结果X=0,Y=2",Result_pic);
cvSobel(Gray_pic,Result_pic,1,0,3);
ShowConvertImage("Sobel结果X=1,Y=0",Result_pic);
cvSobel(Gray_pic,Result_pic,1,1,3);
ShowConvertImage("Sobel结果X=1,Y=1",Result_pic);
cvSobel(Gray_pic,Result_pic,1,2,3);
ShowConvertImage("Sobel结果X=1,Y=2",Result_pic);
cvSobel(Gray_pic,Result_pic,2,0,3);
ShowConvertImage("Sobel结果X=2,Y=0",Result_pic);
cvSobel(Gray_pic,Result_pic,2,1,3);
ShowConvertImage("Sobel结果X=2,Y=1",Result_pic);
cvSobel(Gray_pic,Result_pic,2,2,3);
ShowConvertImage("Sobel结果X=2,Y=2",Result_pic);
cvWaitKey(0);
cvReleaseImage(&Result_pic);
cvReleaseImage(&Gray_pic);
cvReleaseImage(&pic);
cvReleaseMat(&kernel);
}