OpenCV2马拉松第14圈——边缘检測(Sobel,prewitt,roberts)-白红宇

OpenCV2马拉松第14圈——边缘检測(Sobel,prewitt,roberts)

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发布时间：2019-06-08

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收入囊中

差分在边缘检測的角色

Sobel算子

OpenCV sobel函数

OpenCV Scharr函数

prewitt算子

Roberts算子

葵花宝典

差分在边缘检測究竟有什么用呢？先看以下的图片

作为人，我们能够非常easy发现图中红圈有边界，边界处肯定是非常明显，变化陡峭的，在数学中，什么能够表示变化的快慢，自然就是导数，微分了。

想像有例如以下的一维图片。

红圈处变化最陡峭，再看导数图

红圈在最高值，也就是导数能够非常好表示边缘，由于变化非常剧烈

图像中的Sobel算子

是离散差分算子.

结合了高斯滤波.

$I$ 是原始图像:

我们计算水平和竖直方向的梯度:
1. 水平方向: Gx是我们Kernel size为3的水平sober算子，与I作卷积
  
  $G_{x} = \begin{bmatrix}-1 & 0 & +1 \\-2 & 0 & +2 \\-1 & 0 & +1\end{bmatrix} * I$
2. 竖直方向:Gy是我们Kernel size为3的水平sober算子，与I作卷积
  
  $G_{y} = \begin{bmatrix}-1 & -2 & -1 \\0 & 0 & 0 \\+1 & +2 & +1\end{bmatrix} * I$

对每一个点，再计算以下的值，得到方向无关梯度

$G = \sqrt{ G_{x}^{2} + G_{y}^{2} }$

有时候也能够这样计算:

$G = |G_{x}| + |G_{y}|$

初识API

C++:

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

)

	src – 输入. dst – 输出 ddepth – output image depth; the following combinations of `src.depth()` and `ddepth` are supported: `src.depth()` = `CV_8U`, `ddepth` = -1/`CV_16S`/`CV_32F`/`CV_64F` `src.depth()` = `CV_16U`/`CV_16S`, `ddepth` = -1/`CV_32F`/`CV_64F` `src.depth()` = `CV_32F`, `ddepth` = -1/`CV_32F`/`CV_64F` `src.depth()` = `CV_64F`, `ddepth` = -1/`CV_64F` when `ddepth=-1`, the destination image will have the same depth as the source; in the case of 8-bit input images it will result in truncated derivatives.这里要特别注意了，我们的depth不能为－1，由于我们的输入是uchar8类型的，而算出来的值可能>255也可能 <0 ,都会被截断，CV_16S是推荐的 xorder – order of the derivative x. yorder – order of the derivative y. ksize – sobel核大小，必须为1, 3, 5, or 7. scale – 扩大系数 delta – 附加系数 borderType – 边界类型

src – 输入.

dst – 输出

ddepth –
output image depth; the following combinations of
src.depth() and
ddepth are supported:
- src.depth() = CV_8U, ddepth = -1/CV_16S/CV_32F/CV_64F
- src.depth() = CV_16U/CV_16S, ddepth = -1/CV_32F/CV_64F
- src.depth() = CV_32F, ddepth = -1/CV_32F/CV_64F
- src.depth() = CV_64F, ddepth = -1/CV_64F
when ddepth=-1, the destination image will have the same depth as the source; in the case of 8-bit input images it will result in truncated derivatives.这里要特别注意了，我们的depth不能为－1，由于我们的输入是uchar8类型的，而算出来的值可能>255也可能 <0 ,都会被截断，CV_16S是推荐的

xorder – order of the derivative x.

yorder – order of the derivative y.

ksize – sobel核大小，必须为1, 3, 5, or 7.

scale – 扩大系数

delta – 附加系数

borderType – 边界类型

计算的时候，利用了可分离的滤波进行加速(Ksize=1的时候，用了1*3和 3*1的算子，无法加速)

当Ksize = 3,Sobel採用的算子会不准确，因此还有特殊的值ksize = CV_SCHARR(-1) 相当于使用 $3\times3$ Scharr filter 比 $3\times3$ Sobel算子能获得更准确的结果. Scharr 算子例如以下

$\vecthreethree{-3}{0}{3}{-10}{0}{10}{-3}{0}{3}$

C++:

void

Scharr

(InputArray

src, OutputArray

dst, int

ddepth, int

dx, int

dy, double

scale=1, double

delta=0, int

borderType=BORDER_DEFAULT

)

	src – input image. dst – output image of the same size and the same number of channels as `src`. ddepth – output image depth (see for the list of supported combination of `src.depth()` and `ddepth`). dx – order of the derivative x. dy – order of the derivative y. scale – optional scale factor for the computed derivative values; by default, no scaling is applied (see for details). delta – optional delta value that is added to the results prior to storing them in `dst`. borderType – pixel extrapolation method (see for details).

src – input image.

dst – output image of the same size and the same number of channels as src.

ddepth – output image depth (see for the list of supported combination of src.depth() and ddepth).

dx – order of the derivative x.

dy – order of the derivative y.

scale – optional scale factor for the computed derivative values; by default, no scaling is applied (see for details).

delta – optional delta value that is added to the results prior to storing them in dst.

borderType – pixel extrapolation method (see for details).

The function computes the first x- or y- spatial image derivative using the Scharr operator. The call

$\texttt{Scharr(src, dst, ddepth, dx, dy, scale, delta, borderType)}$

is equivalent to

$\texttt{Sobel(src, dst, ddepth, dx, dy, CV\_SCHARR, scale, delta, borderType)} .$

用法一样～～

荷枪实弹

#include "opencv2/imgproc/imgproc.hpp"#include "opencv2/highgui/highgui.hpp"#include 
       
        #include 
        
         using namespace cv;int main( int, char** argv ){  Mat src, src_gray;  Mat grad;  const char* window_name = "Sobel Demo - Simple Edge Detector";    //由于以Sobel方式求完导数后会有负值，还有会大于255的值而你建的Sobel的图像是 CV_8U，也就是8位无符号数，所以Sobel建立的图像位数不够，要16位有符号的，也就是 CV_16S  int ddepth = CV_16S;  src = imread( argv[1] );  if( !src.data )    { return -1; }  GaussianBlur( src, src, Size(3,3), 0, 0, BORDER_DEFAULT );  cvtColor( src, src_gray, CV_RGB2GRAY );  namedWindow( window_name, CV_WINDOW_AUTOSIZE );  // Generate grad_x and grad_y  Mat grad_x, grad_y;  Mat abs_grad_x, abs_grad_y;  // Gradient X  //Scharr( src_gray, grad_x, ddepth, 1, 0);  Sobel( src_gray, grad_x, ddepth, 1, 0, 3);  convertScaleAbs( grad_x, abs_grad_x );  // Gradient Y  //Scharr( src_gray, grad_y, ddepth, 0, 1);  Sobel( src_gray, grad_y, ddepth, 0, 1, 3);  convertScaleAbs( grad_y, abs_grad_y );  // Total Gradient (approximate)  addWeighted( abs_grad_x, 0.5, abs_grad_y, 0.5, 0, grad );  imshow( window_name, grad );  waitKey(0);  return 0;}

效果图：

举一反三

该算子与Sobel算子类似，仅仅是权值有所变化，但两者实现起来功能还是有差距的，据经验得知Sobel要比Prewitt更能准确检測图像边缘。

Robert算子是一种梯度算子，它用交叉的差分表示梯度，是一种利用局部差分算子寻找边缘的算子，对具有陡峭的低噪声的图像效果最好：

以下我们来用prewitt算子作边缘检測，还记得我们曾经在用过的自己定义滤波不，以下我们又要用上了。

#include "opencv2/highgui/highgui.hpp"  #include "opencv2/imgproc/imgproc.hpp"  using namespace cv;   int main( int, char** argv )  {  	Mat src,gray,Kernelx,Kernely;	     src = imread( argv[1] );      cvtColor( src, gray, CV_RGB2GRAY );    namedWindow("srcImage", 1);      namedWindow("dstImage", 1);        Kernelx = (Mat_
       
        (3,3) << 1, 1, 1, 0, 0, 0, -1, -1, -1);      Kernely = (Mat_
        
         (3,3) << -1, 0, 1, -1, 0, 1, -1, 0, 1);         Mat grad_x, grad_y;  	Mat abs_grad_x, abs_grad_y, grad;      filter2D(gray, grad_x, CV_16S , Kernelx, Point(-1,-1));      filter2D(gray, grad_y, CV_16S , Kernely, Point(-1,-1));    convertScaleAbs( grad_x, abs_grad_x );    convertScaleAbs( grad_y, abs_grad_y );        addWeighted( abs_grad_x, 0.5, abs_grad_y, 0.5, 0, grad );     imshow("dstImage", grad);       waitKey();      return 0;  }

效果图：