（9） Opencv Canny edge detection

1. Basic principle

Reference from 《 Digital image processing 》 Chapter ten

And OpenCV Tutorial Canny Edge Detector

1.1 Overview of edge detection

Edge detection is a common method to segment an image according to gray mutation . Edge models can be classified according to their gray Profile , Usually divided into step model , Slope model and roof edge model . Step models are often found in computer-generated images , Such as solid modeling and animation . Most of the actual images are slope edge models . When using two-step degree to obtain image edge , The second derivative will produce a local maximum positive value and a local minimum negative value , Reflected in the image as a bilinear effect .

1.2Canny edge detection

1986 Year by year John F. Canny stay A computational approach to edge detection. It is proposed that ,Canny The algorithm is mainly divided into the following steps ：

• Use Gaussian kernel to smooth the input image
• Calculate gradient amplitude image and angle image
• Apply non maximum suppression to gradient amplitude images
• Use double threshold processing and connectivity analysis to detect and connect edges

Discuss separately ,

• Gaussian kernel smoothing image denoising

• Calculate the gradient amplitude diagram and gradient direction diagram , Make f(x,y) Represents the input image , The gradient amplitude and direction are ：
  
  $M(x,y)=||▽f(x,y)||=\sqrt{g_x^2(x,y)+g_y^2(x,y)}$
  $\alpha (x,y)=arctan[\frac{g_y(x,y)}{g_x(x,y)}]$,
  among ,$g_x(x,y)=\frac{\partial f(x,y)}{\partial x}$, $g_y(x,y)=\frac{\partial f(x,y)}{\partial y}$, You can use （ 7、 ... and ） Operators commonly used in image processing Laplacian\Sobel\Roberts\Prewitt\Kirsch To find $g_x(x,y)$ and $g_y(x,y)$.

• Apply non maximum suppression to gradient amplitude images , Gradient image $||▽f(x,y)||$ It usually contains some wide ridges near the local maximum , You can use non maximum suppression to refine these wide ridges . In a 3x3 In the area , Can define 4 Edge normals ( Gradient vector ) Of 4 A direction , level , vertical ,+45 degree , -45 degree , The angle range in each direction is shown in the figure below ,
  

Use $d_1,d_2,d_3,d_4$ Represents the foregoing 3x3 Regional 4 Basic edge directions , To $\alpha$ Any point in $(x,y)$ Centred 3x3 Area , The corresponding non maximum suppression scheme is ：
- 1) seek $\alpha (x,y)$ The direction of $d_k$
- 2) Make K Express $||▽f||$ stay $(x,y)$ Place the value of the . if K Less than $d_k$ Point in the direction (x,y) At one or two adjacent points of $||▽f||$ value , Then order $g_N(x,y)=0$; otherwise , Make $g_N(x,y)=K$
Yes （x,y) Repeat this process for all values of , Get a picture with $f(x,y)$ Non maximum suppression image with the same size $g_N(x,y)$, Images $g_N(x,y)$ Only the refined edges are included in .

• Use double threshold processing and connectivity analysis to detect and connect edges , obtain $g_N(x,y)$ After that, threshold processing is carried out to obtain the edge .Canny The algorithm uses lag threshold processing , Set two thresholds , Low threshold $T_L$ And high threshold $T_H$. The hysteresis threshold operation can be regarded as creating two additional images ：
  $g_{NH}(x,y)=g_N(x,y)\ge T_H$
  
  $g_{NL}(x,y)=g_N(x,y)\ge T_L$
  And $g_{NL}(x,y)$ comparison $g_{NH}(x,y)$ Non zero values are less ,$g_{NH}(x,y)$ All non-zero pixels in $g_{NL}(x,y)$ in , adopt
  
  $g_{NL}(x,y)=g_{NL}(x,y)-g_{NH}(x,y)$ from $g_{NL}(x,y)$ Delete from $g_{NH}(x,y)$ Non zero pixels of . After the above reduction $g_{NL}(x,y)$ and $g_{NH}(x,y)$ respectively “ weak ” Edge pixels and “ strong ” Edge pixels .$g_{NH}(x,y)$ The edge pixels in are assumed to be valid edge pixels , But it usually has cracks , It is usually necessary to form longer edges by the following treatment ：
  • 1） stay $g_{NH}(x,y)$ Locate the next edge pixel that is not accessed p
  • 2） take $g_{NL}(x,y)$ China and p 8 All weak pixels in the connected domain are marked as effective edge pixels
  • 3） if $g_{NH}(x,y)$ All non-zero pixels in have been accessed , Go to 4, Otherwise return to 1
  • 4） take $g_{NL}(x,y)$ All pixels in that are not marked as valid edge pixels are set to 0
    Go through the above steps , take $g_{NL}(x,y)$ All non-zero pixels in are appended to $g_{NH}(x,y)$ On , formation Canny The final image output by the operator .

2.OpenCV API

Canny()

void cv::Canny	(	
    InputArray 	image,
    OutputArray 	edges,
    double 	threshold1,
    double 	threshold2,
    int 	apertureSize = 3,
    bool 	L2gradient = false 
)

• image: Single channel grayscale
• edges： Store images of edge pixels
• threshold1: Super parameter of hysteresis threshold processing
• threshold2: Super parameter of hysteresis threshold processing
• apertureSize： Use Sobel The convolution kernel size of the operator
• L2gradient: Whether to use $L_2$ norm

3. Example

#include <opencv2/imgproc.hpp>
#include <opencv2/highgui.hpp>
#include <opencv2/imgcodecs.hpp>
#include <iostream>

using namespace std;
using namespace cv;

Mat src, src_gray;
Mat dst, detected_edges;

int low_threshold = 0;
const int max_low_threshold = 100;
const int ratio = 3;
const int ks = 3;
const char *win_name = "Canny Edge Map";

static void CannyThreshold(int, void*)
{
    
    blur(src_gray, detected_edges, Size(3,3));
    Canny(detected_edges, detected_edges, low_threshold, low_threshold*ratio, ks);
    dst = Scalar::all(0);
    src.copyTo(dst, detected_edges);
    imshow(win_name, dst);
    imwrite("seg_res.png", dst);
}

int main(int argc, char **argv)
{
    
    CommandLineParser parser( argc, argv, "{@input | fruits.jpg | input image}" );
    src = imread( samples::findFile( parser.get<String>( "@input" ) ), IMREAD_COLOR ); // Load an image
    if( src.empty() )
    {
    
    std::cout << "Could not open or find the image!\n" << std::endl;
    std::cout << "Usage: " << argv[0] << " <Input image>" << std::endl;
    return -1;
    }
    dst.create( src.size(), src.type() );
    cvtColor( src, src_gray, COLOR_BGR2GRAY );
    namedWindow( win_name, WINDOW_AUTOSIZE);
    createTrackbar( "Min Threshold:", win_name, &low_threshold, max_low_threshold, CannyThreshold );
    CannyThreshold(0, 0);
    waitKey(0);
    return 0;
}