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Harris corner detection principle-

2022-06-12 04:44:00 【Avocado yogurt】

This article is my view bilibili The teaching is combined with the observation notes of official documents , Link below ：

（ whole ） be based on python Of Opencv Project practice _ Bili, Bili _bilibili

If there is anything that is not well understood , Welcome to correct .

theory ：

Define the corner first （ Baidu Encyclopedia ）： Corner point It's extreme value spot , That is, those with outstanding properties in some aspects spot . Of course , You can define Corner point Properties of （ Set a specific entropy value to Corner point testing ）. Corner point It can be the intersection of two lines , It can also be located on two adjacent things with different main directions spot .

opencv Explanation in :corners are regions in the image with large variation in intensity in all the directions.

Show on the image ： Pixel values vary greatly in different directions .

So we can take advantage of the different intensity of movement in each direction , Judge whether it is a corner , The formula is as follows ：

$\large E(u,v) = \sum_{xy}^{}w(x,y)[f(x+u,y+v)-f(x,y)]^2$

The first term is the weight function , The square can be weighted , It can also be Gaussian weighted

The second term is based on Taylor expansion

among ： Taylor formula ：

$\large f(x+u,y+v) = f(x,y)+uf'x(x,y)+vf'y(x,y)+O(x^2)$

Can be approximately equal to ：

$\large E(u,v) = (uf'x(x,y)+vf'y(x,y))^2$

Two of the partial derivatives can be calculated by gradient function , for example ：cv.sobel()

The formula is easily derived as a quadratic form , Can be written as ：

$\large E(u,v)\approx \begin{bmatrix} u & v \end{bmatrix}M\begin{bmatrix} u\\ v \end{bmatrix}$

among ：

$M = \sum_{x y}^{}w(x,y)\begin{bmatrix} f'x(x,y)^2 &f'x(x,y)f'y(x,y) \\ f'x(x,y)f'y(x,y)&f'y(x,y)^2 \end{bmatrix}$

Add according to the matrix , Change the accumulator into the matrix .

From the mathematical theorem we can know ： A real symmetric matrix must be similarly diagonalized . therefore M The matrix in can be reduced to diagonal matrix ：

$\large E(U,V) = w(x,y)\begin{bmatrix} U & V \end{bmatrix}\begin{bmatrix} \lambda 1 &0 \\ 0& \lambda 2 \end{bmatrix}\begin{bmatrix} U\\ V \end{bmatrix}$

It's actually an elliptic equation ：

$\begin{bmatrix} U & V \end{bmatrix}\begin{bmatrix} \lambda 1 & 0\\ 0 & \lambda 2 \end{bmatrix}\begin{bmatrix} U\\ V \end{bmatrix}=1$

Write it as an equation ：

$\frac{U^2}{\frac{1}{\lambda 1}}+\frac{V^2}{\frac{1}{\lambda 2}}=1$

therefore ：

When λ1 And λ2 When it's big , It means that U,V The direction changes rapidly , Corner expected .

so , A function can be used to describe the relationship between image features , From official documents ：

When |R| Small values , signify ：λ1 And λ2 Very small , The detection point is flat

When R<0, signify λ1>>λ2 perhaps λ2>>λ1, The detection point is the boundary

When R Great value , signify ：λ1 And λ2 It's big , And it's almost the same , The detection point is a corner

function ：

cornerHarris(img,blocksize,ksize,k)->dst

•dst - Returns a single channel array

• img - The data type is float32 The input image of .
　　• blockSize - The specified area in corner detection is small .
　　• ksize - Sobel Window size used in derivation
　　• k - The value parameter is [0,04,0.06]

Code ：

import cv2 as cv
import numpy as np
img = cv.imread("test_1.jpg"
# You need to pass in a grayscale image 
grayimg = cv.cvtColor(img,cv.COLOR_BGR2GRAY)
# The result returned is a single channel array 
grayimg = np.float32(grayimg)
dst= cv.cornerHarris(grayimg,2,3,0.04)
img[dst>0.01*dst.max()] = [0,0,255]
cv.imshow("Harris corner",img)
cv.waitKey(）