Harris Corner point algorithm for image feature detection

Image detection is the basis of image segmentation and image recognition, and is also an indispensable key. In the framework of visual computing theory, extracting the basic features of two-dimensional image, such as edge, corner and texture, is the first step of the whole frame. This article has made a detailed theory introduction and related realization to the Harris Corner point algorithm.

Part One : Corner type Introduction

In the real world, corner points correspond to objects ' corners, road intersections, and T-junctions. There are two definitions for defining corner points from the perspective of image analysis:

The corner point can be a corner point of two edges;

                  Corner point is a feature point with two main directions in a neighborhood           &NBSP ;                          ,         &NB Sp                          ,         &NB Sp                          ,         &NB Sp                          ,         &NB Sp                          ,         &NB Sp                              The former often needs to encode the edge of the image, which is To a large extent, it relies on image segmentation and edge extraction, which has considerable difficulty and computational complexity, and it is likely to cause the failure of operation once the target is changed locally. Early mainly have Rosenfeld and Freeman and other people's methods, later there are CSS methods. Based on the gray-scale method, the angular point is detected by calculating the curvature and gradient of the point, which avoidsThere are some defects in the first kind of methods, such as Moravec operator, Forstner operator, Harris operator, Susan operator and so on.

This article mainly introduced the Harris Corner Point detection algorithm principle, the more famous corner detection method also has Jianbo Shi and Carlo Tomasi proposed Shi-tomasi algorithm, this algorithm starts mainly to solve the tracking question, uses in the measurement two images the similarity degree, We can also look at it as an improvement in the Harris algorithm. It has been implemented in OPENCV and the interface function is named Goodfeaturestotrack (). There is also a well-known corner detection operator, the Susan operator, and Susan is the abbreviation for smallest univalue Segment assimilating Nucleus (minimum core value similarity zone). Susan uses a circular template and a circle's center point to count the number of cells that approximate the circle center pixel by comparing the center point pixel of the circle to the other pixel values within the template circle, which is considered to be the corner point to be detected when the number of cells is less than a certain threshold value. I think the Susan operator can be seen as a simplification of the Harris algorithm. The principle of this algorithm is very simple, the algorithm is also high efficiency, so in OPENCV, its interface function name is: FAST ().

Part Two:harris theory of corner point algorithm

The recognition of the diagonal point of the human eye is usually done in a small area of a local or small window. If the small window of the feature is moved in all directions, the grayscale of the area in the window changes greatly, then it is considered that a corner point is encountered in the window. If this particular window moves in all directions of the image, the gray level of the image in the window does not change, so there is no corner point in the window, and if the window is moving in one direction, the grayscale of the image in the window changes greatly, and in some other directions it is not changed. The image inside the window may be a line segment.

For image I (x, y), when the self-similarity is shifted (δx,δy) at the point (x, y), it can be given by autocorrelation functions:

C (x,y;δx,δy) =∑ (u,v) ∈w (x, y) W (u,v) (I (u,v) –I (u+δx,v+δy)) 2

where w (x, y) is a point (x, Y)-centric window, W (u,v) is a weighted function, which is either a constant or a Gaussian-weighted function.

Based on Taylor expansion, a first-order approximation of the image I (x, y) after translation (Δx,δy) is performed:

Where Ix,iy is the partial derivative of the image I (x, y), then the autocorrelation function can be simplified to:

which

That is, the autocorrelation function of the image I (x, y) at point (x, y) translation (δx,δy) can approximate two functions:

which

A=∑wi2x,b=∑wi2y,c=∑wixiy
The two-time function is essentially an elliptical function. The flattening rate and size of the ellipse are determined by the eigenvalues of M (x, y) λ 1, λ2, and the direction of the ellipsometry is determined by the characteristic vectors of M (x, y), as shown in the following figure, the elliptic equation is:

The relationship between the elliptic function eigenvalues and the corners, lines (edges), and planes in the image is shown in the following figure. The total can be divided into three kinds of situations: