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This article introduces the "Harris corner detection principle and process introduction" related knowledge, in the actual case of the operation process, many people will encounter such a dilemma, and then let the editor lead you to learn how to deal with these situations! I hope you can read it carefully and be able to achieve something!

1. Corner Overview

Corner is a very important feature of image, which plays a very important role in the understanding and analysis of image graphics. While retaining the important features of image graphics, corner points can effectively reduce the amount of data of information, make the content of information very high, effectively improve the speed of calculation, facilitate reliable image matching, and make real-time processing possible. Corners play a very important role in the field of computer vision, such as 3D scene reconstruction motion estimation, target tracking, target recognition, image registration and matching.

In the real world, the corner corresponds to the corner of the object, the intersection of the road, the T-intersection and so on. From the perspective of image analysis, corners can be defined in the following two ways:

a. The corner can be the corner of two edges.

b. A corner is a feature point with two principal directions in a neighborhood.

The former often needs to encode the image edge, which largely depends on image segmentation and edge extraction, which has considerable difficulty and computation, and once the target to be detected changes locally, it is likely to lead to the failure of the operation. In the early stage, there are mainly methods such as Rosenfeld and Freeman, and in the later stage, there are CSS methods. The method based on image grayscale detects corners by calculating the curvature and gradient of points, which avoids the defects of the first kind of methods, such as Moravec operator, Forstner operator, Harris operator, SUSAN operator and so on. This article mainly introduces the algorithm principle of Harris corner detection.

2. The basic principle of Harris corner detection

The recognition of corners of human eyes is usually done in a local small area or window. If the small window of this feature is moved in all directions, and the grayscale of the area in the window has changed greatly, then it is considered that a corner has been encountered in the window. If the grayscale of the image in the window does not change when the particular window moves in all directions, then there are no corners in the window; if the grayscale of the image in the window changes greatly when the window moves in one direction, but does not change in other directions, then the image in the window may be a straight line segment. As shown below:

First of all, the autocorrelation function of the grayscale change caused by translating the image window [uPowerv] is as follows:

The window function can be flat or Gaussian, as shown below:

However, the translated formula is expanded by Taylor as follows:

Then

Because it is a small amount of local movement, it can be approximately obtained that the following expression after ignoring the remainder is a binomial function:

Again.

So,

Among them, the expression of M is as follows, which can be obtained from the derivative of the image:

As we said above, the expression after ignoring the remainder is a binomial function, but the binomial function is essentially an elliptic function. The oblateness and size of the ellipse are determined by the eigenvalues λ 1 and λ 2 of M (xMagy). The direction of the ellipse is determined by the eigenvector of M (xMagy). As shown in the following figure, the elliptic equation is:

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

a. A straight line in an image. One eigenvalue is large, the other is small, λ 1 > λ 2 or λ 2 > λ 1. The value of autocorrelation function is large in one direction and small in other directions.

b. The plane in the image. The two eigenvalues are small and approximately equal, and the values of autocorrelation functions are small in all directions.

c. The corner in the image. The two eigenvalues are large and approximately equal, and the autocorrelation function increases in all directions.

Because we classify the image by the size of the two eigenvalues of M, we define the corner corresponding function R:

Where k is an empirical constant, generally taking k from 0.04 to 0.06.

So, the above figure can be translated into:

Where:

R is only related to the eigenvalue of M

Corner: r is a large positive number

Edge: r is a large negative number

Flat area: r is a decimal value

When judging the corner, the threshold of the corner response function R is processed: r > threshold, and the local maximum of R is extracted.

3. Example effect

The original picture is as follows:

The figure after Harris corner detection:

This is the end of the introduction of the principle and process of Harris corner detection. Thank you for your reading. If you want to know more about the industry, you can follow the website, the editor will output more high-quality practical articles for you!

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