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Today, I will introduce to you what the characteristic points of Harris are. The content of the article is good. Now I would like to share it with you. Friends who feel in need can understand it. I hope it will be helpful to you. Let's read it along with the editor's ideas.

The following is an introduction to the improvements made in Harris corners to address its shortcomings.

1) anisotropic response of Moravec operator

The Moravec operator only calculates the grayscale change in eight directions (horizontal, vertical and four diagonal directions). In order to expand it, it is necessary to design a function that can measure the grayscale change in any direction. In 1988, Harris and Stephen derived the Prewitt operator, namely the Harris operator, by expanding the Moravec operator.

Let's first take a look at the background related to Harris. Usually, the Prewitt operator is used to approximate the gradient of the image. However, in practical application, the first-order gradient is approximated by the formula in the following figure:

By analyzing the Morevec operator, we can find that the sum of the corresponding pixel difference in the two Morevec windows can be used as a reasonable approximation of the image gradient. Let's take a look at the following picture:

Through the analysis of the above image, we can further get that the grayscale change in the morevec operator can be approximated by image gradient.

Through the above analysis, the change of grayscale can be expressed as a function of image gradient, and the formula is as follows:

Among them, (ugraine v) represents sliding, the x direction is (1d0), and the y direction is (0Power1). The calculation of the differential is shown in the figure above.

At this point, we are very clear: the above formula can accurately approximate the grayscale change calculation in the moravec operator. But what is different from the grayscale change in the Moravec operator is that the grayscale change in any direction can be measured by reasonable selection (ufocus v).

2) noise response

In the Moravec operator, the sliding window is square, and the square window changes the Euclidean distance between the center pixel and the boundary pixel in different directions. In order to overcome this problem, Harris&Stephen proposed that it is only necessary to change the directional window into a round window. At the same time, each pixel in the window has the same status, in theory, the closer to the center, the greater the weight, and the farther away from the center, the smaller the weight, so we add Gaussian weight. Therefore, the new measure of grayscale change can be represented by the following image:

It is expressed by the formula as follows:

Where wi represents the Gaussian weight at position I.

Strong response at the edge

Because the Moravec operator is prone to false detection at the edge, Harris&Stephen forms a new angle measure (cornerness measure) by considering grayscale metrics in different directions. Then, we change the above formula, such as the following formula:

Harris&Stephen also noticed that the above expression can be written as:

For the above matrix M, its eigenvalue is proportional to the principal curvature of the image surface, and forms a rotation invariant description of M (Proportional to the principle curvature of the image surface and form a rotationally invariant description of M). Then, since M is approximated by horizontal and vertical gradients, they are not really rotational invariant.

Again, like the Moravec operator, let's look at the following four pictures:

In the figure A shows that in the interior or background of an object, the grayscale value in the window is relatively constant, so there is almost no curvature on the surface of the window, so the eigenvalue of M is relatively small; B window is at an edge, perpendicular to the edge will have a significantly large curvature, while parallel to the edge will have little curvature, so one of the eigenvalues of M will be larger and the other smaller. C and D correspond to angles and discrete points and will have large curvature in both directions, so the eigenvalues of M will be very large. Assuming that R1 and R2 are two eigenvalues of M, through the above analysis, a plane can be represented as the following three distinguishable regions:

Harris&Stephen proposed the following corner measure: the general value of k is 040.6.

Finally, let's summarize the calculation steps of the Harris operator:

(1) calculate the autocorrelation matrix M for each pixel.

(2) construct corner mapping (Construct cornerness map)

(3) threshold, carry on the threshold to the obtained C (x _ () _ y)

(4) non-maximum suppression

The above is the whole content of what Harris feature points are, and more content related to what Harris feature points are can be searched for previous articles or browse the following articles to learn ha! I believe the editor will add more knowledge to you. I hope you can support it!

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