Image Local feature learning (note 1, Harris corner Point)

Corner Point: There are two more common definitionsThe corner point is the intersection point of two edges is a feature point with two main directions in the neighborhood (this main direction, in fact, I have been confused, but the reference to the PCA, I think it is in two directions in the gray scale changes relatively large, that is, the point of the corner in the neighborhood, is no longer a two-dimensional point (x, But a three-dimensional point (x,y,i) where I is the grayscale value corresponding to the pixel position (x, y). When there are two main directions, it means that there are two large eigenvalues. ） The main idea of corner detection:The first method based on the edge of the image, corresponding to the corner of the definition of 1, the detection of the edge also detects the corner point. However, this method is very dependent on the image edge detection, but we know that edge detection is a more troublesome and complex problem. The second is based on the image gray-scale method, the method mainly through the calculation of the curvature of the point and gradient to detect corner points, such methods are more representative of: Moravec,forstner,harris,susan. Harris Corner Point detection:

The following figure illustrates the principle of Harris Corner point detection:

A simple introduction is to set a small window with a fixed size and move the window. Statistic the change of pixels in the window before and after moving to make the judgment of corner point. Written as a mathematical expression is:

The weight factor W (u,v) can be a constant or a Gaussian weighted function:

The first-order expansion of the Taylor series is performed on the upper, and the simplification can be obtained by the following formula:

which

As the second definition of the corner point, the corner point is the gray scale in its neighborhood has a large change in two directions, corresponding to the existence of two large eigenvalues; While the gray level in the neighborhood has a large change in a certain direction, there is a large characteristic value; The plane is in the neighborhood gray scale change is not small, there are two smaller eigenvalues The following diagram depicts the relationship between the eigenvalues and the test results:

However, when solving the eigenvalues of the matrix M, the computational amount is relatively large and time consuming, because we generally do not calculate its characteristics directly. Using the following formula to indirectly compare its characteristics of the size relationship, the corner to judge:


and then make λ1=λ,λ2=kλ1, where (λ1>=λ2, so k<=1)

hypothesis r>0, there is (high school mathematics of the extremum problem of the hook function , or direct derivation):

So you can set the value range of K by adjusting α:

When α increases to 0.25, K can only fetch 1; when α is reduced to 0 o'clock, the value of K is (0,1), that is, the alpha value increases, K value interval is reduced, then the detected corner is less, that is, the detection sensitivity is reduced (but more accurate), the α value decreases, the K value interval increases, then the detected corner is more, that is, detect sensitive (but will lead to false detection)