eed to mathematically find the subpixel location
DoG is very simple. Subtract two adjacent blur images within the same octave obtained in the previous step. Figure 5 illustrates the process.
Then, as a result, you will get 16 DoG images, 4 each. Let's dive a bit deeper into LoG and DoG here for a moment. Replacing LoG with DoG has other advantages besides taking less time. LoG is for scale invariance We need to normalize the Laplacian operator with . That is, the LoG operator changes to scale-normalized LoG as shown below.
The maxima and minima of the scale-normalized LoG characterize the image very reliably. So these maxima and minima are candidates for keypoints. So how on earth can LoG be replaced by DoG? The thermal diffusion equation is applied to prove this. ...(5) It is said that this relationship is formed by the heat diffusion equation. Gaussian The derivative with respect to is given by LoG It means the same as multiplying by . Using the properties of differential functions, this can be expanded as follows. ...(6) Multiplying both sides by the den
In the end, the sum of Gaussian images with different scales, or DoG, is almost equal to the scale-normalized LoG multiplied by (k-1). Therefore, DoG guarantees scale invariance. It naturally includes the scale normalization process. And the multiplication of (k-1) can be ignored as it has no effect on finding maxima or minima. Anyway, in this way, LoG can be easily replaced with DoG. (Rather, it is replaced with a significant benefit.) Now, we will use these DoG images to find interesting keypoints.
find keypoints in the DoG images
Three DoG images within the same octave are required to determine the maxima and minima of a pixel.
If the value of the currently checked pixel is the smallest or largest among 26 neighboring pixel values, it is recognized as a keypoint
In this way, keypoints are found in every pixel of the DoG imag
The maximum and minimum values
I created a Gaussian blur image with 5 steps when creating the scale space. 4 DoG images come out of 5 blur images, and 2 extrema images come out of 4 DoG images.
But we can't access the location of these real minima and maxima
among the keypoints found as extreme values in the previous step, we need to remove those that have low utility value
remove the ones that exist on the edge.
Simply remove keypoints in the DoG image if the pixel values are smaller than a certain threshold.
remove the keypoints that exist on the edge
However, if there is a large change in the vertical direction (or horizontal direction), but a small change in the horizontal direction (or vertical direction), it can be judged as an edge.
Hessian Matrix can be used to determine whether a corner is a corner or not.
In the previous step, we found suitable keypoints.
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