Laplacian of Gaussian (LoG)

In the Chapter 3Convolution and Frequency Domain Filtering, we saw that the cross correlation of an image with a filter can be viewed as pattern matching; that is, comparing a (small) template image (of what we want to find) against all local regions in the image. The key idea in blob detection comes from this fact. We have already seen how an LoG filter with zero crossing can be used for edge detection in the last chapter. LoG can also be used to find scale invariant regions by searching 3D (location + scale) extrema of the LoG with the concept of Scale Space. If the scale of the Laplacian (σ of the LoG filter) gets matched with the scale of the blob, the magnitude of the Laplacian response attains a maximum at the center of the blob. With this approach, the LoG-convolved images are computed with gradually increasing σ and they are stacked up in a cube. The blobs correspond to the local maximums in this cube. This approach only detects the bright blobs on the dark backgrounds. It is accurate, but slow (particularly for detecting larger blobs).

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