What is the relationship between the sigma in the Laplacian of Gaussian and the two sigmas in the Difference of Gaussians?

1. What does Laplacian of Gaussian do?
2. Why the Laplacian of Gaussian LoG is better than simple Laplacian in computer vision?
3. What can Laplacian of Gaussian filters detect?
4. What is the difference between DoG and LoG?

What does Laplacian of Gaussian do?

The Laplacian of Gaussian is useful for detecting edges that appear at various image scales or degrees of image focus. The exact values of sizes of the two kernels that are used to approximate the Laplacian of Gaussian will determine the scale of the difference image, which may appear blurry as a result.

Why the Laplacian of Gaussian LoG is better than simple Laplacian in computer vision?

Since both the Gaussian and the Laplacian kernels are usually much smaller than the image, this method usually requires far fewer arithmetic operations. The LoG (`Laplacian of Gaussian') kernel can be precalculated in advance so only one convolution needs to be performed at run-time on the image.

What can Laplacian of Gaussian filters detect?

The Laplacian filter is used to detect the edges in the images. But it has a disadvantage over the noisy images. It amplifies the noise in the image. Hence, first, we use a Gaussian filter on the noisy image to smoothen it and then subsequently use the Laplacian filter for edge detection.

What is the difference between DoG and LoG?

As I understand it currently: DoG is an approximation of LoG. Both are used in blob detection, and both perform essentially as band-pass filters. Convolution with a Mexican Hat/Ricker wavelet seems to achieve very much the same effect.