Normalized Laplacian of Gaussian

1. How do you normalize a Laplacian image?
2. What is Laplacian of Gaussian operator?
3. What does Laplacian of Gaussian filter do?

How do you normalize a Laplacian image?

in scale-space related processing of digital images, to make the Laplacian of Gaussian operator invariant to scales, it is always said to normalize LoG by multiplying σ2, that is LoGnormalized(x,y)=σ2⋅LoG(x,y)=1πσ2(x2+y22σ2−1)e−x2+y22σ2. I wonder why multiply by σ2 not σ4 or anything else?

What is Laplacian of Gaussian operator?

The Laplacian is a 2-D isotropic measure of the 2nd spatial derivative of an image. The Laplacian of an image highlights regions of rapid intensity change and is therefore often used for edge detection (see zero crossing edge detectors).

What does Laplacian of Gaussian filter do?

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.