how does the image laplacian filter change with its shape?

when I call fspecial('laplacian', alpha) to obtain an laplacian filter for image processing, I get matrix with different scale:

I went into the code, it writes:

       alpha = p2;
       alpha = max(0,min(alpha,1));
       h1    = alpha/(alpha+1); h2 = (1-alpha)/(alpha+1);
       h     = [h1 h2 h1;h2 -4/(alpha+1) h2;h1 h2 h1];

I think this promise the scale of the pixel value stay the same when you change the shape of the filter. So what certain rule does the code follow to make this happen?

[Ge Mu]

In the document it writes:

My question is, why the factor 4/(1+alpha) in front, not any others? in Gaussian and LOG filter, there are normalization operation to ensure the sum of the filter template is 1. what is the normalization operation for Laplacian?

The reason I concern about this detail is that in OpenCV, for different shape, the output is [ 0 1 0 1 -4 1 0 1 0] for one, and [2 0 2 0 -8 0 2 0 2] for another. but MATLAB the latter one is scaled down by 4. The difference in scale will affect how much high order component I add to the original image. I think the shape should not affect this. I think MATLAB is accurate than OpenCV, I just want to know why. Hope I say this clearly.

Answer 1

[KALYAN ACHARJYA]

[KALYAN ACHARJYA]

I hope this will clear you

[Ge Mu]

thank, but I mean, why the factor 4/(alpha+1)? why not any other factor?

[KALYAN ACHARJYA]

Normalization: Multiply and Add all elements its gives 0

Is the question Answered?

[Ge Mu]

no. Any factor in front will give the sum of elements 0. so why 4/(alpha+1)?