When I convolute two normalized 2D normal distributions, will the result also be normalized?

Hello,

when I convolute two normalized 2D normal distributions, will the result also be normalized?

Wolfram tells me that the resulting volume will be the product of the distributions for 1D.

(<http://mathworld.wolfram.com/Convolution.html>)

Is this also true for nD?

Edit: In the meantime I found out, that I have to multiply the result of a convolution with the sampling size to get the correct result. But why?

Kind regards,

joe

Answer 1

[Image Analyst]

No it won't. If you want the range of the convolution to be roughly the same as the input, then you need to make sure the convolution kernel sums to 1. Otherwise, the range will be different, perhaps a lot different. However, you can normalize the output afterwards to any range you want. The function mat2gray() may be useful to you as it normalizes the 2D array to the range 0-1.