3D Gaussian Decay from 1 to 0

I'm doing a model in matlab and I want that, when my variable k is 1, it decays to 0 by a gaussian pattern. It's a 3D model, so the maximum 1 would decay in every direction. The result would be a matrix with the ones k gave me and the other elements between 0 and 1. Could you please help me?

Answer 1

[Image Analyst]

If you have the Image Processing Toolbox, you can use fspecial(). Of course since it's Gaussian, it will decay towards zero, not to zero. Gaussians can never equal zero.

If you don't have that toolbox, just use meshgrid() and exp() to create the Gaussian pattern. In fact, this might be easier for the 3D case since with fspecial, it just creates a 2D Gaussian so you'd have to call it repeatedly to get the third dimension of a 3D Gaussian "ball".

[Inês Rodrigues]

I've tried to do that, but then with exp() I would have to have x and y with negative coordinates:

[X,Y] = meshgrid(-2:.2:2, -2:.2:2); for Z=0:0.0001:1 Z = exp(-X.^2 - Y.^2); end surf(X,Y,Z)

Is there any way to put them positive and create the same matrix?

[Image Analyst]

Of course, just use x - xCenter. The usual offset formula like for all mathematical formula like you're used to. But you're not creating a 3D matrix, you're creating a 2D one. Just look - 2 indexes. That means it's 2D. If it were 3D, you'd have to have 3 indexes, one for x, one for y, and one for z.

[Inês Rodrigues]

Thank you!