Relationship between Sigma and grid size in imgaussfilt3

Hello,

I am using the imgaussfilt3 function to smooth out my velocity fields in three dimensions. I understand that there are two variables to manipulate, i.e., Sigma and Filterwidth. I am manipulating only Sigma and leaving Filterwidth untouched (By default, the filter width is 4*Sigma + 1). What I am unable to find the documentation is the precise relationship between Sigma and the number of grid cells. My guess is that 1 Sigma is equal to 1 grid cell, but this most certainly need not be the case. Can a person with access to the source code please tell me the precise relationship between Sigma or Filterwidth to the grid dimensions?

Thank you!

Answer 1

[Walter Roberson]

If "number of grid cells" refers to the size of the filter, then according to the documentation,

%   'FilterSize'    -   Scalar or 3-element vector, of positive, odd
%                       integers that specifies the size of the Gaussian
%                       filter. If a scalar Q is specified, then a square
%                       Gaussian filter of size [Q Q Q] is used. 
%
%                       Default value is 2*ceil(2*SIGMA)+1.

[saipb]

Dear Walter,

Thank you for the response. The response does not completely answer my question though. It is true that if I specify Q, then the scalar Q refers to a filter width of QxQxQ grid cells. However, if I am using the default value, then the filter size is merely a function of Sigma. Now, theoretically, it is possible to have many number of grid cells for the same value of Sigma. This is why, I guess that Matlab must assume some correlation between Sigma and number of grid cells. I think it is 1 Sigma = 1 grid-cell. Could you please confirm if this is the case?

[Walter Roberson]

No. The default is 2*ceil(2*SIGMA)+1 .

One possible interpretation of that is 2*Sigma relative to the center of the filter. But the choice could have been arbitrary. If you want to know why they choose 2*ceil(2*SIGMA)+1 then you will need to open a support case and ask for their reasoning.