How to do a Gaussian filtering in 3D

Question

How do i do a gaussi smoothing in the 3th dimension?

I have this detection pyramid, votes accumulated at four scales. Objects are found at each peak.

Answer 1

Gaussian filters are separable. You apply 1D filter at each dimension as follows:

for (dim = 0; dim < D; dim++)
    tensor = gaussian_filter(tensor, dim);

I would recommend OpenCV for an implementation of a gaussian filter (and image processing in general) in C++.

Note that this assumes that your pyramid levels are all of the same size. You can have your own functions that sample your scale-space pyramid on the fly while convolving the third dimension, but if you have enough memory I believe that it would be faster to scale up your coarser level to have the same size of the finest level.