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.

Answer 2

Long ago (in 2008-2009) I have developed a small C++ template lib to apply some simple transformations and convolution filters. The library's source can be found in the Linderdaum Engine - it has nothing to do with the rest of the engine and does not use any of the engine's features. The license is MIT, so do whatever you want with it.

Take a look into the Linderdaum's source code (http://www.linderdaum.com) at Src/Linderdaum/Images/VolumeLib.*

The function to prepare the kernel is PrepareGaussianFilter() and MakeScalarVolumeConvolution() applies the filter. It is easy to adapt the library for the different data sources because the I/O is implemented using callback functions.