Bilateral filtration (C Tomasi, R Manduchi. Bilateral filtering for gray and color images. Proc IEEE International Conference on Computer Vision, 839-846, January 1998) is a local, non-linear, edge-sensitive filtration scheme which considers both the intensity range and the geometric distribution of voxels around the center of the processing kernel. These distributions are often modeled by Gaussians. By extending the filtration into 4 dimensions and combining it with deformable registration using an ITK-based toolkit called Advanced Normalization Tools (ANTs), bilateral filtration provides a powerful denoising and regularization scheme for post-processing 4D cardiac micro-CT data in the mouse. (The National Library of Medicine's Insight Segmentation and Registration Toolkit [ITK] is an open-source, cross-platform system that provides developers with an extensive suite of software tools for image analysis.)
Performing bilateral filtration in 4D reduces the standard deviation of the noise in this contrast-enhanced, cardiac micro-CT dataset from 52.7 HU (left) to 22.6 HU (middle).
As shown in the difference image (right), the edge sensitivity of the filtration scheme preserves high-frequency detail.
This is a movie of bilateral filtration.