Volume-preserving smoothing of three-dimensional surfaces: application to intravascular ultrasound

A volume-preserving three-dimensional smoothing approach is described that can be directly applied to 3D medical image data consisting of sets of 2D image slices, e.g., segmented intravascular ultrasound image sequences. Two local smoothing filters ℱ and 𝒢 were designed according to different smoothing goals and their performance was compared. Filtering with the ℱ filter of a relatively large frequency window keeps the important local characteristics of the object and results in little shrinkage while removing noise. Filtering with the Gaussian filter G that has an added volume compensation step results in no global shrinkage and may be used for multiscale filtering. The two filters can be easily extended to n-dimensional filtering.