Triangle mesh skeletonization using non-deterministic voxel thinning and graph spectrum segmentation

Abstract

In the context of shape processing, the estimation of the medial axis is relevant for the simplification and re-parameterization of 3D bodies. The currently used methods are based on (1) General fields, (2) Geometric methods and (3) voxel-based thinning. They present shortcomings such as (1) overrepresentation and non-smoothness of the medial axis due to high frequency nodes and (2) biased-skeletons due to skewed thinning. To partially overcome these limitations, this article presents a non-deterministic algorithm for the estimation of the 1D skeleton of triangular B-Reps or voxel-based body representations. Our method articulates (1) a novel randomized thinning algorithm that avoids possible skewings in the final skeletonization, (2) spectral-based segmentation that eliminates short dead-end branches, and (3) a maximal excursion method for reduction of high frequencies. The test results show that the randomized order in the removal of the instantaneous skin of the solid region eliminates bias of the skeleton, thus respecting features of the initial solid. An Alpha Shape-based inversion of the skeleton encoding results in triangular boundary Representations of the original body, which present reasonable quality for fast non-minute scenes. Future work is needed to (a) tune the spectral filtering of high frequencies off the basic skeleton and (b) extend the algorithm to solid regions whose skeletons mix 1D and 2D entities.