Lazy Wavelet Simplification using Scale-dependent Dense Geometric Variability Descriptors

Abstract

Partitioning geometric data into two sets, one corresponding to high frequencies and the other to low frequencies, is a critical operation in the second generation wavelet multiresolution analysis. From a geometric point of view, a region with high variability within a vertex neighborhood at a certain scale indicates a correlation with a signal having a frequency that dominates at that scale. We thus prospect the abilities of several geometric variability descriptors to robustly identify features. We consider three descriptor families: based on principal component analysis, surface fitting and quadric error metrics. To assess the quality of each descriptor, we employ a lazy wavelet simplification of digitized 3D models since these usually contain noisy geometric structures from which multiple scales of resolutions can be inferred. The difference between a simplified model and the highest resolution representation is measured objectively using averaged local distance functions.