Spectral Total-Variation Processing of Shapes: Theory and Applications

TL;DR

This paper develops a theoretical framework for spectral total-variation on 3D shapes, introduces new shape deformation methods based on TV eigenfunctions, and demonstrates applications in shape filtering and exaggeration.

Contribution

It generalizes spectral TV to non-Euclidean surfaces, introduces a shape deformation technique using TV eigenfunctions, and expands the toolkit for shape processing in 3D graphics.

Findings

Characterization of TV eigenfunctions on surfaces

Relationship between TV eigenfunctions and shape features

First TV-based shape deformation method

Abstract

We present an analysis of total-variation (TV) on non-Euclidean parameterized surfaces, a natural representation of the shapes used in 3D graphics. Our work explains recent experimental findings in shape spectral TV [Fumero et al., 2020] and adaptive anisotropic spectral TV [Biton and Gilboa, 2022]. A new way to generalize set convexity from the plane to surfaces is derived by characterizing the TV eigenfunctions on surfaces. Relationships between TV, area, eigenvalue, eigenfunctions and their discontinuities are discovered. Further, we expand the shape spectral TV toolkit to include versatile zero-homogeneous flows demonstrated through smoothing and exaggerating filters. Last but not least, we propose the first TV-based method for shape deformation, characterized by deformations along geometrical bottlenecks. We show these bottlenecks to be aligned with eigenfunction discontinuities. This research advances the field of spectral TV on surfaces and its application in 3D graphics, offering new perspectives for shape filtering and deformation.