Unified Shape Analysis and Synthesis via Deformable Voxel Grids

This paper extends the investigation and application of Deformable Voxel Grids (DVGs) into a unified framework for 3D shape analysis and synthesis. DVGs consist in a grid that approximates a shape’s silhouette via energy-minimization. This provides an improved embedding space over a regular voxel grid as it aligns with the geometry of the shape, and subsequently allows for the deformation of the shape by manipulating the DVG’s control points. We demonstrate how DVGs directly and naturally serve for an array of applications: correspondences, style transfer, shape retrieval, and PCA deformations. We further address the challenge of morphing non-parametric shapes, an ill-posed problem because of the trade-off between plausibility and smoothness, particularly under large topology changes. Thanks to DVGs, we extract a shape content descriptor, and propose a similarity metric adapted to the extracted content and a formulation of morphings as minimal paths in a graph. Our approach leverages the strengths and interpretability of DVGs while achieving morphing capabilities comparable to those provided by neural networks. Throughout the course of our study, we conducted qualitative and quantitative analyses on the robustness and quality of our proposed methods, and we provide valuable insights into the effective manual intervention that can enhance quality, given the interpretability of each component in our method. In conclusion, this work elucidates the wide-ranging implications and potential of DVGs in 3D shape comparison, processing, and morphing, paving the way for future research and applications in the field.