2024/06/17 by Bo Sun, Thibault Groueix, Sun, Bo +7 · 2 citations
Engineering · #3D Shape Modeling and Analysis #Advanced Numerical Analysis Techniques #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Manufacturing Process and Optimization
paper · pdf · doi:10.48550/arxiv.2406.12121
openalex publication_date 2024/06/17 · openalex created_date 2024/06/20 · openalex updated_date 2026/08/01
This work proposes a novel representation of injective deformations of 3D space, which overcomes existing limitations of injective methods: inaccuracy, lack of robustness, and incompatibility with general learning and optimization frameworks. The core idea is to reduce the problem to a deep composition of multiple 2D mesh-based piecewise-linear maps. Namely, we build differentiable layers that produce mesh deformations through Tutte's embedding (guaranteed to be injective in 2D), and compose these layers over different planes to create complex 3D injective deformations of the 3D volume. We show our method provides the ability to efficiently and accurately optimize and learn complex deformations, outperforming other injective approaches. As a main application, we produce complex and artifact-free NeRF and SDF deformations.