This paper presents a novel approach for the differentiable rendering of convex polyhedra, addressing the limitations of recent methods that rely on implicit field supervision. Our technique introduces a strategy that combines non-differentiable computation of hyperplane intersection through duality transform with differentiable optimization for vertex positioning with three-plane intersection, enabling gradient-based optimization without the need for 3D implicit fields. This allows for efficient shape representation across a range of applications, from shape parsing to compact mesh reconstruction. This work not only overcomes the challenges of previous approaches but also sets a new standard for representing shapes with convex polyhedra.
@article{arxiv.2407.15686,
title = {Differentiable Convex Polyhedra Optimization from Multi-view Images},
author = {Daxuan Ren and Haiyi Mei and Hezi Shi and Jianmin Zheng and Jianfei Cai and Lei Yang},
journal= {arXiv preprint arXiv:2407.15686},
year = {2024}
}