Differentiable Convex Polyhedra Optimization from Multi-view Images

TL;DR

This paper introduces a differentiable method for convex polyhedra rendering from multi-view images, enabling gradient-based shape optimization without relying on implicit 3D fields, thus broadening applications in shape parsing and mesh reconstruction.

Contribution

It proposes a novel approach combining duality transform and differentiable optimization for convex polyhedra, overcoming limitations of implicit field methods.

Findings

Enables efficient gradient-based shape optimization.

Supports shape parsing and mesh reconstruction.

Sets new standards for convex shape representation.

Abstract

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.