Differentiable Convex Polyhedra Optimization from Multi-view Images
This work addresses shape representation challenges in computer vision and graphics, offering a novel approach for researchers and practitioners, though it appears incremental as it builds on existing methods to overcome specific limitations.
The paper tackles the problem of differentiable rendering of convex polyhedra by introducing a method that combines non-differentiable hyperplane intersection with differentiable vertex optimization, enabling gradient-based optimization without 3D implicit fields, resulting in efficient shape representation for applications like shape parsing and mesh reconstruction.
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.