Inverse Rendering for High-Genus 3D Surface Meshes from Multi-view Images with Persistent Homology Priors

TL;DR

This work tackles the ill-posed problem of reconstructing high-genus 3D surfaces from multi-view images, where topology can be ambiguous and prone to collapse. It introduces a collaborative inverse rendering framework that leverages persistent homology priors to steer camera placement toward topological tunnels and to preserve handle/tunnel loops during gradient-based mesh optimization. The method formulates a topology-aware objective that combines rendering fidelity, smoothness, and topology-preserving penalties, and it computes persistent homology to identify and reinforce critical topological features (handle and tunnel loops). Empirical results on eight challenging high-genus models show lower Chamfer Distance and higher Volume IoU than the state-of-the-art, with qualitative evidence that tunnels and handles are consistently preserved. The approach offers a principled, topology-aware avenue for robust high-genus surface reconstruction and points to extensions toward non-mesh and deep-learning image-to-3D tasks.

Abstract

Reconstructing 3D objects from images is inherently an ill-posed problem due to ambiguities in geometry, appearance, and topology. This paper introduces collaborative inverse rendering with persistent homology priors, a novel strategy that leverages topological constraints to resolve these ambiguities. By incorporating priors that capture critical features such as tunnel loops and handle loops, our approach directly addresses the difficulty of reconstructing high-genus surfaces. The collaboration between photometric consistency from multi-view images and homology-based guidance enables recovery of complex high-genus geometry while circumventing catastrophic failures such as collapsing tunnels or losing high-genus structure. Instead of neural networks, our method relies on gradient-based optimization within a mesh-based inverse rendering framework to highlight the role of topological priors. Experimental results show that incorporating persistent homology priors leads to lower Chamfer Distance (CD) and higher Volume IoU compared to state-of-the-art mesh-based methods, demonstrating improved geometric accuracy and robustness against topological failure.

Figures (5)

• Figure 1: The pipeline of computing a persistent diagram. (a). Comparison between Čech Complex $\mathcal{C}_\varepsilon$ and Vietoris-Rips Complex $\mathcal{R}_\varepsilon$ghrist2008barcodes. (b). The evolution of filtered Cech complexes with varying scale parameters. (c). Persistent Diagram.
• Figure 2: Topological invariants captured by our implemented two-stage persistent homology algorithm on a torus-3 topology. (a) Exterior and interior volumetric meshes. (b) Handle and tunnel loops.
• Figure 3: Collaborative rendering for the Botijo model. The top two rows show views obtained under the uniform-sphere assumption, while the bottom two rows show views guided by persistent homology priors.
• Figure 4: Qualitative comparison on high-genus surface meshes with Nicolet et al. Nicolet2021Large. Our method, incorporating persistent homology priors, better preserves overall topological structures, particularly in regions with multiple tunnels.
• Figure 5: Qualitative comparisons on high-genus surface meshes with tunnel loops (orange) and handle loops (green), compared to Nicolet et al. Nicolet2021Large.