用拓扑先验提升多视角图像重建高亏格三维网格的准确性
Inverse Rendering for High-Genus 3D Surface Meshes from Multi-view Images with Persistent Homology Priors
- 引入持久同调先验约束，指导高亏格表面重建
- 相比现有方法，切比雪夫距离更低，体积交并比更高
- 无需神经网络，适合需要可解释性的几何重建场景
从图像重建3D物体本质上是病态问题，因几何、外观和拓扑存在歧义。本文提出基于持久同调先验的协同逆渲染方法，利用拓扑约束解决这些歧义。通过引入捕捉隧道环和把手环等关键特征的先验，直接应对高亏格表面重建难题。多视角图像的光度一致性与同调引导协同作用，恢复复杂高亏格几何结构，避免塌陷隧道或丢失高亏格结构等灾难性失败。本方法不依赖神经网络，采用基于网格的逆渲染框架中的梯度优化，凸显拓扑先验的作用。实验表明，引入持久同调先验后，切比雪夫距离（CD）更低，体积交并比（Volume IoU）更高，相较于最先进网格方法，显著提升几何精度与拓扑鲁棒性。
原文摘要 · Abstract (English)
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.
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