用拓扑约束提升稀疏点云的隐式表面重建质量
STITCH: Surface reconstrucTion using Implicit neural representations with Topology Constraints and persistent Homology
- 基于可微分持久同调设计拓扑损失，强制单连通结构
- 在复杂几何体上保持拓扑正确性，视觉与实证均优于对比方法
- 适合需要精确拓扑结构的3D重建任务，如工业建模
我们提出STITCH，一种针对稀疏且不规则分布点云的神经隐式表面重建新方法，同时施加拓扑约束（如单连通分量）。我们构建了一种基于持久同调的可微分框架，定义拓扑损失项以强制实现单2-流形对象的先验。该方法在保留复杂三维几何拓扑结构方面表现优异，通过视觉和实证对比均得到验证。我们还提供了理论分析，严格证明使用随机（子）梯度下降优化该损失函数可收敛，并能重建具有单连通分量的形状。本方法展示了可微分拓扑数据分析工具在隐式表面重建中的集成应用。
原文摘要 · Abstract (English)
We present STITCH, a novel approach for neural implicit surface reconstruction of a sparse and irregularly spaced point cloud while enforcing topological constraints (such as having a single connected component). We develop a new differentiable framework based on persistent homology to formulate topological loss terms that enforce the prior of a single 2-manifold object. Our method demonstrates excellent performance in preserving the topology of complex 3D geometries, evident through both visual and empirical comparisons. We supplement this with a theoretical analysis, and provably show that optimizing the loss with stochastic (sub)gradient descent leads to convergence and enables reconstructing shapes with a single connected component. Our approach showcases the integration of differentiable topological data analysis tools for implicit surface reconstruction.
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