Abstract
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.
Abstract (translated)
我们介绍了STITCH,这是一种新颖的方法,用于从稀疏且不规则间隔的点云中重建神经隐式曲面,并强制执行拓扑约束(例如保持单一连通分量)。我们开发了一个基于持久同调的新可微框架来制定拓扑损失项,以确保单个2-流形对象的前提条件。我们的方法在复杂3D几何形状的拓扑结构保存方面表现出色,通过视觉和实证比较可以明显看出这一点。我们还进行了理论分析,并证明了使用随机(子)梯度下降优化损失会导致收敛并能够重建具有单一连通分量的形状。我们的方法展示了隐式曲面重建中可微拓扑数据分析工具集成的应用。
URL
https://arxiv.org/abs/2412.18696