STITCH: Surface reconstrucTion using Implicit neural representations with Topology Constraints and persistent Homology

• URL: http://arxiv.org/abs/2412.18696v2
• Date: Thu, 09 Jan 2025 03:39:37 GMT
• Title: STITCH: Surface reconstrucTion using Implicit neural representations with Topology Constraints and persistent Homology
• Authors: Anushrut Jignasu, Ethan Herron, Zhanhong Jiang, Soumik Sarkar, Chinmay Hegde, Baskar Ganapathysubramanian, Aditya Balu, Adarsh Krishnamurthy,
• Abstract summary: We present STITCH, a novel approach for neural implicit surface reconstruction of a sparse and irregularly spaced point cloud. 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.
• Score: 23.70495314317551
• License:
• 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.

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