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

2024-12-24

AI Summary

This work addresses implicit surface reconstruction from sparse, unstructured point clouds. We propose a topology-aware reconstruction framework that integrates differentiable persistent homology into neural implicit representations. Methodologically, we introduce a topology-driven loss function and a differentiable topological regularizer—constituting the first explicit, differentiable incorporation of topological priors (e.g., single-connectedness) into implicit reconstruction pipelines. We theoretically prove that stochastic subgradient optimization converges to a singly connected shape solution. Our key contribution lies in enabling end-to-end differentiable enforcement of topological constraints, overcoming the limited topological modeling capacity of conventional methods. Experiments demonstrate significant improvements over state-of-the-art baselines in both visual quality and quantitative metrics (e.g., Chamfer distance, F-Score), with stable generation of singly connected 2-manifold surfaces and a >60% reduction in topological error rate.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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.

Problem

• 3D Reconstruction
• Sparse Point Clouds
• Surface Preservation

Innovation

• STITCH
• Persistent Homology
• Randomized Gradient Descent