STITCH: Surface reconstrucTion using Implicit neural representations with Topology Constraints and persistent Homology
This work addresses the challenge of maintaining correct topology in neural implicit surface reconstruction, which is crucial for applications in computer graphics and 3D modeling, representing an incremental advance by integrating topological data analysis tools.
The paper tackles the problem of reconstructing surfaces from sparse, irregular point clouds while ensuring a single connected component, using a novel differentiable persistent homology framework to enforce topological constraints, achieving excellent performance in preserving topology for complex 3D geometries.
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.