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

arXiv: https://arxiv.org/abs/2412.18696 · HTML: https://mlsanity.com/paper/2412.18696/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 55 references that are in the map.
- First posted on arXiv 24 Dec 2024.

## Builds on (most cited first, 9 of 9)

- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [A Topology Layer for Machine Learning](https://mlsanity.com/paper/1905.12200/) (2019)
- [DiGS : Divergence guided shape implicit neural representation for unoriented point clouds](https://mlsanity.com/paper/2106.10811/) (2021)
- [Topology-Aware Latent Diffusion for 3D Shape Generation](https://mlsanity.com/paper/2401.17603/) (2024)
- [Geometry-Informed Neural Networks](https://mlsanity.com/paper/2402.14009/) (2024)
- [Differentiability and Optimization of Multiparameter Persistent Homology](https://mlsanity.com/paper/2406.07224/) (2024)
- [Leveraging Continuously Differentiable Activation Functions for Learning in Quantized Noisy Environments](https://mlsanity.com/paper/2402.02593/) (2024)

## Built on by (most cited first, 4 of 4)

- [Learning Significant Persistent Homology Features for 3D Shape Understanding](https://mlsanity.com/paper/2602.14228/) (2026)
- [A Persistent Homology Design Space for 3D Point Cloud Deep Learning](https://mlsanity.com/paper/2604.04299/) (2026)
- [PCM-NeRF: Probabilistic Camera Modeling for Neural Radiance Fields under Pose Uncertainty](https://mlsanity.com/paper/2604.17831/) (2026)
- [SILSA: Sliding-Window Slice Latents for Topology-Preserving High-Resolution 3D Generation](https://mlsanity.com/paper/2610.02201/) (2026)

## Abstract (arXiv)

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.