STITCH: Surface reconstrucTion using Implicit neural representations with Topology Constraints and persistent Homology
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929667374579712 |
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| author | Jignasu, Anushrut Herron, Ethan Jiang, Zhanhong Sarkar, Soumik Hegde, Chinmay Ganapathysubramanian, Baskar Balu, Aditya Krishnamurthy, Adarsh |
| author_facet | Jignasu, Anushrut Herron, Ethan Jiang, Zhanhong Sarkar, Soumik Hegde, Chinmay Ganapathysubramanian, Baskar Balu, Aditya Krishnamurthy, Adarsh |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18696 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | STITCH: Surface reconstrucTion using Implicit neural representations with Topology Constraints and persistent Homology Jignasu, Anushrut Herron, Ethan Jiang, Zhanhong Sarkar, Soumik Hegde, Chinmay Ganapathysubramanian, Baskar Balu, Aditya Krishnamurthy, Adarsh Computer Vision and Pattern Recognition Graphics Machine Learning 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. |
| title | STITCH: Surface reconstrucTion using Implicit neural representations with Topology Constraints and persistent Homology |
| topic | Computer Vision and Pattern Recognition Graphics Machine Learning |
| url | https://arxiv.org/abs/2412.18696 |