Learning Bijective Surface Parameterization for Inferring Signed Distance Functions from Sparse Point Clouds with Grid Deformation

2025-03-31

AI Summary

To address the challenge of learning signed distance functions (SDFs) from sparse point clouds—where insufficient geometric detail impairs surface reconstruction—this paper proposes an end-to-end dynamic deformation framework. The method jointly optimizes an explicit parametric surface and an implicit SDF field through three core components: (1) a bijective surface parameterization (BSP) that establishes invertible mappings between local surface patches and the global shape; (2) a grid-based deformation optimization (GDO) strategy that co-refines both the parameterized surface and the implicit field; and (3) a synergistic learning mechanism integrating bijective neural mappings, local patch embeddings, and differentiable rendering. Evaluated on both synthetic and real-world scanned datasets, the approach achieves significant improvements in SDF reconstruction accuracy and topological consistency over state-of-the-art methods.

Technology Category

• Machine Learning: Learning with Manifolds
• Search and Optimization: Learning to Search
• Computer Vision: 3D Computer Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Inferring signed distance functions (SDFs) from sparse point clouds remains a challenge in surface reconstruction. The key lies in the lack of detailed geometric information in sparse point clouds, which is essential for learning a continuous field. To resolve this issue, we present a novel approach that learns a dynamic deformation network to predict SDFs in an end-to-end manner. To parameterize a continuous surface from sparse points, we propose a bijective surface parameterization (BSP) that learns the global shape from local patches. Specifically, we construct a bijective mapping for sparse points from the parametric domain to 3D local patches, integrating patches into the global surface. Meanwhile, we introduce grid deformation optimization (GDO) into the surface approximation to optimize the deformation of grid points and further refine the parametric surfaces. Experimental results on synthetic and real scanned datasets demonstrate that our method significantly outperforms the current state-of-the-art methods. Project page: https://takeshie.github.io/Bijective-SDF

Problem

• Inferring signed distance functions from sparse point clouds
• Learning global shape from local patches via bijective parameterization
• Optimizing grid deformation for refined surface approximation

Innovation

• Dynamic deformation network predicts SDFs end-to-end
• Bijective surface parameterization integrates local patches globally
• Grid deformation optimization refines parametric surfaces