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