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

CVPR 2025

Takehi Noda1*, Chao Chen1*, Junsheng Zhou1, Weiqi Zhang1, Yu-Shen Liu1, Zhizhong Han2
1School of Software, Tsinghua University, Beijing, China, 2Department of Computer Science, Wayne State University, Detroit, USA
Paper Code

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.

Method

Overview of Our method. Given a sparse point cloud \( Q \), we first learn a mapping function \( \Phi \) to encode \( Q \) into a unit sphere parametric domain. We consider each point as center point and sample local patches on the parametric surface. Next, we learn the inverse mapping \( \Psi \) to predict the positions of these local patches in 3D space and integrate them to obtain \( S \). We leverage \( S \) as the supervision for the grid deformation network \( g \) and predict the signed distance field through the GDO optimization strategy. We further extract dense point cloud \( \bar{V} \) from the implicit field and optimize the parameterized surface \( S \).

Visualization Results

Comparison on ShapeNet Dataset

Comparison on D-FAUST Dataset

Comparison on SRB Dataset

Comparison on 3DScene Dataset

Comparison on KITTI Dataset

BibTeX

@inproceedings{noda2025learning,
      title={Learning bijective surface parameterization for inferring signed distance functions from sparse point clouds with grid deformation},
      author={Noda, Takeshi and Chen, Chao and Zhou, Junsheng and Zhang, Weiqi and Liu, Yu-Shen and Han, Zhizhong},
      booktitle={Proceedings of the Computer Vision and Pattern Recognition Conference},
      pages={22139--22149},
      year={2025}}