GenSP: Consistent Spherical Parameterization via Learning Shape Generative Models

2026-07-01

AI Summary

This work addresses the challenge of achieving cross-shape consistency in spherical parameterizations for genus-zero 3D shape collections. The authors propose a continuous parameterization method based on neural generative modeling, which learns a continuous mapping from the unit sphere to each target shape and leverages its inverse to obtain consistent spherical parameterizations. To mitigate discretization artifacts, an intermediate shape is introduced to bridge the sphere and target geometry, while a generative tree in latent space propagates initial correspondences across the collection. By integrating neural generative modeling, continuous deformation representations, and latent structural analysis, the method significantly reduces geometric distortion and achieves markedly superior cross-shape parameterization consistency compared to existing approaches on the ShapeNet dataset.

Abstract

We introduce GenSP, a data-driven framework that learns consistent spherical parameterizations across a collection of genus-0 shapes. Instead of optimizing the parameterization of each shape independently, our method learns a neural generative model that predicts a continuous mapping from the unit sphere to shapes in a dataset. Under this formulation, spherical parameterizations are obtained through the inverse mappings of the learned generator, which encourages similar shapes to share consistent parameterizations. To make this formulation practical, we address several key challenges in learning such a generative model. First, we introduce a continuous neural deformation model that predicts surface points from sphere coordinates and latent shape codes, avoiding discretization artifacts common in mesh-based formulations. Second, we augment the training space with intermediate shapes that bridge the sphere and input shapes, allowing the model to learn meaningful deformations across a heterogeneous shape collection. Third, we compute reliable initial correspondences by propagating mappings along a spanning tree of training shapes in the latent space. Experiments on the ShapeNet dataset demonstrate that our approach significantly reduces geometric distortion and improves cross-shape consistency compared with state-of-the-art spherical parameterization methods.

Problem

• spherical parameterization
• shape consistency
• genus-0 shapes
• cross-shape correspondence
• 3D shape analysis

Innovation

• spherical parameterization
• generative model
• neural deformation
• shape correspondence
• genus-0 shapes