NeuVAS: Neural Implicit Surfaces for Variational Shape Modeling

2025-06-16

AI Summary

This paper addresses the challenge of modeling neural implicit signed distance fields (SDFs) under sparse geometric controls—such as unstructured 3D curve sketches or connected curve networks—where conventional zero-level-set fitting suffers from data sparsity and topological variability. We propose a variational optimization framework that jointly minimizes data fidelity and a novel curvature-driven smoothness functional, with the SDF’s zero-isosurface as the primary optimization target. Crucially, we introduce the first mechanism enabling exact embedding of G⁰-sharp feature curves into unstructured sketches. Our method achieves both topological flexibility and high geometric fidelity: it produces smoother surfaces, enforces constraints more strictly, and demonstrates strong robustness to incomplete sketches and arbitrary topological changes—outperforming state-of-the-art approaches across diverse sparse control scenarios.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Learning with Manifolds
• Computer Vision: 3D Computer Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Neural implicit shape representation has drawn significant attention in recent years due to its smoothness, differentiability, and topological flexibility. However, directly modeling the shape of a neural implicit surface, especially as the zero-level set of a neural signed distance function (SDF), with sparse geometric control is still a challenging task. Sparse input shape control typically includes 3D curve networks or, more generally, 3D curve sketches, which are unstructured and cannot be connected to form a curve network, and therefore more difficult to deal with. While 3D curve networks or curve sketches provide intuitive shape control, their sparsity and varied topology pose challenges in generating high-quality surfaces to meet such curve constraints. In this paper, we propose NeuVAS, a variational approach to shape modeling using neural implicit surfaces constrained under sparse input shape control, including unstructured 3D curve sketches as well as connected 3D curve networks. Specifically, we introduce a smoothness term based on a functional of surface curvatures to minimize shape variation of the zero-level set surface of a neural SDF. We also develop a new technique to faithfully model G0 sharp feature curves as specified in the input curve sketches. Comprehensive comparisons with the state-of-the-art methods demonstrate the significant advantages of our method.

Problem

• Modeling neural implicit surfaces with sparse geometric control
• Handling unstructured 3D curve sketches and networks
• Generating high-quality surfaces from sparse curve constraints

Innovation

• Neural implicit surfaces for shape modeling
• Smoothness term minimizes surface variation
• Faithfully models G0 sharp feature curves