Dynamic Neural Surfaces for Elastic 4D Shape Representation and Analysis

2025-03-05

AI Summary

Spatiotemporal registration and statistical modeling of zero-genus 4D surfaces—i.e., time-varying 3D surfaces—are challenged by arbitrary parameterizations and non-uniform deformation velocities. Method: We propose Dynamic Spherical Neural Surfaces (D-SNS), a continuous spatiotemporal functional representation that unifies parameterization alignment, geodesic computation, and Riemannian mean estimation directly in the continuous domain. D-SNS integrates implicit neural representations, spherical parameterization, Riemannian manifold optimization, and functional-statistical shape analysis—bypassing reliance on discrete meshes. Results: Evaluated on 4D human and facial datasets, D-SNS achieves significantly improved registration accuracy and computational efficiency, while enhancing fidelity, generalizability, and cross-sequence transferability of deformation modeling.

Technology Category

• Machine Learning: Learning with Manifolds
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Computer Vision: 3D Computer Vision

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

We propose a novel framework for the statistical analysis of genus-zero 4D surfaces, i.e., 3D surfaces that deform and evolve over time. This problem is particularly challenging due to the arbitrary parameterizations of these surfaces and their varying deformation speeds, necessitating effective spatiotemporal registration. Traditionally, 4D surfaces are discretized, in space and time, before computing their spatiotemporal registrations, geodesics, and statistics. However, this approach may result in suboptimal solutions and, as we demonstrate in this paper, is not necessary. In contrast, we treat 4D surfaces as continuous functions in both space and time. We introduce Dynamic Spherical Neural Surfaces (D-SNS), an efficient smooth and continuous spatiotemporal representation for genus-0 4D surfaces. We then demonstrate how to perform core 4D shape analysis tasks such as spatiotemporal registration, geodesics computation, and mean 4D shape estimation, directly on these continuous representations without upfront discretization and meshing. By integrating neural representations with classical Riemannian geometry and statistical shape analysis techniques, we provide the building blocks for enabling full functional shape analysis. We demonstrate the efficiency of the framework on 4D human and face datasets. The source code and additional results are available at https://4d-dsns.github.io/DSNS/.

Problem

• Analyzing genus-zero 4D surfaces with varying deformation speeds.
• Developing continuous spatiotemporal representations for 4D shape analysis.
• Enabling functional shape analysis without upfront discretization and meshing.

Innovation

• Continuous spatiotemporal representation for 4D surfaces
• Dynamic Spherical Neural Surfaces (D-SNS) framework
• Direct 4D shape analysis without upfront discretization