Implicit Neural Surface Deformation with Explicit Velocity Fields

2025-01-23

AI Summary

This paper addresses the problem of unsupervised reconstruction of time-varying 3D implicit surfaces—enabling joint recovery of temporally evolving shapes and surface point clouds for both rigid and non-rigid objects—without requiring intermediate shape annotations or prior deformation models. The proposed method introduces a novel neural implicit framework wherein continuous surface evolution is explicitly governed by a learned velocity field, integrated with a modified level-set equation that enforces the Eikonal constraint to preserve signed distance function (SDF) geometric integrity. Additionally, a volume-preserving smoothness regularizer ensures physically plausible intermediate deformations. By unifying deformation dynamics and geometric evolution within a single differentiable neural representation, the approach achieves end-to-end optimization. Experiments demonstrate significant improvements over state-of-the-art supervised and unsupervised methods in reconstruction accuracy, computational efficiency, and generalization across diverse motion patterns.

Technology Category

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

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
• Web Mining and Content Analysis: Models for Web evolution

Abstract

In this work, we introduce the first unsupervised method that simultaneously predicts time-varying neural implicit surfaces and deformations between pairs of point clouds. We propose to model the point movement using an explicit velocity field and directly deform a time-varying implicit field using the modified level-set equation. This equation utilizes an iso-surface evolution with Eikonal constraints in a compact formulation, ensuring the integrity of the signed distance field. By applying a smooth, volume-preserving constraint to the velocity field, our method successfully recovers physically plausible intermediate shapes. Our method is able to handle both rigid and non-rigid deformations without any intermediate shape supervision. Our experimental results demonstrate that our method significantly outperforms existing works, delivering superior results in both quality and efficiency.

Problem

• Shape Measurement
• Point Cloud Analysis
• Time-Varying Objects

Innovation

• Time-Varying Shape Inference
• Velocity Field Utilization
• Smoothness and Volume Preservation