Preconditioned Deformation Grids

2025-09-22

AI Summary

Dynamic surface reconstruction faces challenges including low accuracy, poor generalization, and temporal inconsistency; existing approaches rely heavily on numerous regularization terms or large-scale annotated data. This paper proposes a correspondence-free deformation field estimation framework: it constructs a multi-resolution voxel grid as a differentiable deformation template and introduces a grid-based Sobolev preconditioning mechanism to enhance gradient optimization stability. Training is driven solely by Chamfer distance and a weak isometric edge loss, eliminating explicit geometric constraints and extensive supervision. The method significantly improves deformation modeling accuracy and temporal coherence. Evaluated on multiple long-sequence point cloud datasets, it outperforms state-of-the-art methods—particularly excelling in generalizing to unseen objects and robustly reconstructing complex, articulated motions.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: Motion & Tracking
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Dynamic surface reconstruction of objects from point cloud sequences is a challenging field in computer graphics. Existing approaches either require multiple regularization terms or extensive training data which, however, lead to compromises in reconstruction accuracy as well as over-smoothing or poor generalization to unseen objects and motions. To address these lim- itations, we introduce Preconditioned Deformation Grids, a novel technique for estimating coherent deformation fields directly from unstructured point cloud sequences without requiring or forming explicit correspondences. Key to our approach is the use of multi-resolution voxel grids that capture the overall motion at varying spatial scales, enabling a more flexible deformation representation. In conjunction with incorporating grid-based Sobolev preconditioning into gradient-based optimization, we show that applying a Chamfer loss between the input point clouds as well as to an evolving template mesh is sufficient to obtain accurate deformations. To ensure temporal consistency along the object surface, we include a weak isometry loss on mesh edges which complements the main objective without constraining deformation fidelity. Extensive evaluations demonstrate that our method achieves superior results, particularly for long sequences, compared to state-of-the-art techniques.

Problem

• Reconstructs dynamic surfaces from point cloud sequences
• Eliminates need for regularization terms or training data
• Ensures temporal consistency without deformation constraints

Innovation

• Multi-resolution voxel grids capture motion at varying scales
• Grid-based Sobolev preconditioning enables gradient-based optimization
• Weak isometry loss ensures temporal consistency on surface edges