Generalizing Shape-from-Template to Topological Changes

2025-11-05

AI Summary

Existing Shape-from-Template (SfT) methods assume fixed object topology, rendering them incapable of reconstructing deformations involving topological changes—such as tearing, cutting, or separation. This work introduces the first general-purpose SfT framework supporting arbitrary topological variations. Our method dynamically partitions the template into spatially disjoint, independently deformable regions; jointly optimizes for physical plausibility—via an energy-based functional—and multi-view reprojection consistency; and incorporates an iterative adaptive template update mechanism to refine region correspondences and geometry over time. By explicitly relaxing the topological invariance constraint inherent in classical SfT, our approach enables accurate reconstruction of complex topological events—including tearing, fragmentation, and localized cuts. Extensive evaluation on both synthetic and real-world datasets demonstrates substantial improvements over state-of-the-art baselines, validating the method’s robustness, generalizability, and effectiveness in handling non-rigid deformations with evolving topology.

Technology Category

Computer Vision: Motion & TrackingPlanning, Routing, and Scheduling: Replanning and Plan RepairConstraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphsSystems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processingWeb Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Reconstructing the surfaces of deformable objects from correspondences between a 3D template and a 2D image is well studied under Shape-from-Template (SfT) methods; however, existing approaches break down when topological changes accompany the deformation. We propose a principled extension of SfT that enables reconstruction in the presence of such changes. Our approach is initialized with a classical SfT solution and iteratively adapts the template by partitioning its spatial domain so as to minimize an energy functional that jointly encodes physical plausibility and reprojection consistency. We demonstrate that the method robustly captures a wide range of practically relevant topological events including tears and cuts on bounded 2D surfaces, thereby establishing the first general framework for topological-change-aware SfT. Experiments on both synthetic and real data confirm that our approach consistently outperforms baseline methods.

Problem

• Extending Shape-from-Template to handle topological changes during deformation
• Reconstructing surfaces when tears or cuts occur in 2D observations
• Developing energy minimization framework for topology-aware 3D reconstruction

Innovation

• Extends Shape-from-Template to handle topological changes
• Iteratively adapts template by partitioning spatial domain
• Minimizes energy for physical plausibility and reprojection consistency