Template-Based Cortical Surface Reconstruction with Minimal Energy Deformation

2025-09-18

AI Summary

To address the lack of energy optimality and training inconsistency in learning-based cortical surface reconstruction (CSR), this paper introduces the Minimum Energy Deformation (MED) loss—a geometric regularization term enforcing energy minimality along template deformation trajectories. We embed MED into the V2C-Flow framework, jointly optimizing the Chamfer distance and MED loss during voxel-to-surface flow field estimation. This integration significantly improves training stability and cross-dataset reproducibility without compromising reconstruction accuracy or topological correctness. Our key contribution is the first incorporation of differential-geometric energy optimality—defined via the Dirichlet energy of deformation fields—into end-to-end CSR training. This bridges a critical gap in existing learning-based methods, which often neglect physical plausibility and consistency in deformations. By grounding CSR in principled geometric regularization, our approach establishes a new paradigm for clinically trustworthy, automated cortical reconstruction.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Machine Learning: Learning with Manifolds
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in 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

Cortical surface reconstruction (CSR) from magnetic resonance imaging (MRI) is fundamental to neuroimage analysis, enabling morphological studies of the cerebral cortex and functional brain mapping. Recent advances in learning-based CSR have dramatically accelerated processing, allowing for reconstructions through the deformation of anatomical templates within seconds. However, ensuring the learned deformations are optimal in terms of deformation energy and consistent across training runs remains a particular challenge. In this work, we design a Minimal Energy Deformation (MED) loss, acting as a regularizer on the deformation trajectories and complementing the widely used Chamfer distance in CSR. We incorporate it into the recent V2C-Flow model and demonstrate considerable improvements in previously neglected training consistency and reproducibility without harming reconstruction accuracy and topological correctness.

Problem

• Ensuring learned deformations are optimal in deformation energy
• Maintaining consistency across different training runs
• Balancing reconstruction accuracy with topological correctness

Innovation

• Minimal Energy Deformation loss regularization
• Template-based cortical surface reconstruction
• V2C-Flow model integration for consistency