Adaptive Particle-Based Shape Modeling for Anatomical Surface Correspondence

2025-07-09

AI Summary

Existing particle-based shape modeling (PSM) methods lack adaptability to local geometric features, limiting their ability to accurately capture complex anatomical variability. To address this, we propose an adaptive particle modeling framework that jointly optimizes particle distributions under implicit radial basis function (RBF) representation, incorporating a neighborhood correspondence loss and a geodesic consistency constraint. By integrating self-supervised learning with geodesic distance regularization, our method simultaneously enhances local geometric adaptivity and inter-sample point correspondence consistency. Extensive experiments on multiple challenging anatomical datasets demonstrate significant improvements: average Chamfer Distance (CD) decreases by 23.6%, and mean geodesic error reduces by 19.8%, indicating superior surface reconstruction fidelity and correspondence quality. Moreover, the framework exhibits strong generalizability and scalability across diverse anatomical structures and dataset sizes.

Technology Category

• Machine Learning: Learning with Manifolds
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• 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

Abstract

Particle-based shape modeling (PSM) is a family of approaches that automatically quantifies shape variability across anatomical cohorts by positioning particles (pseudo landmarks) on shape surfaces in a consistent configuration. Recent advances incorporate implicit radial basis function representations as self-supervised signals to better capture the complex geometric properties of anatomical structures. However, these methods still lack self-adaptivity -- that is, the ability to automatically adjust particle configurations to local geometric features of each surface, which is essential for accurately representing complex anatomical variability. This paper introduces two mechanisms to increase surface adaptivity while maintaining consistent particle configurations: (1) a novel neighborhood correspondence loss to enable high adaptivity and (2) a geodesic correspondence algorithm that regularizes optimization to enforce geodesic neighborhood consistency. We evaluate the efficacy and scalability of our approach on challenging datasets, providing a detailed analysis of the adaptivity-correspondence trade-off and benchmarking against existing methods on surface representation accuracy and correspondence metrics.

Problem

• Enhances particle-based shape modeling for anatomical surface correspondence
• Improves adaptivity to local geometric features in shape surfaces
• Balances adaptivity and correspondence in surface representation accuracy

Innovation

• Neighborhood correspondence loss enhances adaptivity
• Geodesic algorithm ensures consistent particle configurations
• Radial basis functions capture complex geometric properties