SRE-FMaps: A Sinkhorn-Regularized Elastic Functional Map Framework for Non-Isometric 3D Shape Matching.

Area of Science:

• Computer Vision
• Computational Geometry
• Geometric Deep Learning

Background:

• Precise 3D shape correspondence is crucial for medical modeling and visual recognition.
• Traditional methods struggle with non-isometric shapes due to limited sensitivity to local deformations.

Purpose of the Study:

• To propose a novel framework, Sinkhorn-Regularized Elastic Functional Maps (SRE-FMaps), for robust non-isometric 3D shape correspondence.
• To enhance sensitivity to local geometric deformations like stretching and bending.

Main Methods:

• Integration of entropy-regularized optimal transport (Sinkhorn algorithm) for efficient initialization.
• Introduction of a non-orthogonal elastic basis derived from thin-shell energy for improved feature perception.
• Quantification of correspondence stability using a cosine-based elastic distance metric.

Main Results:

• SRE-FMaps reduced correspondence error by up to 32% and achieved 92.3% average classification accuracy.
• Demonstrated superior robustness in handling bending, stretching, and folding deformations compared to LB-based methods.
• Achieved high recall (up to 91.67%) and F1-score (0.94) on benchmark datasets.

Conclusions:

• The SRE-FMaps framework offers a scalable and effective solution for non-isometric 3D shape correspondence.
• It significantly improves accuracy and robustness for applications in medical modeling, 3D reconstruction, and visual recognition.