Higher-Order Graph Principles towards Non-Rigid Surface Registration.

Area of Science:

• Computer Vision
• Geometric Modeling
• Computational Geometry

Background:

• Surface registration is crucial for 3D data analysis, enabling shape comparison and analysis.
• Existing methods often struggle with non-rigid, large deformations, and partial data.

Purpose of the Study:

• To develop robust and efficient surface registration techniques.
• To address challenges posed by arbitrary diffeomorphic deformations and partial surface matching.

Main Methods:

• Formulating surface registration as an energy minimization problem with geometric and appearance costs.
• Proposing two higher-order graph-based formulations: one using conformal geometry for isometric deformations, and another employing a novel diffeomorphic deformation model for dense registration.
• Utilizing dual-decomposition for sparse matching and a parallel, memory-efficient algorithm for dense registration, with candidate selection to manage search space.

Main Results:

• The conformal geometry approach robustly matches sparse points under highly isometric deformations.
• The novel diffeomorphic model significantly improves dense surface registration accuracy for arbitrary deformations.
• The framework demonstrates high accuracy and efficiency, particularly in challenging cases with large, anisometric deformations or partial occlusions.

Conclusions:

• The proposed higher-order graph-based framework offers a powerful solution for surface registration.
• The novel deformation model and efficient inference algorithm advance the state-of-the-art in dense, non-rigid surface registration.
• The methods are effective for real-world applications involving complex 3D shape analysis.