An Implicit Registration Framework Integrating Kolmogorov-Arnold Networks with Velocity Regularization for...

Area of Science:

• Medical Imaging
• Computational Anatomy
• Radiotherapy Physics

Background:

• Deformable image registration is crucial for image-guided radiation therapy (IGRT) but faces challenges with computational cost and data dependency.
• Current methods like iterative algorithms and supervised deep learning have limitations.
• Implicit Neural Representations (INRs) offer potential, but Multilayer Perceptrons (MLPs) may struggle with complex deformations.

Purpose of the Study:

• To develop a novel INR-based framework for deformable image registration using Kolmogorov-Arnold Networks (KANs).
• To model deformations as a continuous, time-varying velocity field parameterized by KANs.
• To establish a new paradigm for medical image registration beyond MLP-based INRs.

Main Methods:

• A novel INR-based registration framework utilizing KANs constructed with Jacobi polynomials to parameterize velocity fields.
• Efficient estimation of low-dimensional principal components of the velocity field by KAN.
• Reconstruction of the velocity field via inverse principal component analysis and temporal integration for deformation derivation.
• Velocity regularization to ensure smooth and topology-preserving transformations.

Main Results:

• The KAN-based approach achieved approximately 70% improvement in computational efficiency compared to direct velocity field modeling.
• Demonstrated up to 6% improvement in registration accuracy over traditional iterative methods.
• ~3% improvement in registration accuracy over MLP-based INR baselines on a pelvic CT-CBCT dataset.

Conclusions:

• The proposed KAN-based INR framework offers an efficient and generalizable alternative for deformable image registration in IGRT.
• This integration of KANs represents a novel approach in medical image registration.
• The method ensures smooth and topology-preserving transformations, enhancing registration accuracy and efficiency.