An Implicit Registration Framework Integrating Kolmogorov-Arnold Networks with Velocity Regularization for Image-Guided Radiation Therapy.

In image-guided radiation therapy (IGRT), deformable image registration between computed tomography (CT) and cone beam computed tomography (CBCT) images remain challenging due to the computational cost of iterative algorithms and the data dependence of supervised deep learning methods. Implicit neural representation (INR) provides a promising alternative, but conventional multilayer perceptron (MLP) might struggle to efficiently represent complex, nonlinear deformations. This study introduces a novel INR-based registration framework that models the deformation as a continuous, time-varying velocity field, parameterized by a Kolmogorov-Arnold Network (KAN) constructed using Jacobi polynomials. To our knowledge, this is the first integration of KAN into medical image registration, establishing a new paradigm beyond standard MLP-based INR. For improved efficiency, the KAN estimates low-dimensional principal components of the velocity field, which are reconstructed via inverse principal component analysis and temporally integrated to derive the final deformation. This approach achieves a ~70% improvement in computational efficiency relative to direct velocity field modeling while ensuring smooth and topology-preserving transformations through velocity regularization. Evaluation on a publicly available pelvic CT-CBCT dataset demonstrates up to 6% improvement in registration accuracy over traditional iterative methods and ~3% over MLP-based INR baselines, indicating the potential of the proposed method as an efficient and generalizable alternative for deformable registration.