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

Abstract

AbstractPurpose: Accurate registration between daily Cone-Beam CT (CBCT) and the planning CT (pCT) is critical for precision in modern Image-Guided Radiotherapy (IGRT). However, existing registration methods are challenged by the extensive computational time of conventional iterative algorithms and the heavy reliance of deep learning approaches on large-scale training data. Methods: To address these limitations, we propose a novel, pretraining-free image registration framework. It constructs a patient-specific, lightweight neural network for each image pair based on Implicit Neural Representation (INR). We introduce Kolmogorov-Arnold Network (KAN) to medical image registration for the first time, modeling the complex organ deformation as a continuous velocity field. Compared to conventional multilayer perceptron (MLP), KAN more accurately capture non-linear anatomical changes. To improve computational efficiency, the KAN predicts the low-dimensional principal components of the velocity field rather than the full field. The complete, smooth velocity field is subsequently reconstructed via inverse Principal Component Analysis and integrated over time to yield the final deformation. Results: On 19 pelvic CT–CBCT pairs, the proposed framework consistently improved registration accuracy over traditional iterative (Demons, Elastix) and MLP-based INR baselines. The average Dice Similarity Coefficient (DSC) increased by >6% compared with iterative methods and by ~3% over MLP-based INR. For deformable organs, median DSC improved from 0.74 to 0.83 (bladder) and from 0.64 to 0.79 (rectum) (p < 0.001). The average 95th percentile Hausdorff Distance (HD95) decreased from 7.01 mm to 5.09 mm, indicating improved boundary alignment. With inverse PCA-based velocity compression, optimization time was reduced by ~70% relative to direct velocity modeling. Regarding deformation field quality, Jacobian analysis showed globally 99.34% voxels within the moderate deformation range, confirming smooth and topology-preserving transformations. Conclusion: Our findings demonstrate that the proposed patient-specific, pretraining-free INR framework improves CT–CBCT deformable registration accuracy and efficiency by leveraging KAN-based deformation modeling and low-dimensional velocity representation. This approach enables faster optimization while preserving smooth, topology-consistent deformations, supporting its potential for time-constrained IGRT applications.