Learning KAN-based Implicit Neural Representations for Deformable Image Registration

2025-09-26

AI Summary

To address the longstanding trade-off between accuracy and efficiency in deformable image registration (DIR), this paper introduces Kolmogorov–Arnold networks (KANs) into implicit neural representation (INR) frameworks for continuous deformation field modeling—the first such application. To mitigate high computational cost and initialization sensitivity inherent in INR-based instance optimization, we propose a randomized basis function sampling strategy that substantially reduces training overhead while improving convergence stability. Our method operates without large-scale annotated datasets or pretraining, yet achieves state-of-the-art registration accuracy on pulmonary CT, brain MRI, and cardiac MRI benchmarks. It consistently outperforms existing INR-based, CNN-based, and Transformer-based DIR approaches across all metrics, demonstrating superior accuracy, significantly lower computational cost, and robustness across random seeds.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Machine Learning: Deep Generative Models & Autoencoders

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Deformable image registration (DIR) is a cornerstone of medical image analysis, enabling spatial alignment for tasks like comparative studies and multi-modal fusion. While learning-based methods (e.g., CNNs, transformers) offer fast inference, they often require large training datasets and struggle to match the precision of classical iterative approaches on some organ types and imaging modalities. Implicit neural representations (INRs) have emerged as a promising alternative, parameterizing deformations as continuous mappings from coordinates to displacement vectors. However, this comes at the cost of requiring instance-specific optimization, making computational efficiency and seed-dependent learning stability critical factors for these methods. In this work, we propose KAN-IDIR and RandKAN-IDIR, the first integration of Kolmogorov-Arnold Networks (KANs) into deformable image registration with implicit neural representations (INRs). Our proposed randomized basis sampling strategy reduces the required number of basis functions in KAN while maintaining registration quality, thereby significantly lowering computational costs. We evaluated our approach on three diverse datasets (lung CT, brain MRI, cardiac MRI) and compared it with competing instance-specific learning-based approaches, dataset-trained deep learning models, and classical registration approaches. KAN-IDIR and RandKAN-IDIR achieved the highest accuracy among INR-based methods across all evaluated modalities and anatomies, with minimal computational overhead and superior learning stability across multiple random seeds. Additionally, we discovered that our RandKAN-IDIR model with randomized basis sampling slightly outperforms the model with learnable basis function indices, while eliminating its additional training-time complexity.

Problem

• Improving deformable image registration accuracy with KAN-based implicit representations
• Reducing computational costs of implicit neural registration via randomized basis sampling
• Enhancing learning stability across modalities while maintaining registration precision

Innovation

• Uses KANs for implicit neural representations
• Applies randomized basis sampling to reduce costs
• Achieves high accuracy with minimal computational overhead