# Deformable Medical Image Registration with KAN-based Implicit Neural Representations

arXiv: https://arxiv.org/abs/2509.22874 · HTML: https://mlsanity.com/paper/2509.22874/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 62 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Builds on (most cited first, 26 of 26)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces](https://mlsanity.com/paper/1903.03545/) (2019)
- [Large Deformation Diffeomorphic Image Registration with Laplacian Pyramid Networks](https://mlsanity.com/paper/2006.16148/) (2020)
- [Beyond Periodicity: Towards a Unifying Framework for Activations in Coordinate-MLPs](https://mlsanity.com/paper/2111.15135/) (2021)
- [Kolmogorov-Arnold Networks are Radial Basis Function Networks](https://mlsanity.com/paper/2405.06721/) (2024)
- [Learn2Reg: comprehensive multi-task medical image registration challenge, dataset and evaluation in the era of deep learning](https://mlsanity.com/paper/2112.04489/) (2021)
- [Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation](https://mlsanity.com/paper/2405.07200/) (2024)
- [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024)
- [Fast Symmetric Diffeomorphic Image Registration with Convolutional Neural Networks](https://mlsanity.com/paper/2003.09514/) (2020)
- [A survey of sparse representation: algorithms and applications](https://mlsanity.com/paper/1602.07017/) (2016)
- [uniGradICON: A Foundation Model for Medical Image Registration](https://mlsanity.com/paper/2403.05780/) (2024)
- [textttGradICON: Approximate Diffeomorphisms via Gradient Inverse Consistency](https://mlsanity.com/paper/2206.05897/) (2022)
- [Correlation-aware Coarse-to-fine MLPs for Deformable Medical Image Registration](https://mlsanity.com/paper/2406.00123/) (2024)
- [Learning Activation Functions: A new paradigm for understanding Neural Networks](https://mlsanity.com/paper/1906.09529/) (2019)
- [Learning the Effect of Registration Hyperparameters with HyperMorph](https://mlsanity.com/paper/2203.16680/) (2022)
- [NODEO: A Neural Ordinary Differential Equation Based Optimization Framework for Deformable Image Registration](https://mlsanity.com/paper/2108.03443/) (2021)
- [ICON: Learning Regular Maps Through Inverse Consistency](https://mlsanity.com/paper/2105.04459/) (2021)
- [Deep Learning in Medical Image Registration: Magic or Mirage?](https://mlsanity.com/paper/2408.05839/) (2024)
- [Robust deformable image registration using cycle-consistent implicit representations](https://mlsanity.com/paper/2310.01934/) (2023)
- [Neural Tangent Kernel Analysis to Probe Convergence in Physics-informed Neural Solvers: PIKANs vs. PINNs](https://mlsanity.com/paper/2506.07958/) (2025)
- [Implicit Neural Representations with Fourier Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2409.09323/) (2024)
- [Predicting the Encoding Error of SIRENs](https://mlsanity.com/paper/2410.21645/) (2024)

## Abstract (arXiv)

Deformable image registration (DIR) is central to medical image analysis, supporting spatial alignment for longitudinal studies and multi-modal fusion. Learning-based methods such as CNNs and transformers provide rapid inference but often require large training datasets and can underperform classical iterative methods for specific anatomies or modalities. Implicit neural representations (INRs) offer a data-efficient alternative by modeling deformation fields as continuous coordinate-to-displacement mappings, yet their per-pair optimization makes runtime efficiency and robustness to initialization essential. We introduce KAN-IDIR and RandKAN-IDIR, the first Kolmogorov--Arnold network (KAN)-based INR framework for pairwise-optimized, resolution-independent DIR, designed to improve seed stability and resource efficiency without dataset-level training. KANs use learnable activation functions that are well suited to continuous, physically structured deformation fields. RandKAN-IDIR further reduces cost through randomized basis sampling, preserving registration quality with fewer basis functions. We evaluate the methods on lung CT, brain MRI, and cardiac MRI datasets against pairwise INR approaches, dataset-trained deep models, and classical baselines. KAN-IDIR and RandKAN-IDIR achieve the highest accuracy among INR-based methods, with low computational overhead and superior stability across random initializations. RandKAN-IDIR slightly outperforms adaptive basis selection variants while avoiding their additional training-time complexity. This makes the approach practical for reproducible clinical research use. Source code is available at https://github.com/anac0der/KAN-IDIR.