用可学习激活函数的神经网络，实现更稳定高效的医学影像配准。
Deformable Medical Image Registration with KAN-based Implicit Neural Representations
- 基于KAN的隐式神经表示，直接建模形变场的连续映射。
- 在肺、脑、心脏MRI数据上精度优于现有方法，且对初始值不敏感。
- 随机基采样降低计算开销，适合临床重复研究使用。
可变形图像配准（DIR）在医学图像分析中至关重要，支持纵向研究和多模态融合中的空间对齐。基于学习的方法如CNN和Transformer推理快速，但通常需要大量训练数据，且在特定解剖结构或模态下表现不如经典迭代方法。隐式神经表示（INRs）通过将形变场建模为坐标到位移的连续映射，提供数据高效替代方案，但其每对图像优化导致运行效率和对初始化的鲁棒性成为关键。本文提出KAN-IDIR与RandKAN-IDIR，首个基于柯尔莫哥洛夫-阿诺德网络（KAN）的INR框架，实现无需数据集训练的成对优化、分辨率无关的DIR，旨在提升种子稳定性与资源效率。KAN采用可学习激活函数，更适合连续且具有物理结构的形变场。RandKAN-IDIR通过随机基函数采样进一步降低开销，在减少基函数数量的同时保持注册质量。我们在肺部CT、脑部MRI和心脏MRI数据集上评估该方法，对比成对INR方法、数据集训练的深度模型及经典基线。KAN-IDIR与RandKAN-IDIR在所有INR方法中达到最高精度，计算开销低，且在不同随机初始化下表现出色。RandKAN-IDIR略优于自适应基选择变体，同时避免了额外的训练复杂度。该方法适用于可复现的临床研究。源代码见https://github.com/anac0der/KAN-IDIR。
原文摘要 · Abstract (English)
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.
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