Abstract

Medical image segmentation plays a vital role in diagnosis and treatment planning, but remains challenging due to the inherent complexity, variability, and diversity of medical imaging modalities, particularly in capturing non-linear relationships and long-range dependencies within the data. To address these issues, this thesis first proposes U-KABS, a novel hybrid framework that integrates the expressive power of Kolmogorov-Arnold Networks (KANs) with a U-shaped encoder-decoder architecture to enhance segmentation performance. The U-KABS model combines a convolutional and squeeze-and-excitation stage that enhances channel-wise feature representations, and a KAN Bernstein Spline (KABS) stage that employs learnable activation functions based on Bernstein polynomials for global smoothness and B-splines for local adaptability. This hybrid design effectively captures both broad contextual trends and fine-grained patterns critical for delineating complex structures, supported by skip connections for multi-scale feature fusion and spatial detail preservation. Building upon these foundations, the thesis also introduces AdaKAN, an adaptive U-shaped model architecture that integrates an efficient attention mechanism with an adaptive KAN (AdaptKAN) block. The AdaKAN model consists of a convolutional stage and efficient KAN (EffiKAN) stage. The latter is comprised of an efficient attention for global feature extraction across resolutions and a dual-branch AdaptKAN block, with the right branch using a KAN layer with Bernstein polynomials for stable, smooth approximations, and the left branch incorporating up- and down-projections with adaptive scaling for channel-wise refinement. This encoder-decoder design captures higher-order dependencies essential for complex segmentations, with skip connections ensuring detail restoration during decoding. Evaluated across diverse benchmark datasets, including multi-class and multi-modal scenarios, both U-KABS and AdaKAN consistently outperform strong baselines, demonstrating improved accuracy, robustness to blurry boundaries, and efficiency in segmenting complex anatomical structures.