Background and Objective: In the realm of ophthalmic imaging, accurate vascular segmentation is paramount for diagnosing and managing various eye diseases. Contemporary deep learning-based vascular segmentation models rival human accuracy but still face substantial challenges in accurately segmenting minuscule blood vessels in neural network applications. Due to the necessity of multiple downsampling operations in the CNN models, fine details from high-resolution images are inevitably lost. The objective of this study is to design a structure to capture the delicate and small blood vessels. Methods: To address these issues, we propose a novel network (KaLDeX) for vascular segmentation leveraging a Kalman filter based linear deformable cross attention (LDCA) module, integrated within a UNet++ framework. Our approach is based on two key components: Kalman filter (KF) based linear deformable convolution (LD) and cross-attention (CA) modules. The LD module is designed to adaptively adjust the focus on thin vessels that might be overlooked in standard convolution. The CA module improves the global understanding of vascular structures by aggregating the detailed features from the LD module with the high level features from the UNet++ architecture. Finally, we adopt a topological loss function based on persistent homology to constrain the topological continuity of the segmentation. Results: The proposed method is evaluated on retinal fundus image datasets (DRIVE, CHASE_BD1, and STARE) as well as the 3mm and 6mm of the OCTA-500 dataset, achieving an average accuracy (ACC) of 97.25%, 97.77%, 97.85%, 98.89%, and 98.21%, respectively. Conclusions: Empirical evidence shows that our method outperforms the current best models on different vessel segmentation datasets. Our source code is available at: https://github.com/AIEyeSystem/KalDeX.

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