Abstract: Vessel segmentation is critical to image processing of fundus images,which is precursor and essential first step to further analysis and diagnosis of diseases.However,this remains a challenge due to the noise and intensity variation in the background of fundus images.In this study,we propose a novel vessel segmentation approach using Hessian-based linear filter and entropic thresholding method to automatically segment vessels on fundus images.Firstly we adapt multi-scale linear filtering based on Hessian matrix to enhance vessels.Further,we generate a novel two-dimensional histogram to capture gray level and directional average gray level of linear neighborhood in results from filtering,and then the threshold values are determined by the maximum class entropies according to this histogram.Finally,the binary segmentation results for the vessels are achieved.The experiments demonstrate that,compared with two other methods,the proposed method can automatically yield more complete and accurate results.