The detection of retinal blood vessels, especially the changes of small vessel condition is the most important indicator to identify the vascular network of the human body. Existing techniques focused mainly on shape of the large vessels, which is not appropriate for the disconnected small and isolated vessels. Paying attention to the low contrast small blood vessel in fundus region, first time we proposed to combine graph based smoothing regularizer with the loss function in the U-net

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... . The proposed regularizer treated the image as two graphs by calculating the graph laplacians on vessel regions and the background regions on the image. The potential of the proposed graph based smoothing regularizer in reconstructing small vessel is compared over the classical U-net with or without regularizer. Numerical and visual results shows that our developed regularizer proved its effectiveness in segmenting the small vessels and reconnecting the fragmented retinal blood vessels.