In this paper, we reformulate the conventional 2-D Frangi vesselness measure into a pre-weighted neural network ("Frangi-Net"), and illustrate that the Frangi-Net is equivalent to the original Frangi filter. Furthermore, we show that, as a neural network, Frangi-Net is trainable. We evaluate the proposed method on a set of 45 high resolution fundus images. After fine-tuning, we observe both qualitative and quantitative improvements in the segmentation quality compared to the original Frangi measure, with an increase up to $17\%$ in F1 score.