Liver vessels generated from computed tomography are usually pretty small, which poses big challenges for satisfactory vessel segmentation, including 1) the scarcity of high-quality and large-volume vessel masks, 2) the difficulty in capturing vessel-specific features, and 3) the heavily imbalanced distribution of vessels and liver tissues. To advance, a sophisticated model and an elaborated dataset have been built. The model has a newly conceived Laplacian salience filter, highlighting vessel-like regions and suppressing other liver regions, to shape the vessel-specific feature learning and to balance vessels against others. It is further coupled with a pyramid deep learning architecture to capture various levels of features, hence the enhancement of feature formulation. Experiments show that this model markedly outperforms the state-of-the-art approaches, achieving a relative improvement of Dice score by at least 1.63% compared to the existing best model on available datasets. More promisingly, the averaged Dice score produced by existing models on the newly con- structed dataset is as high as 0.728 ± 0.067, which is at least 19.1% higher than that obtained from the existing best dataset under the same settings. These observations suggest that the proposed Laplacian salience, along with the elaborated dataset, can be helpful for liver vessel seg- mentation.