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Retinal vessel segmentation methods based on standard overlap losses tend to miss thin peripheral vessels because these structures occupy very few pixels and have low contrast against the background. We propose HMS-VesselNet, a hierarchical multi-scale network that processes fundus images across four parallel branches at different resolutions and combines their outputs using learned fusion weights. The training loss combines Dice, binary cross-entropy, and centerline Dice to jointly optimize area overlap and vessel continuity. Hard example mining is applied from epoch 20 onward to concentrate gradient updates on the most difficult training images. Tested on 68 images from DRIVE, STARE, and CHASE_DB1 using 5-fold cross-validation, the model achieves a mean Dice of 88.72 +/- 0.67%, Sensitivity of 90.78 +/- 1.42%, and AUC of 98.25 +/- 0.21%. In leave-one-dataset-out experiments, AUC remains above 95% on each unseen dataset. The largest improvement is in the recall of thin peripheral vessels, which are the structures most frequently missed by standard methods and most critical for early detection of diabetic retinopathy.