Efficient Dermoscopic Lesion Segmentation via Multi-Directional State-Space Modeling and Frequency-Aware Boundary Refinement

State-space models segment images in linear time, but existing dermoscopic segmenters serialize the two-dimensional feature map along only one or two scan directions and operate purely in the spatial domain, which dilutes the orientation cues and fine boundary information that distinguish a pigmented lesion from surrounding skin. We address both limitations in a single linear-complexity network, Hydra-DermSeg-Net, that unifies three components not previously combined for this task: a four-directional bidirectional Hydra block that aggregates forward and backward selective scans over horizontal, vertical and two diagonal trajectories with learnable fusion weights; a differentiable discrete cosine transform (DCT) branch that decouples high- and low-frequency content so that boundary detail is processed separately from global semantics; and a learnable local contrast-enhancement front-end coupled with a clDice-supervised boundary attention gate. On a merged ISIC 2017/2018 corpus of 3994 images, the model attains a Dice coefficient of 0.9041 and an Intersection-over-Union (IoU) of 0.8386 against five baselines (U-Net, Att-UNet, VM-UNet, TransUNet and MALUNet) trained from scratch under a unified protocol, and it transfers to an unseen HAM10000 subset at 0.9347 Dice. It attains the highest Dice and IoU on each of the three data partitions examined, the highest Sensitivity, and the lowest 95-percentile Hausdorff distance under every random seed; the margin over the strongest convolutional baselines is about 0.002 in Dice and lies within the variation between training runs. An ablation at the full model capacity isolates the contribution of each component: removing the frequency branch costs 0.86 points of Dice and 0.99 points of Boundary IoU, and removing the boundary attention gate 0.66 and 2.85 points respectively. These results show that combining multi-directional state-space scanning with frequency-domain decoupling yields accurate and parameter-efficient segmentation without the quadratic cost of self-attention.