Lesion segmentation in breast ultrasound involves two related challenges. In images with lesions, speckle noise, low tissue contrast, and posterior acoustic shadowing cause boundary leakage and incomplete contour delineation. In images without lesions, those same artifacts generate false-positive activations in regions resembling solid lesion tissue. This study addresses both failure modes through a single modification to the training objective. Rather than weighting every boundary pixel equally, the proposed loss scales contour penalties by per-pixel predictive entropy and the ground-truth boundary map, concentrating gradient emphasis on lesion margin locations where the network remains uncertain. The loss was evaluated on the BUSI dataset through a controlled ablation against two baselines: a model without boundary supervision and a model with uniformly weighted boundary binary cross-entropy. Across 97 lesion-containing test images, mean Dice scores were statistically indistinguishable between the proposed method and the no-boundary baseline (0.7624 versus 0.7616, paired Wilcoxon p = 0.27), confirming that lesion segmentation quality is preserved. The primary effect appears in specificity. False-positive activations on 20 no-lesion test images fell from 14 of 20 and 19 of 20 for the two baselines to 5 of 20 with the proposed approach (McNemar p = 0.012 and 0.0005). Non-overlapping Wilson 95% confidence intervals confirm the difference is both statistically significant and practically substantial. A post-hoc spatial temperature scaling step further reduced expected calibration error from 0.0201 to 0.0095 without altering segmentation masks. Entropy-guided boundary supervision and spatial calibration thus function as complementary training-level and inference-level refinements that improve specificity and probability reliability within a U-Net framework.

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