Class imbalance and errors near anatomical boundaries remain challenges in medical image segmentation, motivating loss functions that account for these difficulties. Adaptive t-vMF Dice Loss adjusts the similarity function during training but requires hyperparameter tuning. We propose Self-Tuned Boundary-Aware t-vMF Dice Loss (STB-tvMF Dice), which adapts the function separately for boundary and interior regions without tuning shape-adaptation parameters. Each region's shape parameter of t-vMF function is determined from its mean prediction-target cosine similarity in the preceding epoch and remains fixed throughout the current epoch. This rule maximizes the slope of the similarity function at the observed mean similarity, providing a principled basis for adaptation without validation-based parameter selection. Experiments on three datasets and architectures demonstrated its effectiveness. On Synapse with U-Net, STB-tvMF Dice achieved a mean DSC of 70.75%, compared with 63.03% for Adaptive t-vMF Dice Loss. Our code will be available soon.

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