Hyperparameter-Free Boundary-Interior t-vMF Dice Loss for Medical Image Segmentation

Hinako Mitsuoka; Kazuhiro Hotta

cs.CVOct 23, 2026

Hyperparameter-Free Boundary-Interior t-vMF Dice Loss for Medical Image Segmentation

Authors: Hinako Mitsuoka, Kazuhiro Hotta

Organizations: Meijo University, 1-501 Shiogamaguchi, Tempaku-ku, Nagoya, 468-8502, Japan

Abstract

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.

Figures & tables

Figure 1: Self-tuning mechanism and performance of STB-tvMF Dice Loss. (a) Boundary and interior shape parameters are updated using mean cosine similarities from the previous training epoch, without hyperparameter search. (b) DSC across three datasets and three architectures. Blue dots show Adaptive t-vMF Dice Loss with $\lambda\in\{2,32,128,256,1024\}$ ; dotted lines connect these settings, not uncertainty intervals. Labels indicate the best $\lambda$ selected retrospectively by test DSC. Red stars denote our method.


	U-Net [ 10 ]			TransUNet [ 3 ]			EMCAD [ 9 ]
Loss	Kvasir	ACDC	Synapse	Kvasir	ACDC	Synapse	Kvasir	ACDC	Synapse
Cross-entropy	89.68	90.07	48.37	92.55	86.89	45.89	93.46	88.04	62.50
Dice [ 8 ]	88.98	89.67	65.02	92.65	89.58	68.19	93.50	90.04	71.10
Tversky [ 12 ]	89.28	89.86	57.52	92.40	90.31	52.41	93.65	90.04	67.97
Focal Tversky [ 1 ]	88.33	89.18	56.93	92.32	89.76	59.21	93.10	89.86	69.08

Table 1: DSC (%) on three datasets using three architectures. The best result in each column is shown in bold.

Figure 2: Qualitative results on three datasets using U-Net. From left to right, show Input image, Ground truth, Cross-entropy Loss, Adaptive t-vMF Dice Loss [ 6 ] , and STB-tvMF Dice Loss (Ours). For Adaptive t-vMF Dice Loss, we show predictions using the $\lambda$ with the highest DSC for each dataset.


Granularity	Kvasir	ACDC	Synapse
Global ( $1$ )	91.21	91.54	52.41
Class-wise ( $C$ )	91.54	91.80	47.38
Boundary-interior ( $2$ )	91.91	91.92	70.75

Table 2: Effect of adaptation granularity with epoch-wise updates. DSC (%) using U-Net is shown. Global and class-wise variants use whole-image losses, whereas our method separates boundary and interior regions.


Update strategy	Kvasir	ACDC	Synapse
Batch-wise	91.47	92.29	70.67
EMA ( $m=0.9$ )	91.87	91.53	69.91
EMA ( $m=0.99$ )	91.63	92.06	70.66
Epoch-wise (Ours)	91.91	91.92	70.75

Table 3: Effect of the shape-parameter update strategy in the boundary-interior formulation. DSC (%) using U-Net is shown. The coefficient

m

denotes EMA momentum.


Kernel size	Kvasir	ACDC	Synapse
$3\times 3$ (default)	91.91	91.92	70.75
$5\times 5$	92.09	91.47	70.29
$7\times 7$	91.81	91.45	68.69

Table 4: Effect of the boundary extraction kernel size. Values are DSC (%) using U-Net.

Medical Image Segmentation

Medical image segmentation delineates organs, lesions, and other structures in scans to support measurement, diagnosis, treatment planning, and research.

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Abstract

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