Ordinal Semantic Segmentation Applied to Medical and Odontological Images

In many prediction problems in medical applications, target labels exhibit an inherent ordinal structure, where class ordering reflects clinically meaningful severity levels. The cost associated with misclassification is often non-uniform and asymmetric, as errors between distant ordinal categories may have substantially more severe consequences than errors between adjacent ones, and overestimating disease severity may have different clinical implications than underestimating it. Traditional loss functions such as multi-class cross-entropy treat all misclassifications equally and fail to incorporate this ordering information. Recent advances in ordinal regression aim to address this limitation by integrating rank-based structures into deep learning models. In this work, we introduce the Ordinal Cross-Entropy (OCE) framework, a general and architecture-independent approach for learning from ordinal data. The proposed method extends the standard cross-entropy formulation to account for misclassification severity through an ordinal cost matrix while preserving the probabilistic interpretation and optimization benefits of the conventional loss. We provide a theoretical analysis of the OCE gradient behavior and show that it yields smoother optimization dynamics and improved ordinal consistency. Experiments on benchmark datasets show that our method achieves lower prediction error costs and better calibration compared to existing state-of-the-art ordinal approaches, establishing OCE as a simple yet effective solution for ordinal regression in deep neural networks.

Ordinal regression is widely used in scenarios where labels are discrete yet inherently ordered. In practice, however, ordinal labels are often obtained by discretizing underlying continuous semantics through subjective human judgment, resulting in ambiguous boundaries and annotation noise. Such uncertainty challenges existing methods that rely on fixed supervision targets, which may reinforce biased ordering under subjective annotations. To address this limitation, we propose D3O, a dynamic distribution distillation framework that replaces static supervision with training-driven evolution of ordinal label distributions via self-distillation. Specifically, we introduce a contrastive ordinal-aware label enhancement module that leverages vision-language alignment to recover refined label distributions capturing both inter-class ambiguity and instance-level uncertainty. Furthermore, we design a CDF-based cross-layer interaction distillation mechanism to propagate cumulative ordinal structure across network hierarchy, ensuring consistent ordinal geometry in intermediate representations. Extensive experiments on four general ordinal regression tasks demonstrate that our proposed D3O consistently outperforms existing approaches, particularly under severe class imbalance and noisy supervision. These results highlight the effectiveness of dynamic supervision in learning robust ordinal representations beyond fixed targets. The code will be publicly available.

Medical image segmentation is a fundamental task for medical image processing and computer-assisted intervention, yet data imbalance and small lesion detection pose significant challenges. Dice Loss, which measures the overlap between predicted and ground truth regions, is widely used to mitigate these issues. To further emphasize its properties, we propose Polynomial Dice Loss, a polynomial extension of Dice Loss. Specifically, by leveraging the geometric characteristics of Dice Loss and formulating the loss function as a polynomial representation via Taylor expansion, we enable the adjustment of the contribution of higher-order components to the loss function. In our experiments, we evaluate the proposed method against loss functions derived from conventional Dice and Tversky coefficients. Experimental results and further analysis show that the polynomial formulation provides a simple way to control the loss shape and achieves competitive performance across multiple segmentation settings.