Ordinal Semantic Segmentation Applied to Medical and Odontological Images

Mariana Dória Prata Lima; Gilson Antonio Giraldi; Jaime S. Cardoso

cs.CVMar 21, 2026

Ordinal Semantic Segmentation Applied to Medical and Odontological Images

Authors: Mariana Dória Prata Lima, Gilson Antonio Giraldi, Jaime S. Cardoso

Organizations: 1, 2National Laboratory for Scientific Computing, Petrópolis, Rio de Janeiro, Brazil. · 3INESC TEC, Faculty of Engineering, University of Porto, Porto, Portugal.

Abstract

Semantic segmentation consists of assigning a semantic label to each pixel according to predefined classes. This process facilitates the understanding of object appearance and spatial relationships, playing an important role in the global interpretation of image content. Although modern deep learning approaches achieve high accuracy, they often ignore ordinal relationships among classes, which may encode important domain knowledge for scene interpretation. In this work, loss functions that incorporate ordinal relationships into deep neural networks are investigated to promote greater semantic consistency in semantic segmentation tasks. These loss functions are categorized as unimodal, quasi-unimodal, and spatial. Unimodal losses constrain the predicted probability distribution according to the class ordering, while quasi-unimodal losses relax this constraint by allowing small variations while preserving ordinal coherence. Spatial losses penalize semantic inconsistencies between neighboring pixels, encouraging smoother transitions in the image space. In particular, this study adapts loss functions originally proposed for ordinal classification to ordinal semantic segmentation. Among them, the Expanded Mean Squared Error (EXP_MSE), the Quasi-Unimodal Loss (QUL), and the spatial Contact Surface Loss using Signal Distance Function (CSSDF) are investigated. These approaches have shown promising results in medical imaging, improving robustness, generalization, and anatomical consistency.

Figures & tables

Figure 1: Sample images and their corresponding ordinal masks from each dataset. The datasets are organized as follows: (a) Breast Cervix-MobileODT; (b) Mobbio; (c)Teeth-UCV; (d) Teeth-ISBI; and (e) Breast Aesthetics.

Dataset	CE	CE + QUL	CE + EXP_MSE	CE + CSSDF
Breast Aesthetics	$0.2\pm 0.2$	$0.1\pm 0.0$	$0.1\pm 0.0$	$0.1\pm 0.1$
Cervix-MobileODT	$14.5\pm 3.3$	$1.2\pm 0.5$	$1.0\pm 0.6$	$13.2\pm 1.5$
Mobbio	$12.3\pm 0.5$	$3.8\pm 0.1$	$3.8\pm 0.5$	$12.1\pm 0.3$
Teeth-ISBI	$30.0\pm 3.9$	$26.2\pm 2.5$	$26.8\pm 2.1$	$27.2\pm 1.5$
Teeth-UCV	$7.0\pm 1.4$	$3.1\pm 0.6$	$5.9\pm 0.9$	$5.6\pm 0.8$

Table 1: Overall results of the contact surface metric (%), a structural metric that evaluates consistency between adjacent pixels. Lower values indicate better performance.

Dataset	CE	CE + QUL	CE + EXP_MSE	CE + CSSDF
Breast Aesthetics	$6.2\pm 0.7$	$7.3\pm 0.6$	$6.5\pm 2.0$	$7.0\pm 1.2$
Cervix-MobileODT	$1.0\pm 0.2$	$1.0\pm 0.2$	$1.6\pm 0.3$	$0.8\pm 0.2$
Mobbio	$0.8\pm 0.1$	$0.9\pm 0.2$	$0.9\pm 0.3$	$0.7\pm 0.3$
Teeth-ISBI	$9.6\pm 3.4$	$12.3\pm 4.2$	$12.1\pm 3.8$	$13.7\pm 3.5$
Teeth-UCV	$18.0\pm 1.8$	$25.5\pm 7.2$	$25.8\pm 6.9$	$20.1\pm 5.0$

Table 2: Overall results for the unimodal pixels metric (%), a representation metric that evaluates ordinal consistency at the pixel level. Higher values indicate better performance.

Dataset	CE	CE + QUL	CE + EXP_MSE	CE + CSSDF
Breast Aesthetics	$93.8\pm 0.5$	$94.4\pm 0.4$	$94.4\pm 0.2$	$93.7\pm 0.8$
Cervix-MobileODT	$77.0\pm 0.7$	$77.2\pm 0.2$	$77.3\pm 0.2$	$76.8\pm 0.3$
Mobbio	$93.8\pm 0.1$	$93.8\pm 0.5$	$94.0\pm 0.1$	$93.8\pm 0.1$
Teeth-ISBI	$74.0\pm 1.6$	$75.6\pm 0.3$	$74.6\pm 0.2$	$75.3\pm 1.5$
Teeth-UCV	$90.2\pm 0.5$	$90.8\pm 0.4$	$90.2\pm 0.4$	$90.1\pm 0.1$

Table 3: Overall results for the Dice coefficient metric (%). Higher values indicate better performance.

Dataset	CE	CE + O2	CE + QUL	CE + EXP_MSE
Breast Aesthetics	$0.2\pm 0.2$	$0.2\pm 0.2$	$0.1\pm 0.0$	$0.1\pm 0.0$
Cervix-MobileODT	$14.5\pm 3.3$	$1.1\pm 0.4$	$1.2\pm 0.5$	$1.0\pm 0.6$
Mobbio	$12.3\pm 0.5$	$4.2\pm 0.2$	$3.8\pm 0.1$	$3.8\pm 0.5$
Teeth-ISBI	$30.0\pm 3.9$	$26.1\pm 2.4$	$26.2\pm 2.5$	$26.8\pm 2.1$
Teeth-UCV	$7.0\pm 1.4$	$3.0\pm 0.7$	$3.1\pm 0.6$	$5.9\pm 0.9$

Table 4: Comparison of the unimodal loss functions proposed in this work with the CE+O2 (Section 2.1.3 ) loss presented in Cruz et al. (2025) , using the contact surface metric (

\%

). Again, lower values indicate better performance.

Dataset	CE	CE + O2	CE + QUL	CE + EXP_MSE
Breast Aesthetics	$6.2\pm 0.7$	$8.1\pm 2.6$	$7.3\pm 0.6$	$6.5\pm 2.0$
Cervix-MobileODT	$1.0\pm 0.2$	$98.9\pm 0.4$	$1.0\pm 0.2$	$1.6\pm 0.3$
Mobbio	$0.8\pm 0.1$	$97.3\pm 2.6$	$0.9\pm 0.2$	$0.9\pm 0.3$
Teeth-ISBI	$9.6\pm 3.4$	$97.1\pm 3.8$	$12.3\pm 4.2$	$12.1\pm 3.8$
Teeth-UCV	$18.0\pm 1.8$	$96.8\pm 1.0$	$25.5\pm 7.2$	$25.8\pm 6.9$

Table 5: Comparison of the unimodal loss functions investigated in this work with the CE+02 (Section 2.1.3 ) loss presented in Cruz et al. (2025) , using the percentage of unimodal pixels metric (

\%

). Again, higher values indicate better performance.

Dataset	CE	CE + O2	CE + QUL	CE + EXP_MSE
Breast Aesthetics	$93.8\pm 0.5$	$94.2\pm 0.6$	$94.4\pm 0.4$	$94.4\pm 0.2$
Cervix-MobileODT	$77.0\pm 0.7$	$77.2\pm 0.4$	$77.2\pm 0.2$	$77.3\pm 0.2$
Mobbio	$93.8\pm 0.1$	$94.1\pm 0.0$	$93.8\pm 0.5$	$94.0\pm 0.1$
Teeth-ISBI	$74.0\pm 1.6$	$74.8\pm 0.4$	$75.6\pm 0.3$	$74.6\pm 0.2$
Teeth-UCV	$90.2\pm 0.5$	$90.8\pm 0.4$	$90.8\pm 0.4$	$90.2\pm 0.4$

Table 6: Comparison of the unimodal loss functions investigated in this work with the CE+02 (Section 2.1.3 ) loss presented in Cruz et al. (2025) , using the Dice coefficient metric (

\%

). Again, higher values indicate better performance.

Dataset	CE	CE + CSNP	CE + CSDT	CE + CSSDF
Breast Aesthetics	$0.2\pm 0.2$	$0.1\pm 0.1$	$0.2\pm 0.2$	$0.1\pm 0.1$
Cervix-MobileODT	$14.5\pm 3.3$	$10.8\pm 2.7$	$13.6\pm 1.7$	$13.2\pm 1.5$
Mobbio	$12.3\pm 0.5$	$12.3\pm 0.4$	$12.4\pm 0.6$	$12.1\pm 0.3$
Teeth-ISBI	$30.0\pm 3.9$	$28.4\pm 1.4$	$27.1\pm 1.8$	$27.2\pm 1.5$
Teeth-UCV	$7.0\pm 1.4$	$2.3\pm 1.0$	$5.5\pm 1.0$	$5.6\pm 0.8$

Table 7: Comparison of the structured loss functions investigated in this work with the CE+CSNP (Section 2.2.2 ) and CE+CSDT (Section 2.1.5 ) losses presented in Cruz et al. (2025) , using the contact surface metric (%). Again, lower values indicate better performance.

Dataset	CE	CE + CSNP	CE + CSDT	CE + CSSDF
Breast Aesthetics	$93.8\pm 0.5$	$94.0\pm 0.5$	$94.0\pm 0.4$	$93.7\pm 0.8$
Cervix-MobileODT	$77.0\pm 0.7$	$77.4\pm 0.2$	$76.9\pm 0.7$	$76.8\pm 0.3$
Mobbio	$93.8\pm 0.1$	$93.8\pm 0.0$	$93.7\pm 0.2$	$93.8\pm 0.1$
Teeth-ISBI	$74.0\pm 1.6$	$74.9\pm 1.4$	$75.3\pm 1.3$	$75.3\pm 1.5$
Teeth-UCV	$90.2\pm 0.5$	$90.5\pm 0.3$	$90.3\pm 0.3$	$90.1\pm 0.1$

Table 8: Comparison of the structured loss functions investigated in this work with the CE+CSNP (Section 2.2.2 ) and CE+CSDT (Section 2.1.5 ) losses presented in Cruz et al. (2025) , using the Dice coefficient metric (%). Again, higher values indicate better performance.

Dataset	CE	CE + CSNP	CE + CSDT	CE + CSSDF
Breast Aesthetics	$6.2\pm 0.7$	$5.9\pm 2.1$	$6.2\pm 1.5$	$7.0\pm 1.2$
Cervix-MobileODT	$1.0\pm 0.2$	$0.5\pm 0.2$	$0.9\pm 0.3$	$0.8\pm 0.2$
Mobbio	$0.8\pm 0.1$	$0.9\pm 0.2$	$0.7\pm 0.2$	$0.7\pm 0.3$
Teeth-ISBI	$9.6\pm 3.4$	$11.2\pm 4.6$	$13.5\pm 3.4$	$13.7\pm 3.5$
Teeth-UCV	$18.0\pm 1.8$	$25.7\pm 6.8$	$19.7\pm 4.1$	$20.1\pm 5.0$

Table 9: Comparison of the structured loss functions investigated in this work with the CE+CSNP (Section 2.2.2 ) and CE+CSDT (Section 2.1.5 ) losses presented in Cruz et al. (2025) , using the unimodal pixels metric (%). Again, higher values indicate better performance.

Semantic Segmentation

Semantic segmentation assigns a class label to every image pixel, enabling detailed scene understanding across domains and sensors.

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Bar-Ilan University Ramat Gan, Israel

Cost-Sensitive Learning Ordinal Regression

Open paper AskPDF arXiv

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.

Abstract

Semantic Segmentation

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