# Learning Ordinality in Semantic Segmentation

arXiv: https://arxiv.org/abs/2407.20959 · HTML: https://mlsanity.com/paper/2407.20959/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 40 references that are in the map.
- First posted on arXiv 30 Jul 2024.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [Pyramid Scene Parsing Network](https://mlsanity.com/paper/1612.01105/) (2016)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [SegNet: A Deep Convolutional Encoder-Decoder Architecture for Image Segmentation](https://mlsanity.com/paper/1511.00561/) (2015)
- [BDD100K: A Diverse Driving Dataset for Heterogeneous Multitask Learning](https://mlsanity.com/paper/1805.04687/) (2018)
- [Deep Ordinal Regression Network for Monocular Depth Estimation](https://mlsanity.com/paper/1806.02446/) (2018)
- [Deep Hierarchical Semantic Segmentation](https://mlsanity.com/paper/2203.14335/) (2022)
- [Unimodal probability distributions for deep ordinal classification](https://mlsanity.com/paper/1705.05278/) (2017)
- [Unimodal Distributions for Ordinal Regression](https://mlsanity.com/paper/2303.04547/) (2023)
- [The Distance Transform and its Computation](https://mlsanity.com/paper/2106.03503/) (2021)

## Built on by (most cited first, 1 of 1)

- [Ordinal Semantic Segmentation Applied to Medical and Odontological Images](https://mlsanity.com/paper/2603.26736/) (2026)

## Abstract (arXiv)

Semantic segmentation consists of predicting a semantic label for each image pixel. While existing deep learning approaches achieve high accuracy, they often overlook the ordinal relationships between classes, which can provide critical domain knowledge (e.g., the pupil lies within the iris, and lane markings are part of the road). This paper introduces novel methods for spatial ordinal segmentation that explicitly incorporate these inter-class dependencies. By treating each pixel as part of a structured image space rather than as an independent observation, we propose two regularization terms and a new metric to enforce ordinal consistency between neighboring pixels. Two loss regularization terms and one metric are proposed for structural ordinal segmentation, which penalizes predictions of non-ordinal adjacent classes. Five biomedical datasets and multiple configurations of autonomous driving datasets demonstrate the efficacy of the proposed methods. Our approach achieves improvements in ordinal metrics and enhances generalization, with up to a 15.7% relative increase in the Dice coefficient. Importantly, these benefits come without additional inference time costs. This work highlights the significance of spatial ordinal relationships in semantic segmentation and provides a foundation for further exploration in structured image representations.