# RankSEG-RMA: An Efficient Segmentation Algorithm via Reciprocal Moment Approximation

arXiv: https://arxiv.org/abs/2510.15362 · HTML: https://mlsanity.com/paper/2510.15362/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 44 references that are in the map.
- First posted on arXiv 17 Oct 2025.

## Builds on (most cited first, 26 of 26)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [SegFormer: Simple and Efficient Design for Semantic Segmentation with Transformers](https://mlsanity.com/paper/2105.15203/) (2021)
- [Pyramid Scene Parsing Network](https://mlsanity.com/paper/1612.01105/) (2016)
- [Rethinking Atrous Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1706.05587/) (2017)
- [Unified Perceptual Parsing for Scene Understanding](https://mlsanity.com/paper/1807.10221/) (2018)
- [Panoptic Segmentation](https://mlsanity.com/paper/1801.00868/) (2018)
- [Generalised Dice overlap as a deep learning loss function for highly unbalanced segmentations](https://mlsanity.com/paper/1707.03237/) (2017)
- [The Liver Tumor Segmentation Benchmark (LiTS)](https://mlsanity.com/paper/1901.04056/) (2019)
- [LAVT: Language-Aware Vision Transformer for Referring Image Segmentation](https://mlsanity.com/paper/2112.02244/) (2021)
- [Deep Multi-modal Object Detection and Semantic Segmentation for Autonomous Driving: Datasets, Methods, and Challenges](https://mlsanity.com/paper/1902.07830/) (2019)
- [GRES: Generalized Referring Expression Segmentation](https://mlsanity.com/paper/2306.00968/) (2023)
- [Cross-Entropy Loss Functions: Theoretical Analysis and Applications](https://mlsanity.com/paper/2304.07288/) (2023)
- [The state of the art in kidney and kidney tumor segmentation in contrast-enhanced CT imaging: Results of the KiTS19 Challenge](https://mlsanity.com/paper/1912.01054/) (2019)
- [The KiTS19 Challenge Data: 300 Kidney Tumor Cases with Clinical Context, CT Semantic Segmentations, and Surgical Outcomes](https://mlsanity.com/paper/1904.00445/) (2019)
- [Optimization for Medical Image Segmentation: Theory and Practice when evaluating with Dice Score or Jaccard Index](https://mlsanity.com/paper/2010.13499/) (2020)
- [Efficient Medical Image Segmentation Based on Knowledge Distillation](https://mlsanity.com/paper/2108.09987/) (2021)
- [The Lov'asz Hinge: A Novel Convex Surrogate for Submodular Losses](https://mlsanity.com/paper/1512.07797/) (2015)
- [Revisiting Evaluation Metrics for Semantic Segmentation: Optimization and Evaluation of Fine-grained Intersection over Union](https://mlsanity.com/paper/2310.19252/) (2023)
- [The Structured Abstain Problem and the Lov'asz Hinge](https://mlsanity.com/paper/2203.08645/) (2022)
- [RankSEG: A Consistent Ranking-based Framework for Segmentation](https://mlsanity.com/paper/2206.13086/) (2022)
- [Dice Semimetric Losses: Optimizing the Dice Score with Soft Labels](https://mlsanity.com/paper/2303.16296/) (2023)

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

- [On the Relaxation of Conditional Independence Assumption for Image Segmentation](https://mlsanity.com/paper/2609.38930/) (2026)

## Abstract (arXiv)

Semantic segmentation labels each pixel in an image with its corresponding class, and is typically evaluated using the Intersection over Union (IoU) and Dice metrics to quantify the overlap between predicted and ground-truth segmentation masks. In the literature, most existing methods estimate pixel-wise class probabilities, then apply argmax or thresholding to obtain the final prediction. These methods have been shown to generally lead to inconsistent or suboptimal results, as they do not directly maximize segmentation metrics. To address this issue, a novel consistent segmentation framework, RankSEG, has been proposed, which includes RankDice and RankIoU specifically designed to optimize the Dice and IoU metrics, respectively. Although RankSEG almost guarantees improved performance, it suffers from two major drawbacks. First, it is its computational expense-RankDice has a complexity of O(d log d) with a substantial constant factor (where d represents the number of pixels), while RankIoU exhibits even higher complexity O(d^2), thus limiting its practical application. For instance, in LiTS, prediction with RankSEG takes 16.33 seconds compared to just 0.01 seconds with the argmax rule. Second, RankSEG is only applicable to overlapping segmentation settings, where multiple classes can occupy the same pixel, which contrasts with standard benchmarks that typically assume non-overlapping segmentation. In this paper, we overcome these two drawbacks via a reciprocal moment approximation (RMA) of RankSEG with the following contributions: (i) we improve RankSEG using RMA, namely RankSEG-RMA, reduces the complexity of both algorithms to O(d) while maintaining comparable performance; (ii) inspired by RMA, we develop a pixel-wise score function that allows efficient implementation for non-overlapping segmentation settings.