# On the Relaxation of Conditional Independence Assumption for Image Segmentation

arXiv: https://arxiv.org/abs/2609.38930 · HTML: https://mlsanity.com/paper/2609.38930/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 32 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 19 of 19)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [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)
- [Semantic Image Segmentation with Deep Convolutional Nets and Fully Connected CRFs](https://mlsanity.com/paper/1412.7062/) (2014)
- [The Liver Tumor Segmentation Benchmark (LiTS)](https://mlsanity.com/paper/1901.04056/) (2019)
- [DeepGlobe 2018: A Challenge to Parse the Earth through Satellite Images](https://mlsanity.com/paper/1805.06561/) (2018)
- [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)
- [Confidence Calibration and Predictive Uncertainty Estimation for Deep Medical Image Segmentation](https://mlsanity.com/paper/1911.13273/) (2019)
- [EditGAN: High-Precision Semantic Image Editing](https://mlsanity.com/paper/2111.03186/) (2021)
- [Optimization for Medical Image Segmentation: Theory and Practice when evaluating with Dice Score or Jaccard Index](https://mlsanity.com/paper/2010.13499/) (2020)
- [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)
- [RankSEG-RMA: An Efficient Segmentation Algorithm via Reciprocal Moment Approximation](https://mlsanity.com/paper/2510.15362/) (2025)

## Abstract (arXiv)

In semantic segmentation, a recent line of RankSEG methods directly optimizes Dice/IoU scores at inference time, improving alignment with evaluation metrics without modifying model training. Despite its theoretical and empirical success, RankSEG relies on the restrictive Conditional Independence Assumption (CIA), which ignores crucial label correlations and therefore degrades performance in ambiguous or low-contrast scenarios. However, accounting for full label dependence is computationally prohibitive, requiring O(d3) time. To address this, we replace the CIA with a Spatially Localized Dependence (SLD) structure that captures local label correlations while keeping the dependence model tractable. We further overcome the remaining computational bottleneck via a Reciprocal Moment Approximation coupled with a novel fixed-point optimization strategy that eliminates exhaustive search. The proposed algorithm achieves a highly practical O(d log d) complexity and consistently outperforms conventional argmax and CIA-based RankSEG across diverse segmentation benchmarks. Improvements are significant in low-contrast or small-object scenarios, where label dependence offers valuable signals complementary to image information for accurate segmentation. The code of experiments is available at https://github.com/ZixunWang/RankSEG-DEP.