Soft Self-labeling and Potts Relaxations for Weakly-Supervised Segmentation

Zhong-fei Zhang, Yuri Boykov
2/10/2026

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Abstract

We consider weakly supervised segmentation where only a fraction of pixels have ground truth labels (scribbles) and focus on a self-labeling approach optimizing relaxations of the standard unsupervised CRF/Potts loss on unlabeled pixels. While WSSS methods can directly optimize such losses via gradient descent, prior work suggests that higher-order optimization can improve network training by introducing hidden pseudo-labels and powerful CRF sub-problem solvers, e.g. graph cut. However, previously used hard pseudo-labels can not represent class uncertainty or errors, which motivates soft self-labeling. We derive a principled auxiliary loss and systematically evaluate standard and new CRF relaxations (convex and non-convex), neighborhood systems, and terms connecting network predictions with soft pseudo-labels. We also propose a general continuous sub-problem solver. Using only standard architectures, soft self-labeling consistently improves scribble-based training and outperforms significantly more complex specialized WSSS systems. It can outperform full pixel-precise supervision. Our general ideas apply to other weakly-supervised problems/systems.

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@article{zhang2026soft,
  title  = {Soft Self-labeling and Potts Relaxations for Weakly-Supervised Segmentation},
  author = {Zhong-fei Zhang and Yuri Boykov},
  year   = {2026},
  eprint = {2507.01721},
  archivePrefix = {arXiv},
  url    = {https://arxiv.org/abs/2507.01721},
  journal = {CVPR 2025 2025}
}

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