[Submitted on 22 Jul 2026]
Title:A Unified Variational Framework for Deep Weakly Supervised Image Segmentation
View a PDF of the paper titled A Unified Variational Framework for Deep Weakly Supervised Image Segmentation, by Yin King Chu and 4 other authors
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Abstract:We propose a unified variational framework for image segmentation under sparse pixel-level supervision. Our method is based on a simplex-constrained Potts model with a smooth perimeter regularizer, yielding a convex, smooth energy functional that can be used as a training loss in weakly supervised deep learning paradigms or optimized efficiently using iterative methods. Sparse labels are incorporated into the data fidelity term by constructing a fuzzy membership function via a function extension problem in a Reproducing Kernel Hilbert Space (RKHS), which can effectively capture inhomogeneous intensity statistics. The derived discrete loss for training standard networks demonstrates robustness and consistent improvements over non-training and partial cross-entropy (PCE) baselines in experiments, achieving comparable performance without requiring ground-truth segmentation images.
Subjects:
Computer Vision and Pattern Recognition (cs.CV)
Cite as: arXiv:2607.19669 [cs.CV]
(or arXiv:2607.19669v1 [cs.CV] for this version)
https://doi.org/10.48550/arXiv.2607.19669
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Lingfeng Li [view email] [v1] Wed, 22 Jul 2026 02:18:15 UTC (14,737 KB)
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