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arXiv · 2607.19669

A Unified Variational Framework for Deep Weakly Supervised Image Segmentation

Yin King Chu·Lingfeng Li·Sung Ha Kang·Jianping Zhang·Xue-Cheng Tai
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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.

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Yin King Chu, Lingfeng Li, Sung Ha Kang, Jianping Zhang, Xue-Cheng Tai. 2026-07-22. A Unified Variational Framework for Deep Weakly Supervised Image Segmentation. https://arxiv.org/abs/2607.19669

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