A Unified Variational Framework for Deep Weakly Supervised Image Segmentation
Yin King Chu, Lingfeng Li, Sung Ha Kang, Jianping Zhang, Xue-Cheng Tai
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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Classified with taxonomy v2 on Wed, 2 Sept 2026.