A Unified Variational Framework for Deep Weakly Supervised Image Segmentation

• URL: http://arxiv.org/abs/2607.19669v1
• Date: Wed, 22 Jul 2026 02:18:15 GMT
• Title: A Unified Variational Framework for Deep Weakly Supervised Image Segmentation
• Abstract summary: We propose a unified variational framework for image segmentation under sparse pixel-level supervision.<n>Our method is based on a simplex-constrained Potts model with a smooth perimeter regularizer.<n>Sparse labels are incorporated into the data fidelity term by constructing a fuzzy membership function.
• Score: 6.232598868087682
• License: http://creativecommons.org/licenses/by/4.0/
• 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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