{"slug": "a-unified-variational-framework-for-deep-weakly-supervised-image-segmentation", "title": "A Unified Variational Framework for Deep Weakly Supervised Image Segmentation", "summary": "A new unified variational framework for deep weakly supervised image segmentation uses a simplex-constrained Potts model with a smooth perimeter regularizer to create a convex, smooth energy functional that serves as a training loss. The method incorporates sparse labels via a fuzzy membership function in a Reproducing Kernel Hilbert Space, achieving comparable performance to full supervision without requiring ground-truth segmentation images.", "body_md": "arXiv:2607.19669v1 Announce Type: new\nAbstract: 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.", "url": "https://wpnews.pro/news/a-unified-variational-framework-for-deep-weakly-supervised-image-segmentation", "canonical_source": "https://arxiv.org/abs/2607.19669", "published_at": "2026-07-23 04:00:00+00:00", "updated_at": "2026-07-23 04:25:59.994343+00:00", "lang": "en", "topics": ["computer-vision", "machine-learning", "neural-networks"], "entities": [], "alternates": {"html": "https://wpnews.pro/news/a-unified-variational-framework-for-deep-weakly-supervised-image-segmentation", "markdown": "https://wpnews.pro/news/a-unified-variational-framework-for-deep-weakly-supervised-image-segmentation.md", "text": "https://wpnews.pro/news/a-unified-variational-framework-for-deep-weakly-supervised-image-segmentation.txt", "jsonld": "https://wpnews.pro/news/a-unified-variational-framework-for-deep-weakly-supervised-image-segmentation.jsonld"}}