Beyond Weak Labels: Prompt-Guided Local Refinement for Weakly Supervised Water Segmentation in High-Resolution Multispectral Imagery

High-resolution (HR) land-cover mapping is often constrained by the high cost of dense HR annotations. We revisit this problem from the perspective of map super-resolution, which enhances coarse low-resolution (LR) land-cover products into HR maps at the resolution of the input imagery. Existing weakly supervised methods can leverage LR labels, but they typically use them to retrain dense predictors with substantial computational cost. We propose MapSR, a prompt-driven framework that decouples supervision from model training. MapSR uses LR labels once to extract class prompts from frozen vision foundation model features through a lightweight linear probe, after which HR mapping proceeds via training-free metric inference and graph-based prediction refinement. Specifically, class prompts are estimated by aggregating high-confidence HR features identified by the linear probe, and HR predictions are obtained by cosine-similarity matching followed by graph-based propagation for spatial refinement. Experiments on the Chesapeake Bay dataset show that MapSR achieves 59.64% mIoU without any HR labels, remaining competitive with the strongest weakly supervised baseline and surpassing a fully supervised baseline. Notably, MapSR reduces trainable parameters by four orders of magnitude and shortens training time from hours to minutes, enabling scalable HR mapping under limited annotation and compute budgets. The code is available at https://github.com/rikirikirikiriki/MapSR.

Weakly supervised semantic segmentation (WSSS) trains dense pixel-level segmentation models from partial or coarse annotations such as bounding boxes, scribbles, or image-level tags. While recent work leverages foundation models such as the Segment Anything Model (SAM) to generate pseudo-labels, these approaches typically depend on heuristic prompt choices and offer limited ways to incorporate prior knowledge or heterogeneous labels. We address this gap by taking a neurosymbolic perspective: integrating differentiable fuzzy logic with deep segmentation models. Weak annotations and domain-specific priors are unified as continuous logical constraints that fine-tune SAM under weak supervision. The refined foundation model then produces improved pseudo-labels, from which we train a second-stage prompt-free segmentation model. Experiments on Pascal VOC 2012 and the REFUGE2 optic disc/cup segmentation dataset show that our logic-guided fine-tuning yields higher-quality pseudo-labels, leading to state-of-the-art segmentation accuracy that often exceeds densely supervised baselines.

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.