Soil sinkholes significantly influence soil degradation, but their irregular shapes, along with interference from shadow and vegetation, make it challenging to accurately quantify their properties using remotely sensed data. We present a novel framework for sinkhole segmentation that combines traditional topographic computations of closed depressions with the newly developed prompt-based Segment Anything Model (SAM). Within this framework, termed SinkSAM, we highlight four key improvements: (1) The integration of topographic computations with SAM enables pixel-level refinement of sinkhole boundaries segmentation; (2) A coherent mathematical prompting strategy, based on closed depressions, addresses the limitations of purely learning-based models (CNNs) in detecting and segmenting undefined sinkhole features, while improving generalization to new, unseen regions; (3) Using Depth Anything V2 monocular depth for automatic prompts eliminates photogrammetric biases, enabling sinkhole mapping without the dependence on LiDAR data; and (4) An established sinkhole database facilitates fine-tuning of SAM, improving its zero-shot performance in sinkhole segmentation. These advancements allow the deployment of SinkSAM, in an unseen test area, in the highly variable semiarid region, achieving an intersection-over-union (IoU) of 40.27\% and surpassing previous results. This paper also presents the first SAM implementation for sinkhole segmentation and demonstrates the robustness of SinkSAM in extracting sinkhole maps using a single RGB image.
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