Morphological methods play a crucial role in remote sensing image processing, due to their ability to capture and preserve small structural details. However, most of the existing deep learning models for semantic segmentation are based on the encoder-decoder architecture including U-net and Segment Anything Model (SAM), where the downsampling process tends to discard fine details. In this paper, we propose a new approach that integrates learnable morphological skeleton prior into deep neural networks using the variational method. To address the difficulty in backpropagation in neural networks caused by the non-differentiability presented in classical morphological operations, we provide a smooth representation of the morphological skeleton and design a variational segmentation model integrating morphological skeleton prior by employing operator splitting and dual methods. Then, we integrate this model into the network architecture of SAM, which is achieved by adding a token to mask decoder and modifying the final sigmoid layer, ensuring the final segmentation results preserve the skeleton structure as much as possible. Experimental results on remote sensing datasets, including buildings and roads, demonstrate that our method outperforms the original SAM on slender object segmentation and exhibits better generalization capability.
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