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SoftMorph: Differentiable probabilistic morphological operators for image analysis
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DOI：10.1016/j.media.2026.104284.png)
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Abstract
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• SoftMorph makes morphological operations differentiable for deep learning models.
• Converts any Boolean operator into differentiable probabilistic expressions.
• Uses fuzzy logic and multilinear polynomials for smooth morphological filters.
• Enables integration of morphology in CNN last layers and loss functions.
• Improves topological accuracy in medical image segmentation on 2D and 3D datasets.
Keywords:
Morphological operations
Image analysis
Deep learning
Fuzzy logic
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