Fixed Point Layers for Geodesic Morphological Operations
Résumé
Morphological reconstruction is a contour-preserved geodesic transformation that is useful in many fields of image processing. On the other hand, deep learning methods achieved state-of-the-art performance in almost all computer vision tasks. This paper proposes new deep learning layers based on fixed-point morphological reconstruction operations. First, we show that they can be implemented in modern deep learning frameworks and analyse how they affect the learning process of gradientbased methods. Because of the Jacobian properties and the constraint nature of the morphological operators, our layers provide interpretability in both the output and the gradient flow. As examples of application, we consider the use of combining our layers and CNNs to a) improve the performance in the prediction of geometric attributes of objects on images, b) improve the robustness against additive random noise perturbation. Additionally, we study the case of only one noise level and only one database during training to analyse the generalisation capacity of the proposed layer.
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