Adaptive fuzzy morphological filtering of images

In this paper we introduce a neural network implementation of fuzzy mathematical morphology operators and apply it to image denoising. Using a supervised training method and differentiable equivalent representations for the fuzzy morphological operators, we derive efficient adaptation algorithms to optimize the structuring elements. We can then design fuzzy morphological filters for processing multi-level or binary images. The convergence behavior of basic structuring elements for the opening filter and different signals, and its significance for other structuring elements of different shape is discussed. To illustrate the performance of the fuzzy opening filter we consider the removal of impulse noise in multi-level and binary images.