Adaptive fuzzy morphological filtering of impulse noise in images

In this paper we first introduce a neural network implementation for fuzzy morphological operators, and by means of a training method and differentiable equivalent representations for the operators we then derive efficient adaptation algorithms to optimize the structuring elements. Thus we are able to design fuzzy morphological filters for processing multi-level or binary images. The convergence behavior of basic structuring elements and its significance for other structuring elements of different shape is discussed. Besides the filter design, the localized structuring elements obtained from the training method give a structural characterization of the image which is useful in many applications. The performance of the fuzzy morphological filters in removing impulse noise in multi-level and binary images is illustrated and compared with existing procedures.