A General Self-Dual Adaptative Filtering Toggle Operator

In the mathematical morphology context, a filter is an operator that is increasing and idempotent. We propose an alternative way to build self-dual morphological filters, extending some results obtained for morphological centers to a different class of toggle operators whose decision rule is based on which primitive value is closer to the original one. With this new approach, a wider range of primitives can be considered without causing oscillations, a common problem in toggle mappings. We also explore the use of non-flat structuring elements which are shown to produce sharper filtered images. To evaluate the proposed approach, we carry out tests on images with different kinds of noise using different pairs of primitives. Experimental tests on Synthetic Aperture Radar (SAR) images show promising results, outperforming some well-known filters related to this type of pictures.