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The basic goal of this article is to present an abstract system-theoretic approach to morphological filtering and the theory of translation invariant systems which is mainly based on residuated semigroups. Some new results as well as a number of basic questions are also introduced  

In this paper we present, for the first time, complete proofs of the facts that have already been announced in [A. Daneshgar, A. Hashemi, A general model for I/O system theory, Proc. AIMC31, 2000, 292-299]. Our approach here is to focus on the aspects related to fuzzy set theory and we leave other connections to mathematical disciplines such as quantum groups, categorical logic, homological algebra and measure theory to appear elsewhere. The main contribution is to introduce a general framework based on enriched category theory that covers the theory of translation invariant systems as a special case, as well as the construction of the Haar fraction on a locally compact group  

Synthetic aperture radar (SAR) appropriate image processing in conjunction with noise reduction is crucial in proper image segmentation. The authors present a new algorithm, logarithmic adaptive soft morphological (LASM) filter, utilising collectivity and flexibility of order-statistic soft morphological filters. This method not only reduces the speckle noise of the single-look SAR imagery considerably, but it significantly enhances the segmentation results. To verify the performance, a simulated SAR image is first created by applying an imagery method to an original noiseless image. The resulting image has characteristics identical to a real SAR image. The LASM method, as well as several... 

Morphological filtering is a useful technique for the processing and analysis of binary and gray scale images. The extension of morphological techniques to color images is not a straightforward task because this extension stems from the multivariate ordering problem. Since multivariate ordering is ambiguous, existing approaches have used known vector ordering schemes for the color ordering purpose. In the. last decade, many different color morphological operators have been introduced in the literature. Some of them have focused on noise suppression purposes. However, none has shown good performance, especially on edgy regions. In this paper, new color morphological operators, based on a...