A novel signal representation using fuzzy mathematical morphology is developed. We take advantage of the optimum fuzzy fitting and the efficient implementation of morphological operators to extract geometric information from signals. The new representation provides results analogous to those given by the polynomial transform. Geometrical decomposition of a signal is achieved by windowing and ap...

In this study, we show from helium (He) plasma irradiation to tantalum and iron surfaces that morphology changes in nanoscale occur on the both metals. In particular, from systematic irradiation experiments, it is identified that fuzzy nanostructures are grown on the both metals. The necessary conditions for the morphology changes are discussed based on the experimental results in terms of the ...

In this paper we address the question of defining and computing Hausdorff distances between distributions in a general sense. We exhibit some links between Prokhorov-Lévy distances and dilation-based distances. In particular, mathematical morphology provides an elegant way to deal with periodic distributions. The case of possibility distributions is addressed using fuzzy mathematical morphology...

To overcome the limitation of artificial judgment of meibomian gland morphology, we proposed a solution based on an improved fuzzy c-means (FCM) algorithm and rough sets theory. The rough sets reduced the redundant attributes while ensuring classification accuracy, and greatly reduced the amount of computation to achieve information dimension compression and knowledge system simplification. How...

Ćurić, V. 2014. Distance Functions and Their Use in Adaptive Mathematical Morphology. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1137. 88 pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 978-91-554-8923-6. One of the main problems in image analysis is a comparison of different shapes in images. It is often desirable to determine the exte...

Foreword The intention of this report is to list and analyze some of the published results related to different approaches of applying fuzzy set theory to fuzzy shape analysis. These results provide a good background for further development of fuzzy shape analysis methods, which is our main goal. It should be noted that only fuzzy shape analysis techniques are considered, and not other approach...

We propose in this paper to construct modal logics based on mathematical morphology. The contribution of this paper is twofold. First we show that mathematical morphology can be used to define modal operators in the context of normal modal logics. We propose definitions of modal operators as algebraic dilations and erosions, based on the notion of adjunction. We detail the particular case of mo...