Fuzzy Morphological Operations Research Articles

Adaptive Fuzzy Morphological Filtering of Impulse Noisein 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.

An Application of Fuzzy Mathematical Morphology to Interval-Valued Knowledge Representation: A Remark

Mathematical morphology is known by its useful tools for processing binary (black-and-white) and gray-tone images. Due to the success of mathematical morphology in processing binary images, there have been many successful attempts to generalize its methods to more general, i.e. gray-tone images. One of these attempts—the most intuitive one is based on replacing sets by fuzzy sets, thus defining so called fuzzy morphological operations. In this paper we show that these operations can be used successfully in nonimage applications. We can use methods developed in fuzzy mathematical morphology to compute the membership functions of different "approximate" statements. Also, an application to interval-valued knowledge representation is given.

Convexity indicators based on fuzzy morphology

This study results in a very general class of convexity indicators, which measure the degree of convexity of objects on grey-tone and binary images. They are based on fuzzy set theory, more precisely, on the fuzzy inclusion indicators defined by Sinha and Dougherty. Consideration is given to the fuzzy morphological operations which are used in the construction of inclusion and convexity indicators.

Optical intrinsically fuzzy mathematical morphology for gray-scale image processing

Intrinsically fuzzy morphological erosion and dilation are extended to a total of eight operations that have been formulated in terms of a single morphological operation-biased dilation. Based on the spatial coding of a fuzzy variable, a bidirectional projection concept is proposed. Thus, fuzzy logic operations, arithmetic operations, gray-scale dilation, and erosion for the extended intrinsically fuzzy morphological operations can be included in a unified algorithm with only biased dilation and fuzzy logic operations. To execute this image algebra approach we present a cellular two-layer processing architecture that consists of a biased dilation processor and a fuzzy logic processor.

THE FUNDAMENTALS OF FUZZY MATHEMATICAL MORPHOLOGY PART 2: IDEMPOTENCE, CONVEXITY AND DECOMPOSITION

Fuzzy mathematical morphology is an alternative extension of binary mathematical morphology to grayscale images. This paper discusses some of the more advanced properties of the fuzzy morphological operations. The possible extensivity of the fuzzy closing, anti-extensivity of the fuzzy opening and idem-potence of the fuzzy closing and fuzzy opening are studied in detail. It is demonstrated that these properties only partially hold. On the other hand, it is shown that the fuzzy morphological operations satisfy the same translation invariance and have the same convexity properties as the binary morphological operations. Finally, the paper investigates the possible decomposition, by taking (strict) α-cuts, of the fuzzy morphological operations into binary morphological operations.