Agustina Bouchet

ARITHMETIC MEAN BASED COMPENSATORY FUZZY LOGIC

Fuzzy Logic is a multi-valued logic model based on fuzzy set theory, which may be considered as an extension of Boolean Logic. One of the fields of this theory is the Compensatory Fuzzy Logic, based on the removal of some axioms in order to achieve a sensitive and idempotent multi-valued system. This system is based on a quadruple of continuous operators: conjunction, disjunction, order and negation. In this work we present a new model of Compensatory Fuzzy Logic based on a different set of operators, conjunction and disjunction, than the ones used in the original definition, and then prove that this new model satisfies the required axioms. As an example, we present an application to decision-making, comparing the results against the ones based on the original model.

Medical Image Segmentation using the HSI color space and Fuzzy Mathematical Morphology

Diabetic retinopathy is the most common cause of blindness among the active population in developed countries. An early ophthalmologic examination followed by proper treatment can prevent blindness. The purpose of this work is develop an automated method for segmentation the vasculature in retinal images in order to assist the expert in the evolution of a specific treatment or in the diagnosis of a potential pathology. Since the HSI space has the ability to separate the intensity of the intrinsic color information, its use is recommended for the digital processing images when they are affected by lighting changes, characteristic of the images under study. By the application of color filters, is achieved artificially change the tone of blood vessels, to better distinguish them from the bottom. This technique, combined with the application of fuzzy mathematical morphology tools as the Top-Hat transformation, creates images of the retina, where vascular branches are markedly enhanced over the original. These images provide the visualization of blood vessels by the specialist.

Fuzzy mathematical morphology for color images defined by fuzzy preference relations

Nowadays, the representation and the treatment of color images are still open problems. Mathematical morphology is the natural area for a rigorous formulation of many problems in image analysis. Moreover, it comprises powerful non-linear techniques for filtering, texture analysis, shape analysis, edge detection or segmentation. A large number of morphological operators have been widely defined and tested to process binary and gray scale images. However, the extension of mathematical morphology operators to multi-valued functions, and in particular to color images, is neither direct nor general due to the vectorial nature of the data. In this paper, basic morphological operators, erosion and dilation, are extended to color images from a new vector ordering scheme based on a fuzzy order in the RGB color space. Experimental results show that the proposed color operators can be efficiently used for color image processing. HighlightsFuzzy mathematical morphology for color images.Erosion and dilation operators avoid false colors.Proposed order considers all the components with the same weight.

Characterization of bio-dynamic speckles through classical and fuzzy mathematical morphology tools

In this paper we characterize dynamic speckle signals, obtaining selective information through the differentiation of morphological patterns of the temporal history of each pixel, using the morphological granulometric function. This method is applied to the analysis of images of apples and corn seeds. Studies on the first ones were focused on the activity on their surface, related to healthy and damaged areas, while for seeds on the viability of the embryo and endosperm. Subsequently, the analysis was repeated using fuzzy mathematical morphology techniques, comparing the results obtained by both methods.

Enhancement of medical images in HSI color space

In this paper we use the HSI color space as an alternative to RGB space. The HSI space considers the image as a combination of the components: hue, saturation and intensity. In this paper we propose to design a chromatic filter in order to obtain improvements in the enhancement of medical images. In image processing systems it is usual specify colors in a form compatible with the hardware used. The RGB color model, where is computationally convenient, is not very useful in the specification and color recognition. The human being does not recognize a color by having an amount of red, green or blue components, but uses attributes perceptual of hue, saturation and intensity. The chromatics models HSI, HLS, HSV, and its variants, encodes the color with the above attributes and are defined as intuitive spaces.

Type-2 Fuzzy Logic in Decision Support Systems

Decision Support Systems have been widely used in expert knowledge modeling. One of the known implementation approaches is through definition of Fuzzy Sets and Fuzzy Predicates, whose evaluation determines the system’s output. Despite Type-1 Fuzzy Sets have been widely used in this type of implementation, there are uncertainty sources that cannot be adequately modeled when using expert knowledge minimizing their effect on system’s output, especially when it comes from several experts opinions. Type-2 Fuzzy Sets deal with fuzzy membership degrees, which can represent adequately the typical uncertainties of these systems. In this chapter, we generalize the operators of Fuzzy Logic in order to evaluate Fuzzy Predicates with Type-2 Fuzzy Sets and we define measures to assess the degree of truth of these predicates to define the theoretical background of the Decision Support Systems using this methodology. We present an example application of decision-making and a brief discussion of the results.

Dynamic laser speckle and fuzzy mathematical morphology applied to studies of chemotaxis towards hydrocarbons

The movement of the microorganisms towards a higher concentration of the chemical attractant is called positive chemotaxis and is involved in the efficiency of chemical degradation. Several studies are focused in this field related to genomics, and towards demonstrating chemotactic responses by bacteria, but there is little information related to the activity and morphology of their response. In this work, we use a recently reported dynamic speckle laser method, to process images and to distinguish motile surface patterns per area of colonisation by applying image processing techniques called fuzzy mathematical morphology (FMM). The images of bacterial colonies are usually surfaced, with vague edges and non-homogeneous grey levels. Hence, conventional image processing methods for shape analysis cannot be applied in these cases. In this paper, we propose the application FMM to solve this problem. The approach given was effective to segment, detect and also to describe colonisation patterns.

Linguistic Interpretation of Mathematical Morphology

Mathematical Morphology is a theory based on geometry, algebra, topology and set theory, with strong application to digital image processing. This theory is characterized by two basic operators: dilation and erosion. In this work we redefine these operators based on compensatory fuzzy logic using a linguistic definition, compatible with previous definitions of Fuzzy Mathematical Morphology. A comparison to previous definitions is presented, assessing robustness against noise.

Gray Scale Edge Detection using Interval-Valued Fuzzy Relations

AbstractGray scale edge detection can be modeled using Fuzzy Sets and, in particular, Interval-Valued Fuzzy Sets. This work is focused on studying the performance of several Interval-Valued Fuzzy Sets construction methods for detecting edges in a gray scale image. These construction methods are based on considering information related to the neighborhood of each point. Thus, several construction methods are proposed and tested, showing the approach performing better.

Fuzzy Mathematical Morphology Toolbox and Graphical Interface

The task of solving problems using Digital Image Processing requires of the choice of the correct methodology for the issues to be tackled, and a sound selection of parameters for each algorithm to be used. Fuzzy Mathematical Morphology is one of the existing techniques for image processing, being already applied with success on several problems of medical images analysis. However, the selection and use of its operators requires of the continual observation of the results, over a varied range of parameters, for the selection of the optimal ones. Toward that goal, in this work we develop a library of Fuzzy Mathematical Morphology operators, plus a flexible graphical interface, which is of great help in the selection of the optimal parameters and the implementation of Fuzzy operators, with the addition of several classical Image Processing operators. We describe the properties of the library and analyze the simplicity of the graphical interface.