Virginia L. Ballarin

Segmentation of brain magnetic resonance images through morphological operators and geodesic distance

When segmenting magnetic resonance (MR) images, a wide range of useless information arises, which has to be discarded as a step prior to classifying the different cerebral cortex areas. To obtain effective results during the classification process, it is necessary to work with images solely containing the brain and eliminate the cranium and surrounding meninges. This work introduces an automatic method for the detection of said structures based on the application of morphology alternating sequential filters by reconstruction with structuring elements of growing size. Apart from enhancing and filtering in this way, this method captures the interior of a closed simple curve employing geodesic distance. Said curve represents the external brain boundary.

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.

Evaluation of speckle-interferometry descriptors to measuring drying-of-coatings

In the industrial process of painting, paint-drying is an important stage because of its high impact in the final result. Its study is of relevance to improve the properties of the resulting coating. Amalvys experiments to measure the speed of drying on surfaces, based on techniques of speckle interferometry, have been used as a starting point in the evaluation of other methods, which allow to measure the process with greater accuracy. Haralicks descriptors have been studied in depth, then filters based on mathematical morphology techniques, a natural complexity measure and, finally, local binary patterns. Measures of speed of drying based on gravimetrical information were obtained and used as a gold standard. The comparison of different techniques was based on their ability to predict its values through a linear regression model. Morphological descriptors showed a low dependance with the sampling time, a desired property. Permutation entropy and local binary patterns evinced similar drying curves, showing a remarkable inflection point, coincident with the passage on the constant drying area to a later state, defined by a slower diffusion of the solvent through the dry coat of the surface. More precise descriptors of drying phenomena have been identified in this study.

Automatic design of interpretable fuzzy predicate systems for clustering using self-organizing maps

Abstract In the area of pattern recognition, clustering algorithms are a family of unsupervised classifiers designed with the aim to discover unrevealed structures in the data. While this is a never ending research topic, many methods have been developed with good theoretical and practical properties. One of such methods is based on self organizing maps (SOM), which have been successfully used for data clustering, using a two levels clustering approach. Newer on the field, clustering systems based on fuzzy logic improve the performance of traditional approaches. In this paper we combine both approaches. Most of the previous works on fuzzy clustering are based on fuzzy inference systems, but we propose the design of a new clustering system in which we use predicate fuzzy logic to perform the clustering task, being automatically designed based on data. Given a datum, degrees of truth of fuzzy predicates associated with each cluster are computed using continuous membership functions defined over data features. The predicate with the maximum degree of truth determines the cluster to be assigned. Knowledge is discovered from data, obtained using the SOM generalization aptitude and taking advantage of the well-known SOM abilities to discover natural data grouping when compared with direct clustering. In addition, the proposed approach adds linguistic interpretability when membership functions are analyzed by a field expert. We also present how this approach can be used to deal with partitioned data. Results show that clustering accuracy obtained is high and it outperforms other methods in the majority of datasets tested.

A framework for tissue discrimination in Magnetic Resonance brain images based on predicates analysis and Compensatory Fuzzy Logic

Abstract One of the advantages of Magnetic Resonance images is their ability to discriminate tissues for their subsequent quantification. In this work, magnetic resonance brain images are analyzed pixelwise by fuzzy logical predicates, reproducing in a computational way the considerations that experts employ when they interpret these images, in order to identify the tissues that pixels represent. We used Compensatory Fuzzy Logic operators to implement the logical connectives. The problem has been addressed as one pertaining to the discipline of decision-making support. The aim is to determine which tissue corresponds to each pixel. The system is optimized by a Genetic Algorithm that search an adequate set of parameters for fuzzy sets included in the predicates. It has been possible to successfully discriminate cerebrospinal fluid, gray matter and white matter in simulated and real images, validating the results using the Tanimoto Coefficient. As the operations involved are simple, processing time is short...

Decomposition of biospeckle signals through granulometric size distribution.

We present a method for the analysis of dynamic speckle signals based on morphological granulometry. We obtain selected information differentiating the morphological patterns of the temporal history of each pixel through the granulometric size distribution. The method is exemplified by detecting bruised regions on apples and studying the germination of corn seeds. Different levels of activity are observed in the bruised and healthy areas of the apple, within a certain range of the morphological spectrum. Likewise, the activity of the corn seed embryo can also be distinguished from the endosperm area.

Multiscale Morphological Operators and Geodesic Distance applied to Computed Axial Tomography Segmentation

Lately, several diagnostic and therapeutic procedures for mediastinal tumors and masses are done by videothoraxcoscopic techniques. Consequently, Computed Axial Tomography (C.A.T.) become a fundamental tool in tumors and masses diagnostic, especially to locate and measure them with accuracy and precision. This paper presents a segmentation method in C.A.T. images through techniques based in Mathematical Morphology. A semi-automatic method for structure segmentation based on Multiscale Morphological Operators is introduced. In addition to filtering and enhancing, this method capture the interior of a closed simple curve by the geodesic distance. These curves represents the external boundary of the different mediastinal structures. This method allows to calculate exactly the external boundary of the segmented structure and also the delimitated area.

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.

Using SOM as a Tool for Automated Design of Clustering Systems Based on Fuzzy Predicates

Clustering task is a never-ending research topic. New methods are permanently proposed. In particular, Fuzzy Logic and Self-organizing Maps and their mutual cooperation have demonstrated to be interesting paradigms. We propose a general approach to obtain membership functions for a ranked clustering system based on fuzzy predicates logical operations, considering Gaussian-shaped curves. We find membership functions parameters from trained Self-organizing Maps, which generalize the statistical characteristics of data. The system is self-configured and it has the advantages of other fuzzy approaches. Clustering quality is assessed by labeled data, which allow computing accuracy. The proposal must be tested with more real datasets, though the preliminary results obtained in well-known datasets suggest that it is a promising clustering scheme.

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.