Processing of microCT implant-bone systems images using Fuzzy Mathematical Morphology

The relationship between a metallic implant and the existing bone in a surgical permanent prosthesis is of great importance since the fixation and osseointegration of the system leads to the failure or success of the surgery. Micro Computed Tomography is atechnique that helps to visualize the structure of the bone. In this study, the microCT is used to analyze implant-bone systems images. However, one of the problems presented in the reconstruction of these images is the effect of the iron based implants, with a halo or fluorescence scattering distorting the micro CT image and leading to bad 3D reconstructions.In this work we introduce an automatic method for eliminate the effect of AISI 316L iron materials in the implant-b one system based on the application of Compensatory Fuzzy Mathematical Morphology for future investigate about the structural and mechanical properties of bone and cancellous materials.Fil: Bouchet, Agustina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Mar del Plata; ArgentinaFil: Colabella, Lucas. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones en Ciencia y Tecnología de Materiales. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones en Ciencia y Tecnología de Materiales; ArgentinaFil: Omar, Sheila Ayelén. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones en Ciencia y Tecnología de Materiales. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones en Ciencia y Tecnología de Materiales; ArgentinaFil: Ballarre, Josefina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones en Ciencia y Tecnología de Materiales. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones en Ciencia y Tecnología de Materiales; ArgentinaFil: Pastore, Juan Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Mar del Plata; Argentin

Interval-valued and intuitionistic fuzzy mathematical morphologies as special cases of L-fuzzy mathematical morphology

Mathematical morphology (MM) offers a wide range of tools for image processing and computer vision. MM was originally conceived for the processing of binary images and later extended to gray-scale morphology. Extensions of classical binary morphology to gray-scale morphology include approaches based on fuzzy set theory that give rise to fuzzy mathematical morphology (FMM). From a mathematical point of view, FMM relies on the fact that the class of all fuzzy sets over a certain universe forms a complete lattice. Recall that complete lattices provide for the most general framework in which MM can be conducted. The concept of L-fuzzy set generalizes not only the concept of fuzzy set but also the concepts of interval-valued fuzzy set and Atanassov’s intuitionistic fuzzy set. In addition, the class of L-fuzzy sets forms a complete lattice whenever the underlying set L constitutes a complete lattice. Based on these observations, we develop a general approach towards L-fuzzy mathematical morphology in this paper. Our focus is in particular on the construction of connectives for interval-valued and intuitionistic fuzzy mathematical morphologies that arise as special, isomorphic cases of L-fuzzy MM. As an application of these ideas, we generate a combination of some well-known medical image reconstruction techniques in terms of interval-valued fuzzy image processing

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.Fil: Bouchet, Agustina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Mar del Plata; ArgentinaFil: Meschino, Gustavo. Universidad Nacional de Mar del Plata; ArgentinaFil: Brun, Marcel. Universidad Nacional de Mar del Plata; ArgentinaFil: Espin Andrade, Rafael. Instituto Superior Politécnico José Antonio Echeverría Cujae; CubaFil: Ballarin, Virginia. Universidad Nacional de Mar del Plata; Argentin

Learning spatial relationships in hand-drawn patterns using fuzzy mathematical morphology

International audienceWe introduce in this work a new approach for learning spatial relationships between elements of hand-drawn patterns with the help of fuzzy mathematical morphology operators. Relying on mathematical morphology allows to take into account the actual shapes of hand-drawn patterns when modeling their spatial relationships, and thus to cope with the variability of handwriting signal. Extension of mathematical morphology to the fuzzy set framework further allows to handle imprecision of handwriting and to deal with the ambiguity of spatial relationships. The novelty lies in the generative aspect of the models we propose, in the sense that they can exhibit the region of space where the learnt relation is satisfied with respect to a reference object, and can thus be used for driving structural analysis of complex patterns. Experiments over on-line handwritten data show their performance, and prove their ability to deal with variability of handwriting and reasoning under imprecision

Fuzzy techniques for noise removal in image sequences and interval-valued fuzzy mathematical morphology

Image sequences play an important role in today's world. They provide us a lot of information. Videos are for example used for traffic observations, surveillance systems, autonomous navigation and so on. Due to bad acquisition, transmission or recording, the sequences are however usually corrupted by noise, which hampers the functioning of many image processing techniques. A preprocessing module to filter the images often becomes necessary. After an introduction to fuzzy set theory and image processing, in the first main part of the thesis, several fuzzy logic based video filters are proposed: one filter for grayscale video sequences corrupted by additive Gaussian noise and two color extensions of it and two grayscale filters and one color filter for sequences affected by the random valued impulse noise type. In the second main part of the thesis, interval-valued fuzzy mathematical morphology is studied. Mathematical morphology is a theory intended for the analysis of spatial structures that has found application in e.g. edge detection, object recognition, pattern recognition, image segmentation, image magnification… In the thesis, an overview is given of the evolution from binary mathematical morphology over the different grayscale morphology theories to interval-valued fuzzy mathematical morphology and the interval-valued image model. Additionally, the basic properties of the interval-valued fuzzy morphological operators are investigated. Next, also the decomposition of the interval-valued fuzzy morphological operators is investigated. We investigate the relationship between the cut of the result of such operator applied on an interval-valued image and structuring element and the result of the corresponding binary operator applied on the cut of the image and structuring element. These results are first of all interesting because they provide a link between interval-valued fuzzy mathematical morphology and binary mathematical morphology, but such conversion into binary operators also reduces the computation. Finally, also the reverse problem is tackled, i.e., the construction of interval-valued morphological operators from the binary ones. Using the results from a more general study in which the construction of an interval-valued fuzzy set from a nested family of crisp sets is constructed, increasing binary operators (e.g. the binary dilation) are extended to interval-valued fuzzy operators

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

Segmentation of Medical Images using Fuzzy Mathematical Morphology

Currently, Mathematical Morphology (MM) has become a powerful tool in Digital Image Processing (DIP). It allows processing images to enhance fuzzy areas, segment objects, detect edges and analyze structures. The techniques developed for binary images are a major step forward in the application of this theory to gray level images. One of these techniques is based on fuzzy logic and on the theory of fuzzy sets. Fuzzy sets have proved to be strongly advantageous when representing inaccuracies, not only regarding the spatial localization of objects in an image but also the membership of a certain pixel to a given class. Such inaccuracies are inherent to real images either because of the presence of indefinite limits between the structures or objects to be segmented within the image due to noisy acquisitions or directly because they are inherent to the image formation methods. Our approach is to show how the fuzzy sets specifically utilized in MM have turned into a functional tool in DIP.Facultad de Informátic

Generation of fuzzy mathematical morphologies

Fuzzy Mathematical Morphology aims to extend the binary morphological operators to grey-level images. In order to define the basic morphological operations fuzzy erosion, dilation, opening and closing, we introduce a general method based upon fuzzy implication and inclusion grade operators, including as particular case, other ones existing in related literature In the definition of fuzzy erosion and dilation we use several fuzzy implications (Annexe A, Table of fuzzy implications), the paper includes a study on their practical effects on digital image processing. We also present some graphic examples of erosion and dilation with three different structuring elements $B(i, j)=1$, $B(i, j)=0.7$, $B(i, j)=0.4$, $i, j \in \{ 1,2, 3\}$ and various fuzzy implications

Fuzzy morphological operators in image processing

First of all, in this paper we propose a family of fuzzy implication operators, which the generalised Luckasiewicz's one, and to analyse the impacts of Smets and Magrez properties on these operators. The result of this approach will be a characterisation of a proposed family of inclusion grade operators (in Bandler and Kohout's manner) that satisfies the axioms of Divyendu and Dogherty. Second, we propose a method to define fuzzy morphological operators (erosions and dilations). A family of fuzzy implication operators and the inclusion grade are the basis for this method