In a large number of applications, the processing relies on objects or area of interests, and the pixel-based image representation is notwell adapted. These applications would benefit from a region-based processing. Early examples of region-based processing can be found in the area of image segmentation, such as the quad tree. Recently, in mathematical morphology, the connected operators have received much attention. They are region-based filtering tools that act by merging flat zones. They have good contour preservation properties in the sense that they do not create any new boundaries, neither do they shift the existing ones. One popular implementation for connected operators relies on tree-based image representations, notably threshold decomposition representations and hierarchical representations. Those tree-based image representations are widely used in many image processing and computer vision applications. Tree-based connected operators consist in constructing a set of nested or disjoint connected components, followed by a filtering of these connected components based on an attribute function characterizing each connected component. Finally, the filtered image is reconstructed from the simplified tree composed of the remaining connected components. In the work presented in this thesis, we propose to expand the ideas of tree-based connected operators. We introduce the notion of tree-based shape spaces, built from tree-based image representations. Many state-of-the-art methods relying on tree-based image representations consist of analyzing this shape space. A first consequence of this change of point of view is our proposition of a local feature detector, called the tree-based Morse regions (TBMR). It can be seen as a variant of the MSER method. The selection of TBMRs is based on topological information, and hence it extracts the regions independently of the contrast, which makes it truly contrast invariant and quasi parameters free. The accuracy and robustness of the TBMR approach are demonstrated by the repeatability test and by applications to image registration and 3D reconstruction, as compared to some state-of-the-art methods. The basic idea of the main proposition in this thesis is to apply connected filters on the shape space. Such a processing is called the framework of shape-based morphology. It is a versatile framework that deals with region-based image representations. It has three main consequences. 1) For filtering purpose, it is a generalization of the existing tree-based connected operators. Indeed, the framework encompasses classical existing connected operators by attributes. Besides, It also allows us to propose two classes of novel connected operators: shape-based lower/upper levelings and shapings. 2) This framework can be used to object detection/segmentation by selecting relevant points in the shape space. 3) We can also use this framework to transform the hierarchies using the extinction values, so that a hierarchical simplification or segmentation is obtained. Some applications are developed using the framework of shape-based morphology to demonstrate its usefulness. The applications of the shape-based filtering to retinal image analysis show that a mere filtering step that we compare to more evolved processings, achieves state-of-the-art results. An efficient shaping used for image simplification is proposed by minimizing Mumford-Shah functional subordinated to the topographic map. For object detection/segmentation, we proposed a context-based energy estimator that is suitable to characterize object meaningfulness. Last, we extend the hierarchy of constrained connectivity using the aspect of hierarchy transformation of constrained connectivity using the aspect ofhierarchy transformation.

The focus of this research is the extension of topological operators with the addition of a inclusion measure. This extension is carried out in both crisp and fuzzy topological spaces. The mathematical properties of the new operators are discussed and compared with traditional operators. Ignoring small errors due to imperfections and noise in digital images is the main motivation in introducing the proposed operators. To show the effectiveness of the new operators, we demonstrate their utility in image database classification and shape classification. Each image (shape) category is modeled with a topological space and the interior of the query image is obtained with respect to different topologies. This novel way of looking at the image categories and classifying a query image shows some promising results. Moreover, the proposed interior and closure operators with inclusion degree is utilized in mathematical morphology area. The morphological operators with inclusion degree outperform traditional morphology in noise removal and edge detection in a noisy environment

De nombreuses applications issues de la vision par ordinateur et de la reconnaissance des formes requièrent une analyse de l'image multi-échelle basée sur ses régions. De nos jours, personne ne considérerait une approche orientée « pixel » comme une solution viable pour traiter ce genre de problèmes. Pour répondre à cette demande, la Morphologie Mathématique a fourni des représentations hiérarchiques des régions de l'image telles que l'Arbre des Formes (AdF). L'AdF représente l'image par un arbre d'inclusion de ses lignes de niveaux. L'AdF est ainsi auto-dual et invariant au changement de contraste, ce qui fait de lui une structure bien adaptée aux traitements d'images de haut niveau. Néanmoins, il est seulement défini aux images en niveaux de gris et la plupart des tentatives d'extension aux images multivariées (e.g. en imposant un ordre total «arbitraire ») ne sont pas satisfaisantes. Dans ce manuscrit, nous présentons une nouvelle approche pour étendre l'AdF scalaire aux images multivariées : l'Arbre des Formes Multivarié (AdFM). Cette représentation est une « fusion » des AdFs calculés marginalement sur chaque composante de l'image. On vise à fusionner les formes marginales de manière « sensée » en préservant un nombre maximal d'inclusion. La méthode proposée a des fondements théoriques qui consistent en l'expression de l'AdF par une carte topographique de la variation totale curvilinéaire depuis la bordure de l'image. C'est cette reformulation qui a permis l'extension de l'AdF aux données multivariées. De plus, l'AdFM partage des propriétés similaires avec l'AdF scalaire ; la plus importante étant son invariance à tout changement ou inversion de contraste marginal (une sorte d'auto-dualité dans le cas multidimensionnel). Puisqu'il est évident que, vis-à-vis du nombre sans cesse croissant de données à traiter, nous ayons besoin de techniques rapides de traitement d'images, nous proposons un algorithme efficace qui permet de construire l'AdF en temps quasi-linéaire vis-à-vis du nombre de pixels et quadratique vis-à-vis du nombre de composantes. Nous proposons également des algorithmes permettant de manipuler l'arbre, montrant ainsi que, en pratique, l'AdFM est une structure facile à manipuler, polyvalente, et efficace. Finalement, pour valider la pertinence de notre approche, nous proposons quelques expériences testant la robustesse de notre structure aux composantes non-pertinentes (e.g. avec du bruit ou à faible dynamique) et nous montrons que ces défauts n'affectent pas la structure globale de l'AdFM. De plus, nous proposons des applications concrètes utilisant l'AdFM. Certaines sont juste des modifications mineures aux méthodes employant d'ores et déjà l'AdF scalaire mais adaptées à notre nouvelle structure. Par exemple, nous utilisons l'AdFM à des fins de filtrage, segmentation, classification et de détection d'objet. De ces applications, nous montrons ainsi que les méthodes basées sur l'AdFM surpassent généralement leur analogue basé sur l'AdF, démontrant ainsi le potentiel de notre approche / Nowadays, the demand for multi-scale and region-based analysis in many computer vision and pattern recognition applications is obvious. No one would consider a pixel-based approach as a good candidate to solve such problems. To meet this need, the Mathematical Morphology (MM) framework has supplied region-based hierarchical representations of images such as the Tree of Shapes (ToS). The ToS represents the image in terms of a tree of the inclusion of its level-lines. The ToS is thus self-dual and contrast-change invariant which make it well-adapted for high-level image processing. Yet, it is only defined on grayscale images and most attempts to extend it on multivariate images - e.g. by imposing an “arbitrary” total ordering - are not satisfactory. In this dissertation, we present the Multivariate Tree of Shapes (MToS) as a novel approach to extend the grayscale ToS on multivariate images. This representation is a mix of the ToS's computed marginally on each channel of the image; it aims at merging the marginal shapes in a “sensible” way by preserving the maximum number of inclusion. The method proposed has theoretical foundations expressing the ToS in terms of a topographic map of the curvilinear total variation computed from the image border; which has allowed its extension on multivariate data. In addition, the MToS features similar properties as the grayscale ToS, the most important one being its invariance to any marginal change of contrast and any marginal inversion of contrast (a somewhat “self-duality” in the multidimensional case). As the need for efficient image processing techniques is obvious regarding the larger and larger amount of data to process, we propose an efficient algorithm that can be build the MToS in quasi-linear time w.r.t. the number of pixels and quadraticw.r.t. the number of channels. We also propose tree-based processing algorithms to demonstrate in practice, that the MToS is a versatile, easy-to-use, and efficient structure. Eventually, to validate the soundness of our approach, we propose some experiments testing the robustness of the structure to non-relevant components (e.g. with noise or with low dynamics) and we show that such defaults do not affect the overall structure of the MToS. In addition, we propose many real-case applications using the MToS. Many of them are just a slight modification of methods employing the “regular” ToS and adapted to our new structure. For example, we successfully use the MToS for image filtering, image simplification, image segmentation, image classification and object detection. From these applications, we show that the MToS generally outperforms its ToS-based counterpart, demonstrating the potential of our approach

L’objectif de ces travaux est de fournir une méthode de segmentation sémantique qui soit générale et automatique, c’est-à-dire une méthode qui puisse s’adapter par elle-même à tout type de base d’images, afin d’être utilisée directement par les non experts en traitement d’image, comme les biologistes par exemple. Pour cela, nous proposons d’utiliser la classification de pixel, une approche classique d’apprentissage supervisé, où l’objectif est d’attribuer à chaque pixel l’étiquette de l’objet auquel il appartient. Les descripteurs des pixels à classer sont souvent calculés sur des supports fixes, par exemple une fenêtre centrée sur chaque pixel, ce qui conduit à des erreurs de classification, notamment au niveau des contours d’objets. Nous nous intéressons donc à un autre support, plus large que le pixel et s’adaptant au contenu de l’image: le superpixel. Les superpixels sont des régions homogènes et plutôt régulières, issues d’une segmentation de bas niveau. Nous proposons une nouvelle façon de les générer grâce à la ligne de partage des eaux, les waterpixels, méthode rapide, performante et facile à prendre en main par l’utilisateur. Ces superpixels sont ensuite utilisés dans la chaîne de classification, soit à la place des pixels à classer, soit comme support pertinent pour calculer les descripteurs, appelés SAF (Superpixel-Adaptive Features). Cette seconde approche constitue une méthode générale de segmentation dont la pertinence est vérifiée qualitativement et quantitativement sur trois bases d’images provenant du milieu biomédical. / In this work, we would like to provide a general method for automatic semantic segmentation, which could adapt itself to any image database in order to be directly used by non-experts in image analysis (such as biologists). To address this problem, we first propose to use pixel classification, a classic approach based on supervised learning, where the aim is to assign to each pixel the label of the object it belongs to. Features describing each pixel properties, and which are used to determine the class label, are often computed on a fixed-shape support (such as a centered window), which leads, in particular, to misclassifcations on object contours. Therefore, we consider another support which is wider than the pixel itself and adapts to the image content: the superpixel. Superpixels are homogeneous and rather regular regions resulting from a low-level segmentation. We propose a new superpixel generation method based on the watershed, the waterpixels, which are efficient, fast to compute and easy to handle by the user. They are then inserted in the classification pipeline, either in replacement of pixels to be classified, or as pertinent supports to compute the features, called Superpixel-Adaptive Features (SAF). This second approach constitutes a general segmentation method whose pertinence is qualitatively and quantitatively highlighted on three databases from the biological field.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / A morfologia matemÃtica à uma abordagem utilizada em problemas de processamento e anÃlise de imagens em que sÃo realizadas transformaÃÃes de um objeto (imagem) por padrÃes de formas prÃ-definidas. Tais transformaÃÃes sÃo efetuadas por operadores morfolÃgicos, sendo a erosÃo e a dilataÃÃo os operadores morfolÃgicos elementares. Neste trabalho à apresentado um mecanismo de aprendizagem destinado à geraÃÃo automÃtica de templates, a serem utilizados em operadores morfolÃgicos de casamento inexato de padrÃes (em que o casamento nÃo precisa ser perfeito). Esse modelo de operador à aqui denominado de Operador MorfolÃgico Adaptativo de Casamento de PadrÃes (OMACP), e combina o formalismo da morfologia matemÃtica atravÃs de ELUTs (Elementary Look-Up Tables) com tÃcnicas de aprendizagem de mÃquina. Os operadores morfolÃgicos para casamento de padrÃes via ELUTs jà descritos na literatura permitem o casamento inexato de padrÃes, ou detecÃÃo com folga, em imagens digitais atravÃs da definiÃÃo de um intervalo em torno de um padrÃo de referÃncia. Esse intervalo aplicado em todos os pixels do padrÃo de referÃncia possui um valor constante e sua escolha depende de parÃmetros cujo ajuste normalmente à realizado tendo como base resultados empÃricos, alÃm de ser fortemente sensÃvel a idiossincrasia do usuÃrio. Este trabalho propÃe um mecanismo, baseado em parÃmetros estatÃsticos, que automatiza a escolha desse intervalo. AlÃm de nÃo considerÃ-lo mais um valor constante para todos os pixels do padrÃo de referÃncia. Tal mecanismo reduz assim a interferÃncia de um usuÃrio na definiÃÃo dos parÃmetros do operador morfolÃgico. Para comprovar a eficÃcia obtida com a inclusÃo tanto das tÃcnicas de aprendizagem quanto do mecanismo de escolha do intervalo em torno do padrÃo de referÃncia, foram realizados experimentos comparativos entre o OMACP proposto (com a inclusÃo das novas funcionalidades) com os operadores jà descritos na literatura sem essas alteraÃÃes. / Mathematical morphology is an approach applied in processing and image analysis problems that performs transformations in an object (image) by patterns of predefined forms. Such transformations are called morphological operators, with erosion and dilation being the elementary morphological operators. This work presents a machine learning mechanism applied for the automatic generation of templates, to be used by inexact template matching morphological operators. This model of operator is called Template Matching Adaptive Morphological Operator (OMACP), and combines the formalism of mathematical morphology through ELUTs (Elementary Look-Up Tables) with machine learning techniques. The ELUTs based template matching morphological operators already described in the literature allow inexact pattern recognition in digital images by defining a range around a reference pattern. This range has a constant value that is applied to all pixels of reference patterns, and its choice depends on parameters whose adjustments is usually performed based on empirical results, besides being highly sensitive to user idiosyncrasies. This work also proposes a mechanism, based on statistical parameters, which automates the choice of these range. Besides not consider it a constant value for all pixels of reference pattern. Such mechanism reduces the interference of a user to define the parameters of the morphological operator. To prove the effectiveness achieved with the inclusion of learning techniques and the choices mechanism of the range around the pattern reference, were performed comparative experiments between the proposed OMACP (with the inclusion of new features) with operators already studied without these features.

O mapeamento de ambientes é um dos maiores desafios para pesquisadores na área de navegação autônoma. As técnicas existentes estão divididas em dois importantes paradigmas, o mapeamento métrico e o topológico. Diversos métodos de mapeamento que combinam as vantagens de cada um desses paradigmas têm sido propostos. Este projeto consiste na adaptação e extensão de um sistema integrado para navegação autônoma de robôs móveis através do aperfeiçoamento da interface e também da incorporação de uma técnica de mapeamento topológico. Para isso, a técnica conhecida como Grade de Ocupação, utilizada em geral para mapeamento métrico é combinada com um método de esqueletização de imagens para a realização do mapeamento topológico. Além disso, transformações morfológicas de erosão e abertura, adequadas a ambientes reais, foram utilizadas, visando reduzir a influência de ruídos na abordagem proposta, uma vez que devido a ruídos inerentes as leituras sensoriais obtidas pelo robô, o mapa topológico gerado apresenta diversas linhas topológicas desnecessárias, dificultando consequentemente a tarefa de navegação autônoma. Vários experimentos foram executados para verificar a eficiência da combinação de técnicas proposta, tanto em nível de simulação quanto em um robô real. Os resultados obtidos demonstraram que a técnica de esqueletização de imagens combinada ao mapeamento métrico do ambiente é uma forma simples e viável de se obter as linhas topológicas do espaço livre do ambiente. A aplicação das transformações morfológicas demonstrou ser eficiente para a criação de mapas topológicos livres de ruído, uma vez que elimina grande parte das linhas topológicas geradas em conseqüência dos ruídos dos sensores do robô / Environment mapping has been a great challenge for many researchers in the autonomous navigation area. There are two important paradigms for mapping, metric and topological mapping. Several mapping methods that combine the advantages of each paradigm have been proposed. This project consists to the adaptation and extension of a mobile robots autonomous navigation integrated system by improving the interface and incorporation of a topological mapping technique. For this, the technique known as Occupation Grid for metric mapping is combined with an image skeletonization method used for topological mapping. This work also aims to propose a set of morphology transformations to generation of topological maps suitable for real environments, seeking to reduce influence of noise in performed mapping. The topological map generated through this combination presents several unnecessary topological lines, due noise inherent to the own robot ability of capturing sensor signals, hindering consequently the task of autonomous navigation. Several experiments have been performed to verify the efficiency of the proposed approach. The results obtained demonstrate that image skeletonization technique combined with the metric mapping is a simple and feasible method for obtaining the topological lines corresponding to free space of the environment. The application of the morphology transformations demonstrated to be a useful method to the creation of topological maps considerably less noise, since it eliminates most of the topological lines generated in consequence of noise in the sensors

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2017-08-08T13:18:51Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) DISSERTAÇÃO DO MESTRADO - RENAN.pdf: 2412478 bytes, checksum: 4cfaf4abac06be681bb16b4db23db3a2 (MD5) / Made available in DSpace on 2017-08-08T13:18:51Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) DISSERTAÇÃO DO MESTRADO - RENAN.pdf: 2412478 bytes, checksum: 4cfaf4abac06be681bb16b4db23db3a2 (MD5) Previous issue date: 2016-08-29 / A busca de métodos que possam auxiliar na atualização de produtos cartográficos existentes e propiciar uma base cartográfica atual é de fundamental importância para o planejamento urbano e consequentemente para o gerenciamento de todo o território nacional. As feições que devem ser atualizadas nos produtos cartográficos podem ser obtidas a partir de imagens de sensoriamento remoto e fotografias aéreas. E um dos atributos das feições que pode ser usado é a cor que é amplamente utilizado na extração pela análise visual e também pode auxiliar na extração automática das feições. Nessa dissertação, tem-se uma abordagem levando em consideração a extração pela cor usando a morfologia matemática e espaço de cores RGB e HSV. Denota-se Morfologia, por ajudar na análise de formas e objetos, e Matemática, por esta análise se basear na teoria de conjuntos, topologia, reticulados. A morfologia matemática foi inicialmente desenvolvida para análise de imagens binárias, onde a abordagem linear não se mostrava eficiente, e depois foi estendida para níveis de cinza. Nessa dissertação trabalha-se com as imagens no espaço de cores. Utiliza-se as ferramentas da morfologia matemática denotadas de erosão, dilatação e gradiente para a segmentação e detecção de bordas das imagens. Essas ferramentas e os espaços de cores RBG e HSV são a base dos algoritmos para a obtenção das bordas das feições na imagem, obtendo-se como resultados as feições do tipo estradas, edificações e vegetações existentes na imagem de alta resolução (ortofoto). A metodologia com gradiente no espaço HSV gera o melhor resultado e semelhante com fotointerpretação (interpretação visual). / Methods that assist a cartographic updating products and provide a current map base is fundamental importance for urban planning and therefore for managing the entire national territory. Features that must be updated in cartographic products can be obtained from remote sensing images and aerial photographs. And one of the attributes of the features that can be used is the color that is widely used in extraction by visual analysis and can also assist in the selfextracting features. In this dissertation, there is an approach considering the color extraction using mathematical morphology, RGB and HSV color space. It denotes Morphology, because of the analysis of shapes and objects, and mathematics, because this analysis is based on set theory, topology, lattices. Mathematical morphology was initially developed for the analysis of binary images, where the linear approach showed no efficient and was then extended to gray levels. In this dissertation, it works with images in color space. It uses the tools of mathematical morphology denoted erosion, dilation and gradient for segmentation and detection of images of edges. These tools and RBG color space and HSV are the basis of algorithms for obtaining the edges of the features in the image, obtaining thus the features of the type roads, existing buildings and vegetation in high resolution image (orthophoto). Methodology with gradient with HSV space is shown the best result and similar with photointerpretation (visual interpretation).

Orientador: Peter Sussner / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-05T07:48:58Z (GMT). No. of bitstreams: 1 Mesquita_MarcosEduardoRibeirodoValle_M.pdf: 893884 bytes, checksum: 9e4611642968683b375b78c5424ac19d (MD5) Previous issue date: 2005 / Resumo: Memórias associativas neurais são modelos do fenômeno biológico que permite o armazenamento de padrões e a recordação destes apos a apresentação de uma versão ruidosa ou incompleta de um padrão armazenado. Existem vários modelos de memórias associativas neurais na literatura, entretanto, existem poucos trabalhos comparando as varias propostas. Nesta dissertação comparamos sistematicamente o desempenho dos modelos mais influentes de memórias associativas neurais encontrados na literatura. Esta comparação está baseada nos seguintes critérios: capacidade de armazenamento, distribuição da informação nos pesos sinápticos, raio da bacia de atração, memórias espúrias e esforço computacional. Especial ênfase dado para as memórias associativas morfológicas cuja fundamentação matemática encontra-se na morfologia matemática e na álgebra de imagens / Abstract: Associative neural memories are models of biological phenomena that allow for the storage of pattern associations and the retrieval of the desired output pattern upon presentation of a possibly noisy or incomplete version of an input pattern. There are several models of neural associative memories in the literature, however, there are few works relating them. In this thesis, we present a systematic comparison of the performances of some of the most widely known models of neural associative memories. This comparison is based on the following criteria: storage capacity, distribution of the information over the synaptic weights, basin of attraction, number of spurious memories, and computational effort. The thesis places a special emphasis on morphological associative memories whose mathematical foundations lie in mathematical morphology and image algebra / Mestrado / Matematica Aplicada / Mestre em Matemática Aplicada

Orientador: Neucimar Jeronimo Leite / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Computação / Made available in DSpace on 2018-08-11T00:51:01Z (GMT). No. of bitstreams: 1 Souza_RafaelHenriqueCastanheirade_M.pdf: 1199945 bytes, checksum: 9b1286893d0b1751f7fce2dd2117cdbb (MD5) Previous issue date: 2008 / Resumo: O rastreamento automático de animais permite um estudo comportamental mais consistente e rápido do que o feito normalmente utilizando-se registro manual dos parâmetros de experimentos em biologia. O registro automático é realizado por um sistema analisador de imagens que, a partir de uma sequência contínua de quadros de um vídeo, calcula uma série de descritores associados ao movimento das cobaias. O objetivo deste trabalho é criar um sistema de rastreamento para experimentos de laboratório, levando em conta múltiplas cobaias que podem vir a sofrer oclusão. Além disso, pretende-se que o modelo de rastreamento proposto seja robusto a baixa qualidade do vídeo, além de ser geral o suficiente para ser adaptado a outros experimentos com poucas modificações / Abstract: The automatic tracking of animals allows a quicker and more consistent analysis of behaviour than the usual manual method for registering experimental parameters in biology. The automatic register of parameters is performed by a system that analyses a sequence of images and computes a number of descriptors that characterizes the behaviour of each target. Our objective is to create a framework for tracking in biology experiments, with multiple targets that may suffer occlusion. Besides, we intend to create a framework that can deal with low-quality videos and capable of being adapted to other classes of tracking / Mestrado / Processamento de Imagens / Mestre em Ciência da Computação

Orientador: Peter Sussner / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-11T11:23:27Z (GMT). No. of bitstreams: 1 Miyasaki_Rodolfo_M.pdf: 1324947 bytes, checksum: a4ab87815520ddfd33ed0ac1b2ffcac2 (MD5) Previous issue date: 2008 / Resumo: As memórias associativas (AMs - Associative Memories) permitem armazenar associações de padrões e recuperar desejados padrões de saída mesmo após a apresentação de possíveis versões incompletas e/ou distorcidas de um padrão de entrada. As memórias associativas fuzzy (FAMs - Fuzzy Associative emories) s¿ao modelos de AMs cujos padrões de entrada e saída são conjuntos fuzzy. As FAMs mostraram-se poderosas ferramentas na implementação em sistemas de base de regras fuzzy. O fato de modelos de FAMs estarem relacionadas à morfologia matemática (MM) levou ao recente desenvolvimento das memórias associativas morfológicas fuzzy (FMAMs - Fuzzy Morphological Associative Memories), em particular as memórias associativas fuzzy implicativas (IFAMs - Implicative Fuzzy Associative Memories). Os neurônios da FMAM executam uma das operações elementares da MM, i.'é, erosão, dilatação, anti-erosão ou anti-dilatação. Essa dissertação relaciona a existência de soluções nos sistemas de equações relacionais fuzzy (FREs - Fuzzy Relational Equations) à recordação perfeita das IFAMs. Formulamos o problema de escolher um modelo apropriado de IFAM para uma dada aplicação através de um problema de otimização. Mais precisamente, determinamos o modelo de IFAM dado pela t-norma parametrizada de Yager que minimiza o erro entre os padrões recordados e os desejados padrões de saída. Uma imagem em tons de cinza pode ser expressa como uma relação fuzzy e dado uma família de conjuntos fuzzy, pode-se comprimi-la através de FREs. Assim, surge o problema inverso de encontrar uma reconstrução da imagem original a partir da imagem comprimida. Essa dissertação de mestrado determina a melhor aproximação por meio de uma IFAM / Abstract: Associative Memories (AMs) allow for the storage of pattern associations and the retrieval of the desired output patterns upon the presentation of a possibly noisy or imcomplete version of an input pattern. Fuzzy Associative Memories (FAMs) are models of AMs whose input and output patterns are fuzzy sets. FAMs have proven to be a powerful tool for implementing fuzzy rule-based systems. The fact that FAMs models are related to mathematical morphology (MM) has led to the development of fuzzy morphological associative memories (FMAMs), in particular fuzzy implicative fuzzy associative memories (IFAMs). The neurons of an FMAM perform one of the elementary operations of MM which as erosion, dilation, anti-erosion and anti-dilation. This thesis relates the existence of solutions in systems of fuzzy relational equations (FREs) to the perfect recall using IFAMs. We formulated the problem of choosing an appriopriate IFAM model for a given application as an optimization problem. More precisely, we determined the IFAM model given by a parameterized Yager t-norm which minimizes the error between the recalled patterns and the desired output patterns. A gray-scale image can be expressed as a fuzzy relation and, given a family of fuzzy sets, it can be compressed by means of FREs. Thus, the inverse problem arises of finding a reconstruction of the image original based on the compression. This master thesis determines the best approximation by means of a IFAMs / Mestrado / Mestre em Matemática Aplicada