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Marcos Eduardo Valle
Universidade Estadual de Campinas

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Conference paper
Published: 16 May 2021 in Transactions on Petri Nets and Other Models of Concurrency XV
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Mathematical morphology is a useful theory of nonlinear operators widely used for image processing and analysis. Despite the successful application of morphological operators for binary and gray-scale images, extending them to vector-valued images is not straightforward because there are no unambiguous orderings for vectors. Among the many approaches to multivalued mathematical morphology, those based on total orders are particularly promising. Morphological operators based on total orders do not produce the so-called false-colors. On the downside, they often introduce irregularities in the output image. Although the irregularity issue has a rigorous mathematical formulation, we are not aware of an efficient method to quantify it. In this paper, we propose to quantify the irregularity of a vector-valued morphological operator using the Wasserstein metric. The Wasserstein metric yields the minimal transport cost for transforming the input into the output image. We illustrate by examples how to quantify the irregularity of vector-valued morphological operators using the Wasserstein metric.

ACS Style

Marcos Eduardo Valle; Samuel Francisco; Marco Aurélio Granero; Santiago Velasco-Forero. Measuring the Irregularity of Vector-Valued Morphological Operators Using Wasserstein Metric. Transactions on Petri Nets and Other Models of Concurrency XV 2021, 512 -524.

AMA Style

Marcos Eduardo Valle, Samuel Francisco, Marco Aurélio Granero, Santiago Velasco-Forero. Measuring the Irregularity of Vector-Valued Morphological Operators Using Wasserstein Metric. Transactions on Petri Nets and Other Models of Concurrency XV. 2021; ():512-524.

Chicago/Turabian Style

Marcos Eduardo Valle; Samuel Francisco; Marco Aurélio Granero; Santiago Velasco-Forero. 2021. "Measuring the Irregularity of Vector-Valued Morphological Operators Using Wasserstein Metric." Transactions on Petri Nets and Other Models of Concurrency XV , no. : 512-524.

Conference paper
Published: 16 April 2021 in Advances in Intelligent Systems and Computing
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Mathematical morphology (MM) is a theory of non-linear operators used for the processing and analysis of images. Morphological neural networks (MNNs) are neural networks whose neurons compute morphological operators. Dilations and erosions are the elementary operators of MM. From an algebraic point of view, a dilation and an erosion are operators that commute respectively with the supremum and infimum operations. In this paper, we present the linear dilation-erosion perceptron (\(\ell \)-DEP), which is given by applying linear transformations before computing a dilation and an erosion. The decision function of the \(\ell \)-DEP model is defined by adding a dilation and an erosion. Furthermore, training an \(\ell \)-DEP can be formulated as a convex-concave optimization problem. We compare the performance of the \(\ell \)-DEP model with other machine learning techniques using several classification problems. The computational experiments support the potential application of the proposed \(\ell \)-DEP model for binary classification tasks.

ACS Style

Angelica Lourenço Oliveira; Marcos Eduardo Valle. Linear Dilation-Erosion Perceptron Trained Using a Convex-Concave Procedure. Advances in Intelligent Systems and Computing 2021, 245 -255.

AMA Style

Angelica Lourenço Oliveira, Marcos Eduardo Valle. Linear Dilation-Erosion Perceptron Trained Using a Convex-Concave Procedure. Advances in Intelligent Systems and Computing. 2021; ():245-255.

Chicago/Turabian Style

Angelica Lourenço Oliveira; Marcos Eduardo Valle. 2021. "Linear Dilation-Erosion Perceptron Trained Using a Convex-Concave Procedure." Advances in Intelligent Systems and Computing , no. : 245-255.

Journal article
Published: 23 December 2020 in Neurocomputing
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Recurrent correlation neural networks (RCNNs), introduced by Chiueh and Goodman as an improved version of the bipolar correlation-based Hopfield neural network, can be used to implement high-capacity associative memories. In this paper, we extend the bipolar RCNNs for processing hypercomplex-valued data. Precisely, we present the mathematical background for a broad class of hypercomplex-valued RCNNs. Then, we address the stability of the new hypercomplex-valued RCNNs using synchronous and asynchronous update modes. Examples with bipolar, complex, hyperbolic, quaternion, and octonion-valued RCNNs are given to illustrate the theoretical results. Finally, computational experiments confirm the potential application of hypercomplex-valued RCNNs as associative memories designed for the storage and recall of gray-scale images.

ACS Style

Marcos Eduardo Valle; Rodolfo Anibal Lobo. Hypercomplex-valued recurrent correlation neural networks. Neurocomputing 2020, 432, 111 -123.

AMA Style

Marcos Eduardo Valle, Rodolfo Anibal Lobo. Hypercomplex-valued recurrent correlation neural networks. Neurocomputing. 2020; 432 ():111-123.

Chicago/Turabian Style

Marcos Eduardo Valle; Rodolfo Anibal Lobo. 2020. "Hypercomplex-valued recurrent correlation neural networks." Neurocomputing 432, no. : 111-123.

Journal article
Published: 04 September 2020 in Theoretical Computer Science
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Hypercomplex-valued neural networks, including quaternion-valued neural networks, can treat multi-dimensional data as a single entity. In this paper, we present the quaternion-valued recurrent projection neural networks (QRPNNs). Briefly, the QRPNNs are obtained by combining the non-local projection learning with the quaternion-valued recurrent correlation neural network (QRCNNs). We show that the QRPNNs overcome the cross-talk problem of the QRCNNs. Thus, they are appropriate to implement associative memories. Furthermore, computational experiments reveal that the QRPNNs exhibit greater storage capacity and noise tolerance than their corresponding QRCNNs.

ACS Style

Marcos Eduardo Valle; Rodolfo Anibal Lobo. Quaternion-valued recurrent projection neural networks on unit quaternions. Theoretical Computer Science 2020, 843, 136 -152.

AMA Style

Marcos Eduardo Valle, Rodolfo Anibal Lobo. Quaternion-valued recurrent projection neural networks on unit quaternions. Theoretical Computer Science. 2020; 843 ():136-152.

Chicago/Turabian Style

Marcos Eduardo Valle; Rodolfo Anibal Lobo. 2020. "Quaternion-valued recurrent projection neural networks on unit quaternions." Theoretical Computer Science 843, no. : 136-152.

Journal article
Published: 02 April 2020 in Mathematics
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Dilation and erosion are two elementary operations from mathematical morphology, a non-linear lattice computing methodology widely used for image processing and analysis. The dilation-erosion perceptron (DEP) is a morphological neural network obtained by a convex combination of a dilation and an erosion followed by the application of a hard-limiter function for binary classification tasks. A DEP classifier can be trained using a convex-concave procedure along with the minimization of the hinge loss function. As a lattice computing model, the DEP classifier assumes the feature and class spaces are partially ordered sets. In many practical situations, however, there is no natural ordering for the feature patterns. Using concepts from multi-valued mathematical morphology, this paper introduces the reduced dilation-erosion (r-DEP) classifier. An r-DEP classifier is obtained by endowing the feature space with an appropriate reduced ordering. Such reduced ordering can be determined using two approaches: one based on an ensemble of support vector classifiers (SVCs) with different kernels and the other based on a bagging of similar SVCs trained using different samples of the training set. Using several binary classification datasets from the OpenML repository, the ensemble and bagging r-DEP classifiers yielded mean higher balanced accuracy scores than the linear, polynomial, and radial basis function (RBF) SVCs as well as their ensemble and a bagging of RBF SVCs.

ACS Style

Marcos Eduardo Valle. Reduced Dilation-Erosion Perceptron for Binary Classification. Mathematics 2020, 8, 512 .

AMA Style

Marcos Eduardo Valle. Reduced Dilation-Erosion Perceptron for Binary Classification. Mathematics. 2020; 8 (4):512.

Chicago/Turabian Style

Marcos Eduardo Valle. 2020. "Reduced Dilation-Erosion Perceptron for Binary Classification." Mathematics 8, no. 4: 512.

Journal article
Published: 15 January 2020 in Applied Soft Computing
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In this paper, we present a dynamic wildfire warning map that combines both spatial and weather information. In particular, our wildfire early warning model is obtained by aggregating two indexes called wildfire risk and wildfire danger. The wildfire risk index, which is based on georeferenced features such as altitude and forest type, measures the fuel necessary for a wildfire to start at a certain location on a map. The wildfire danger uses weather conditions to yield temporal information concerning the possibility of a wildfire to spread. Machine learning techniques and fuzzy logic operations are used to determine the wildfire risk and danger indexes from available data. Although both wildfire risk and wildfire danger indexes can be used separately, using concepts from fuzzy logic, they can be combined to yield a wildfire warning system that takes into account both weather and static information. We illustrate the wildfire early warning model by considering weather and geographical data for the state of Acre.

ACS Style

I.D.B. Silva; M.E. Valle; L.C. Barros; J.F.C.A. Meyer. A wildfire warning system applied to the state of Acre in the Brazilian Amazon. Applied Soft Computing 2020, 89, 106075 .

AMA Style

I.D.B. Silva, M.E. Valle, L.C. Barros, J.F.C.A. Meyer. A wildfire warning system applied to the state of Acre in the Brazilian Amazon. Applied Soft Computing. 2020; 89 ():106075.

Chicago/Turabian Style

I.D.B. Silva; M.E. Valle; L.C. Barros; J.F.C.A. Meyer. 2020. "A wildfire warning system applied to the state of Acre in the Brazilian Amazon." Applied Soft Computing 89, no. : 106075.

Journal article
Published: 18 October 2019 in Neural Networks
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In this paper, we address the stability of a broad class of discrete-time hypercomplex-valued Hopfield-type neural networks. To ensure the neural networks belonging to this class always settle down at a stationary state, we introduce novel hypercomplex number systems referred to as real-part associative hypercomplex number systems. Real-part associative hypercomplex number systems generalize the well-known Cayley–Dickson algebras and real Clifford algebras and include the systems of real numbers, complex numbers, dual numbers, hyperbolic numbers, quaternions, tessarines, and octonions as particular instances. Apart from the novel hypercomplex number systems, we introduce a family of hypercomplex-valued activation functions called B-projection functions. Broadly speaking, a B-projection function projects the activation potential onto the set of all possible states of a hypercomplex-valued neuron. Using the theory presented in this paper, we confirm the stability analysis of several discrete-time hypercomplex-valued Hopfield-type neural networks from the literature. Moreover, we introduce and provide the stability analysis of a general class of Hopfield-type neural networks on Cayley–Dickson algebras.

ACS Style

Fidelis Zanetti de Castro; Marcos Eduardo Valle. A broad class of discrete-time hypercomplex-valued Hopfield neural networks. Neural Networks 2019, 122, 54 -67.

AMA Style

Fidelis Zanetti de Castro, Marcos Eduardo Valle. A broad class of discrete-time hypercomplex-valued Hopfield neural networks. Neural Networks. 2019; 122 ():54-67.

Chicago/Turabian Style

Fidelis Zanetti de Castro; Marcos Eduardo Valle. 2019. "A broad class of discrete-time hypercomplex-valued Hopfield neural networks." Neural Networks 122, no. : 54-67.

Conference paper
Published: 31 May 2019 in Transactions on Petri Nets and Other Models of Concurrency XV
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Mathematical morphology (MM) is a powerful non-linear theory that can be used for signal and image processing and analysis. Although MM can be very well defined on complete lattices, which are partially ordered sets with well defined extrema operations, there is no natural ordering for multivalued images such as hyper-spectral and color images. Thus, a great deal of effort has been devoted to ordering schemes for multivalued MM. In a reduced ordering, in particular, elements are ranked according to the so-called ordering mapping. Despite successful applications, morphological operators based on reduced orderings are usually too reliant on the ordering mapping. In many practical situations, however, the ordering mapping may be subject to uncertainties such as measurement errors or the arbitrariness in the choice of the mapping. In view of this remark, in this paper we present two approaches to multivalued MM based on an uncertain reduced ordering. The new operators are formulated as the solution of an optimization problem which, apart from the uncertainty, can circumvent the false value problem and deal with irregularity issues.

ACS Style

Mateus Sangalli; Marcos Eduardo Valle. Approaches to Multivalued Mathematical Morphology Based on Uncertain Reduced Orderings. Transactions on Petri Nets and Other Models of Concurrency XV 2019, 228 -240.

AMA Style

Mateus Sangalli, Marcos Eduardo Valle. Approaches to Multivalued Mathematical Morphology Based on Uncertain Reduced Orderings. Transactions on Petri Nets and Other Models of Concurrency XV. 2019; ():228-240.

Chicago/Turabian Style

Mateus Sangalli; Marcos Eduardo Valle. 2019. "Approaches to Multivalued Mathematical Morphology Based on Uncertain Reduced Orderings." Transactions on Petri Nets and Other Models of Concurrency XV , no. : 228-240.

Conference paper
Published: 31 May 2019 in Transactions on Petri Nets and Other Models of Concurrency XV
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Mathematical morphology (MM) is a powerful theory widely used for image processing and analysis. Distance-based morphological operators are parametrized by a reference value so that a dilation enlarges regions of an image similar to the reference while an erosion shrinks them. In this paper, we first characterize distance-based erosions, dilations, and gradients as a function of the reference. Then, assuming the reference is a sample from a random variable, we use a descriptive statistic to obtain relevant information on a certain distance-based morphological operator. We validate our approach by presenting a successful application of some statistics of distance-based morphological operators for edge detection in color images.

ACS Style

Arlyson Alves Do Nascimento; Marcos Eduardo Valle. Characterization and Statistics of Distance-Based Elementary Morphological Operators. Transactions on Petri Nets and Other Models of Concurrency XV 2019, 362 -374.

AMA Style

Arlyson Alves Do Nascimento, Marcos Eduardo Valle. Characterization and Statistics of Distance-Based Elementary Morphological Operators. Transactions on Petri Nets and Other Models of Concurrency XV. 2019; ():362-374.

Chicago/Turabian Style

Arlyson Alves Do Nascimento; Marcos Eduardo Valle. 2019. "Characterization and Statistics of Distance-Based Elementary Morphological Operators." Transactions on Petri Nets and Other Models of Concurrency XV , no. : 362-374.

Preprint
Published: 11 February 2019
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Max-C and min-D projection autoassociative fuzzy morphological memories (max-C and min-D PAFMMs) are two layer feedforward fuzzy morphological neural networks able to implement an associative memory designed for the storage and retrieval of finite fuzzy sets or vectors on a hypercube. In this paper we address the main features of these autoassociative memories, which include unlimited absolute storage capacity, fast retrieval of stored items, few spurious memories, and an excellent tolerance to either dilative noise or erosive noise. Particular attention is given to the so-called PAFMM of Zadeh which, besides performing no floating-point operations, exhibit the largest noise tolerance among max-C and min-D PAFMMs. Computational experiments reveal that Zadeh's max-C PFAMM, combined with a noise masking strategy, yields a fast and robust classifier with strong potential for face recognition.

ACS Style

Alex Santana Dos Santos; Marcos Eduardo Valle. Max-C and Min-D Projection Autoassociative Fuzzy Morphological Memories: Theory and Applications for Face Recognition. 2019, 1 .

AMA Style

Alex Santana Dos Santos, Marcos Eduardo Valle. Max-C and Min-D Projection Autoassociative Fuzzy Morphological Memories: Theory and Applications for Face Recognition. . 2019; ():1.

Chicago/Turabian Style

Alex Santana Dos Santos; Marcos Eduardo Valle. 2019. "Max-C and Min-D Projection Autoassociative Fuzzy Morphological Memories: Theory and Applications for Face Recognition." , no. : 1.

Conference paper
Published: 19 December 2018 in Proceeding Series of the Brazilian Society of Computational and Applied Mathematics
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An autoassociative memory is an input-output system designed for the storage and recall of a finite set of items. In this work, we present the class of complete lattice projection autoassociative memories (CLPAMs). A CLPAM is a non-distributive autoassociative memory defined by a neural network with a hidden layer of morphological neurons. More importantly, a CLPAM is formulated using only the partial ordering of a complete lattice. As an example of CLPAM, we introduce the so called distance-based projection autoassociative memories (DBPAMs) which exhibit an excellent tolerance to salt-and-pepper noise.

ACS Style

Alex Santana Dos Santos; Marcos Eduardo Do Valle; Arlyson Alves Do Nascimento. An Introduction to the Complete Lattice Projection Autoassociative Memories: Definitions and Examples. Proceeding Series of the Brazilian Society of Computational and Applied Mathematics 2018, 6, 1 .

AMA Style

Alex Santana Dos Santos, Marcos Eduardo Do Valle, Arlyson Alves Do Nascimento. An Introduction to the Complete Lattice Projection Autoassociative Memories: Definitions and Examples. Proceeding Series of the Brazilian Society of Computational and Applied Mathematics. 2018; 6 (2):1.

Chicago/Turabian Style

Alex Santana Dos Santos; Marcos Eduardo Do Valle; Arlyson Alves Do Nascimento. 2018. "An Introduction to the Complete Lattice Projection Autoassociative Memories: Definitions and Examples." Proceeding Series of the Brazilian Society of Computational and Applied Mathematics 6, no. 2: 1.

Journal article
Published: 12 September 2018 in TEMA - Tendências em Matemática Aplicada e Computacional
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Associative memories are biologically inspired models designed for the storage and recall by association. Such models aim to store a finite set of associations, called the fundamental memory set. The generalized exponential bidirectional fuzzy associative memory (GEB-FAM) is a heteroassociative memory model designed for the storage and recall of fuzzy sets. A similarity measure, that is, a function that indicates how much two fuzzy sets are equal, is at the core of a GEB-FAM model. In this paper, we present a detailed study on the use of cardinality-based similarity measures in the definition of a GEB-FAM. Moreover, we evaluate the performance of the GEB-FAMs defined using such measures in a face recognition problem.

ACS Style

Aline Cristina Souza; Marcos Eduardo Valle. Generalized Exponential Bidirectional Fuzzy Associative Memory with Fuzzy Cardinality-Based Similarity Measures Applied to Face Recognition. TEMA - Tendências em Matemática Aplicada e Computacional 2018, 19, 221 .

AMA Style

Aline Cristina Souza, Marcos Eduardo Valle. Generalized Exponential Bidirectional Fuzzy Associative Memory with Fuzzy Cardinality-Based Similarity Measures Applied to Face Recognition. TEMA - Tendências em Matemática Aplicada e Computacional. 2018; 19 (2):221.

Chicago/Turabian Style

Aline Cristina Souza; Marcos Eduardo Valle. 2018. "Generalized Exponential Bidirectional Fuzzy Associative Memory with Fuzzy Cardinality-Based Similarity Measures Applied to Face Recognition." TEMA - Tendências em Matemática Aplicada e Computacional 19, no. 2: 221.

Conference paper
Published: 04 July 2018 in Communications in Computer and Information Science
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In this paper we introduce the class of fuzzy kernel associative memories (fuzzy KAMs). Fuzzy KAMs are derived from single-step generalized exponential bidirectional fuzzy associative memories by interpreting the exponential of a fuzzy similarity measure as a kernel function. The output of a fuzzy KAM is obtained by summing the desired responses weighted by a normalized evaluation of the kernel function. Furthermore, in this paper we propose to estimate the parameter of a fuzzy KAM by maximizing the entropy of the model. We also present two approaches for pattern classification using fuzzy KAMs. Computational experiments reveal that fuzzy KAM-based classifiers are competitive with well-known classifiers from the literature.

ACS Style

Aline Cristina De Souza; Marcos Eduardo Valle. Fuzzy Kernel Associative Memories with Application in Classification. Communications in Computer and Information Science 2018, 290 -301.

AMA Style

Aline Cristina De Souza, Marcos Eduardo Valle. Fuzzy Kernel Associative Memories with Application in Classification. Communications in Computer and Information Science. 2018; ():290-301.

Chicago/Turabian Style

Aline Cristina De Souza; Marcos Eduardo Valle. 2018. "Fuzzy Kernel Associative Memories with Application in Classification." Communications in Computer and Information Science , no. : 290-301.

Conference paper
Published: 04 July 2018 in Programmieren für Ingenieure und Naturwissenschaftler
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Mathematical morphology is a theory with applications in image processing and analysis. In a supervised approach to mathematical morphology, pixel values are ranked according to sets of foreground and background elements specified a priori by the user. In this paper, we introduce a supervised fuzzy color-based approach to color mathematical morphology that provides an elegant alternative to the support vector machine-based approach developed by Velasco-Forero and Angulo. Briefly, color elements are ranked according to the degree of truth of the proposition “the considered color is a foreground color but it is not a background color” in the new supervised color morphological approach. Furthermore, the vagueness and uncertainty inherent to the description of colors by humans can be naturally incorporated in the new approach using the concept of fuzzy colors.

ACS Style

Mateus Sangalli; Marcos Eduardo Valle. Color Mathematical Morphology Using a Fuzzy Color-Based Supervised Ordering. Programmieren für Ingenieure und Naturwissenschaftler 2018, 278 -289.

AMA Style

Mateus Sangalli, Marcos Eduardo Valle. Color Mathematical Morphology Using a Fuzzy Color-Based Supervised Ordering. Programmieren für Ingenieure und Naturwissenschaftler. 2018; ():278-289.

Chicago/Turabian Style

Mateus Sangalli; Marcos Eduardo Valle. 2018. "Color Mathematical Morphology Using a Fuzzy Color-Based Supervised Ordering." Programmieren für Ingenieure und Naturwissenschaftler , no. : 278-289.

Journal article
Published: 01 April 2018 in Neural Networks
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Autoassociative morphological memories (AMMs) are robust and computationally efficient memory models with unlimited storage capacity. In this paper, we present the max-plus and min-plus projection autoassociative morphological memories (PAMMs) as well as their compositions. Briefly, the max-plus PAMM yields the largest max-plus combination of the stored vectors which is less than or equal to the input. Dually, the vector recalled by the min-plus PAMM corresponds to the smallest min-plus combination which is larger than or equal to the input. Apart from unlimited absolute storage capacity and one step retrieval, PAMMs and their compositions exhibit an excellent noise tolerance. Furthermore, the new memories yielded quite promising results in classification problems with a large number of features and classes.

ACS Style

Alex Santana Dos Santos; Marcos Eduardo Valle. Max-plus and min-plus projection autoassociative morphological memories and their compositions for pattern classification. Neural Networks 2018, 100, 84 -94.

AMA Style

Alex Santana Dos Santos, Marcos Eduardo Valle. Max-plus and min-plus projection autoassociative morphological memories and their compositions for pattern classification. Neural Networks. 2018; 100 ():84-94.

Chicago/Turabian Style

Alex Santana Dos Santos; Marcos Eduardo Valle. 2018. "Max-plus and min-plus projection autoassociative morphological memories and their compositions for pattern classification." Neural Networks 100, no. : 84-94.

Reference entry
Published: 22 February 2018 in Wiley Encyclopedia of Electrical and Electronics Engineering
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ACS Style

Marcos Eduardo Valle; Peter Sussner; Alex S. Santos. Morphological Associative Memories. Wiley Encyclopedia of Electrical and Electronics Engineering 2018, 1 -20.

AMA Style

Marcos Eduardo Valle, Peter Sussner, Alex S. Santos. Morphological Associative Memories. Wiley Encyclopedia of Electrical and Electronics Engineering. 2018; ():1-20.

Chicago/Turabian Style

Marcos Eduardo Valle; Peter Sussner; Alex S. Santos. 2018. "Morphological Associative Memories." Wiley Encyclopedia of Electrical and Electronics Engineering , no. : 1-20.

Conference paper
Published: 14 February 2018 in CNMAC 2017 - XXXVII Congresso Nacional de Matemática Aplicada e Computacional
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As Memórias Associativas Bidirecionais Exponenciais Fuzzy Generalizadas (GEBFAMs) são modelos heteroassociativos projetados para o armazenamento e recordação de pares de conjuntos fuzzy. Tais modelos são definidos com base em uma medida de similaridade, função que indica o grau com que dois conjutos fuzzy são iguais. Neste trabalho, apresentamos a aplicação da GEB-FAM obtida a partir de uma medida de similaridade estrutural `a um problema de reconhecimento de faces.

ACS Style

Aline Cristina De Souza; Marcos Eduardo Valle. Memória Associativa Bidirecional Exponencial Fuzzy Generalizada com Medida de Similaridade Estrutural Aplicada a um Problema de Reconhecimento de Faces. CNMAC 2017 - XXXVII Congresso Nacional de Matemática Aplicada e Computacional 2018, 6, 1 .

AMA Style

Aline Cristina De Souza, Marcos Eduardo Valle. Memória Associativa Bidirecional Exponencial Fuzzy Generalizada com Medida de Similaridade Estrutural Aplicada a um Problema de Reconhecimento de Faces. CNMAC 2017 - XXXVII Congresso Nacional de Matemática Aplicada e Computacional. 2018; 6 (1):1.

Chicago/Turabian Style

Aline Cristina De Souza; Marcos Eduardo Valle. 2018. "Memória Associativa Bidirecional Exponencial Fuzzy Generalizada com Medida de Similaridade Estrutural Aplicada a um Problema de Reconhecimento de Faces." CNMAC 2017 - XXXVII Congresso Nacional de Matemática Aplicada e Computacional 6, no. 1: 1.

Conference paper
Published: 14 February 2018 in CNMAC 2017 - XXXVII Congresso Nacional de Matemática Aplicada e Computacional
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In this paper, we generalize the famous Hopfield neural network to unit octonions. In the proposed model, referred to as the continuous-valued octonionic Hopfield neural network (CV-OHNN), the next state of a neuron is obtained by setting its octonionic activation potential to length one. We show that, like the traditional Hopfield network, a CV-OHNN operating in an asynchronous update mode always settles down to an equilibrium state under mild conditions on the octonionic synaptic weights.

ACS Style

Fidelis Zanetti De Castro; Marcos Eduardo Valle. Continuous-Valued Octonionic Hopfield Neural Network. CNMAC 2017 - XXXVII Congresso Nacional de Matemática Aplicada e Computacional 2018, 6, 1 .

AMA Style

Fidelis Zanetti De Castro, Marcos Eduardo Valle. Continuous-Valued Octonionic Hopfield Neural Network. CNMAC 2017 - XXXVII Congresso Nacional de Matemática Aplicada e Computacional. 2018; 6 (1):1.

Chicago/Turabian Style

Fidelis Zanetti De Castro; Marcos Eduardo Valle. 2018. "Continuous-Valued Octonionic Hopfield Neural Network." CNMAC 2017 - XXXVII Congresso Nacional de Matemática Aplicada e Computacional 6, no. 1: 1.

Proceedings article
Published: 21 October 2017 in XXV Congresso de Iniciação Científica da Unicamp
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ACS Style

Mateus Sangalli; Marcos Eduardo Valle. Image Processing and Analysis via Fuzzy Transform. XXV Congresso de Iniciação Científica da Unicamp 2017, 1 .

AMA Style

Mateus Sangalli, Marcos Eduardo Valle. Image Processing and Analysis via Fuzzy Transform. XXV Congresso de Iniciação Científica da Unicamp. 2017; ():1.

Chicago/Turabian Style

Mateus Sangalli; Marcos Eduardo Valle. 2017. "Image Processing and Analysis via Fuzzy Transform." XXV Congresso de Iniciação Científica da Unicamp , no. : 1.

Conference paper
Published: 01 October 2017 in 2017 Brazilian Conference on Intelligent Systems (BRACIS)
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Continuous-valued quaternionic Hopfield neural network (CV-QHNN) generalizes the traditional Hopfield network for the storage and retrieval of vectors whose components are unit quaternions. In this paper, we investigate the performance of the CV-QHNN for the retrieval of color images using three different color spaces: RGB, HSV, and CIE-HCL. We point out that a direct conversion from the RGB to unit quaternions may result distortions in which visually different colors are mapped into close quaternions. Preliminary computational experiments reveal that the CV-QHNN based on the HSV color space can be more effective for the removal of noise from a corrupted color image.

ACS Style

Fidelis Zanetti De Castro; Marcos Eduardo Valle. Continuous-Valued Quaternionic Hopfield Neural Network for Image Retrieval: A Color Space Study. 2017 Brazilian Conference on Intelligent Systems (BRACIS) 2017, 186 -191.

AMA Style

Fidelis Zanetti De Castro, Marcos Eduardo Valle. Continuous-Valued Quaternionic Hopfield Neural Network for Image Retrieval: A Color Space Study. 2017 Brazilian Conference on Intelligent Systems (BRACIS). 2017; ():186-191.

Chicago/Turabian Style

Fidelis Zanetti De Castro; Marcos Eduardo Valle. 2017. "Continuous-Valued Quaternionic Hopfield Neural Network for Image Retrieval: A Color Space Study." 2017 Brazilian Conference on Intelligent Systems (BRACIS) , no. : 186-191.