Morphological Associative Memories Research Articles

New binary associative memory model based on the XOR operation

An associative memory is a special type of artificial neural network that has the purpose of store input patterns with their corresponding output patterns and efficiently recall a pattern from a noise-distorted version. Presented in this article is a new framework for constructing a binary associative memory model based on two new autoinverse operations called extended XOR/XNOR; these new operations are generated from the XOR/XNOR operations, respectively. Two types of associative memory are generated with this model: the max type (XOR-AM max), which is constructed with the maximum of the extended XOR operation, and the min type (XOR-AM min), which is constructed with the minimum of the extended XNOR operation. The XOR-AM max exhibits tolerance against the presence of patterns distorted by dilative noise, whereas the XOR-AM min exhibits tolerance against the presence of patterns distorted by erosive noise; both types of memory converge in a single step, use the same extended XOR/XNOR operator for learning and recalling phases, operate in heteroassociative and autoassociative modes, and show infinite storage capacity for the autoassociative mode. Finally, computer simulation results are presented for the new memories based on the extended XOR/XNOR (XOR-AM), which have better or equal performance compared to other associative memories. For the experiments with mixed noise, the conditions established by the kernel method proposed by Ritter for Morphological Associative Memories were conserved, and the solution algorithm proposed by Hattori for the construction of the kernel patterns of these memories was modified.

Intelligent Diagnosis of Rolling Bearing Fault Based on QFMAM

In order to solve the problem that the accuracy is not high when the traditional fuzzy morphological associative memories network (FMAM) is used to classify samples, based on quantum superposition and collapse, the quantum fuzzy morphological associative memories network (QFMAM) is proposed. In QFMAM, the structural element is constructed by the qubit system and the qubit probability represents corresponding membership degree to obtain adaptive structural elements. The samples are preprocessed first and then classified to ensure high classification accuracy. QFMAM, FMAM, support vector machine (SVM) and naive Bayes classifier (NBC) are used to classify simulation data and experimental signals of rolling bearings respectively. Comparing the performance of the four classifiers, it is obvious that the training time of QFMAM is far less than SVM and NBC, and the classification accuracy of the test samples by QFMAM is higher than that by the other three classifiers. QFMAM is very suitable for intelligent diagnosis of rolling bearing fault.

Mobile Application for Breast Cancer Diagnosis Using Morphological Associative Memories Implemented on a Cloud Platform

The astounding advances that have been observed in mobile device technologies and their underlying algorithms have prompted a worldwide surge in attention to their capabilities and potential for improving different human activities. The present work is framed by the academic cooperation process between Mexico and Saudi Arabia; it consists of the description of the design and development of a mobile information system aimed at performing diagnosis and verification of breast cancer using an application for mobile devices. The problem to be solved is represented as a binary classification problem between healthy patients and people that have been confirmed as control cases. The classification algorithm is a hybrid model, consisting of Morphological Associative Memories and the k-Nearest Neighbor classifier. The hybrid model improves upon the performance of its components. The proposed model was implemented on a cloud computing platform in order to optimize the response time for the diagnosis. A comparative study of our proposal and the state of the art shows that the proposed mobile information system has a high classification performance as well as a low false positive rate.

Extreme learning machine for a new hybrid morphological/linear perceptron

Morphological neural networks (MNNs) can be characterized as a class of artificial neural networks that perform an operation of mathematical morphology at every node, possibly followed by the application of an activation function. Morphological perceptrons (MPs) and (gray-scale) morphological associative memories are among the most widely known MNN models. Since their neuronal aggregation functions are not differentiable, classical methods of non-linear optimization can in principle not be directly applied in order to train these networks. The same observation holds true for hybrid morphological/linear perceptrons and other related models. Circumventing these problems of non-differentiability, this paper introduces an extreme learning machine approach for training a hybrid morphological/linear perceptron, whose morphological components were drawn from previous MP models. We apply the resulting model to a number of well-known classification problems from the literature and compare the performance of our model with the ones of several related models, including some recent MNNs and hybrid morphological/linear neural networks.

COMPUTATIONAL INTELLIGENCE FOR SHOEPRINT RECOGNITION

Shoeprint marks present valuable information for forensic investigators to resolve a crime. These marks can be helpful to find the brand of the shoe and can make the investigation easier. In this paper, we present an associative model-based algorithm to match noisy shoeprint patterns with a brand of shoe. The shoeprints are corrupted with additive, subtractive and mixed noises. A particular case of subtractive noise are partial shoeprints such as toe, heel, left-half and right-half prints. The Morphological Associative Memories (MAMs) were applied. Both memories, max and min, recognize noisy shoeprints corrupted with 98% additive and subtractive noise, respectively, with an effectiveness of 100%. The images corrupted with mixed noise were recognized when the additive or subtractive noise applied was greater than the mixed noise; in this case, the recalling was around 70%, otherwise, both memories failed to recognize the shoeprints.

On simulating one-trial learning using morphological neural networks

“Learning once, remembering forever”, this wonderful cognitive phenomenon sometimes occurs in the learning process of human beings. Psychologists call this psychological phenomenon “one-trial learning”. The traditional artificial neural networks can simulate the psychological phenomenon of “implicit learning”, but can’t simulate the cognitive phenomenon of “one-trial learning”. Therefore, cognitive psychology gives a challenge to the traditional artificial neural networks. From two aspects of theory and practice in this paper, the possibility of simulating this kind of psychological phenomenon was explored by using morphological neural networks. This paper takes advantage of morphological associative memory networks to realize the simulation of “one-trial learning” for the first time, and gives 5 simulating practical examples. Theoretical analysis and simulation experiments show that the morphological associative memory networks are a higher effective machine learning method, and can better simulate the cognitive phenomenon of “one-trial learning”, therefore provide a theoretical basis and technological support for the study of intelligent science and cognitive science.

Interval-valued fuzzy morphological associative memories: Some theoretical aspects and applications

Fuzzy morphological associative memories (FMAMs) are generalizations of many well-known fuzzy associative memory (FAM) models from the literature and have been employed to implement fuzzy rule-based systems. Inspired by the advent of type-2 fuzzy systems and in particular interval type-2 fuzzy systems, we present some theoretical foundations of interval-valued fuzzy morphological associative memories (IV-FMAMs), whose weight matrices can be constructed using representable interval-valued fuzzy operators, and we introduce a novel IV-FMAM approach towards interval type-2 fuzzy inference systems. The paper also includes some experimental results in non-linear function identification as well as time series prediction. These results are compared with the ones produced by some interval and general type-2 fuzzy models from the recent literature.

Development of associative memories with transformed data

This study is concerned with the enhancements of performance of associative memories by nonlinear transformations (mappings) of spaces of data to be associated. The data are first transformed into a new space and then the resulting objects (patterns) are stored in the memory. The objective of the transformations is to enhance the recall abilities of the memories. Nonlinear transformations are applied to (i) transform the input space, (ii) transform the output space and (iii) transform both input and output spaces. The transformations are realized in the form of piecewise linear functions whose parameters are optimized with the use of Particle Swarm Optimization (PSO). The optimization is carried out for one-way recall as well as for bi-directional recall. A comprehensive suite of experiments involves several types of associative memories such as correlation associative memories, fuzzy associative memories and morphological associative memories. The experiments reveal some interesting relationships between the parameters of the nonlinear mappings and the resulting quality of the recall. They also help quantify the capabilities of the nonlinear mappings to improve the quality of recall.

A novel image steganography scheme based on morphological associative memory and permutation schema

ABSTRACTSteganography is the art and science of hiding a message in a carrier, in such a manner that no one, except the sender and intended recipient, can guess the existence of the message; it is a form of security through obscurity. Often, steganography algorithms using discrete cosine transform are detectable through steganalysis attacks. To reduce detectability of the stego, we propose an image steganography algorithm in transform domain based on morphological associative memory, permutation approach, and matrix encoding. In our proposed algorithm, in order to insert a secret message in the cover image, first, we map the cover image to a morphological representation containing morphological coefficients, and then bits of secret message are inserted into the image by permutation approach and matrix encoding. Permutation approach leads to unique distribution of secret message in the carrier, and the use of matrix encoding minimizes the number of coefficients needed to be changed because of inserting secret message. In our experiments, we compared the quality of stego, time complexity, and robustness of our method with state‐of‐art image steganography algorithms (F5 and morphological steganography) with an equal payload. The experimental results showed that the proposed method is able to produce insignificant visual distortion compared with other traditional approaches. To test the robustness of our proposed algorithm, we used wavelet‐based and block‐based steganalysis methods. The obtained results showed a high level of robustness of our algorithm against steganalysis attacks. Copyright © 2014 John Wiley & Sons, Ltd.

Morphological Associative Memories for Gray-Scale Image Encryption

This work describes a novel method for encrypting gray-scale images using an associative approach. The image is divided in blocks which are used to build max and min Morphological associative memories. The key is private and it depends on the number of blocks. The main advantage of this method is that the cyphertext does not have the same size than the original image; therefore, since the beginning the adversary cannot know what the image means.

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En este artículo se presenta un método de memorias asociativas alfa-beta para imágenes (MAABI), que origina la transformada alfa-beta (TAB) para imágenes. Esta transformada se aplica a sub-bloques de una imagen en escala de grises y genera una memoria heteroasociativa alfa-beta en cada sub-bloque, a partir de una matriz de transformación dada con la transformada alfa-beta inversa (TABI) recuperamos los patrones de la imagen original. El proceso de compresión de datos se divide en tres fases: transformación, cuantificación y codificación; este modelo se enfoca en la transformación de la imagen para compararse con la transformada morfológica (TM), basada en las memorias asociativas morfológicas (MAM). Se utiliza la entropía de Shannon como medida de la cantidad de bits contenidos en cada imagen. La TM, al igual que métodos tradicionales, como la transformada discreta del coseno (DCT) o la transformada discreta wavelet (DWT), no ofrece compresión alguna de la imagen; por lo que una de las ventajas ofrecidas por la TAB es que la imagen transformada posee una menor entropía que la imagen original. Asimismo, la TAB ofrece rapidez en el procesamiento con un reducido número de operaciones elementales, tales como sumas, restas, máximos y mínimos.

Heteroassociative morphological memories based on four-dimensional storage

The heteroassociative morphological memories (HMMs) are one kind of morphological associative memories (MAMs). Although they have many advantages, there is a serious shortcoming: HMMs are incomplete, that is, they cannot give a guarantee of perfect recall memories, even though without any input noises. This problem has become a bottleneck in the development and applications of HMMs, and also one of difficult subjects in this field. Aiming at the problem, this paper presents a new method of HMMs, called four-dimensional stored HMMs (FDSHMMs). It includes three work stages: pretreatment, memory, and recall. Both computational method and experimental method show that FDSHMMs can significantly improve the HMMs. They can guarantee perfect recall memories for perfect inputs or within a certain noise range, just like the auto-associative morphological memories (AMMs) can do. FDSHMMs remove the bottleneck of HMMs and bring us a bright prospect of applications.

Behavioural study of median associative memory under true-colour image patterns

Median associative memories (MED-AMs) are a special type of associative memory that substitutes the maximum and minimum operators of a morphological associative memory with the median operator. This associative model has been applied to restore grey scale images and provided a better performance than morphological associative memories when the patterns are altered with mixed noise. Despite their power, MED-AMs have not been adopted in problems related with true-colour patterns. In this paper, we describe how MED-AMs can be applied to problems involving true-colour patterns. Furthermore, a complete study of the behaviour of this associative model in the restoration of true-colour images is performed using a benchmark of 16,000 images altered by different noise types.

The Kosko Subsethood Fuzzy Associative Memory (KS-FAM): Mathematical Background and Applications in Computer Vision

Many well-known fuzzy associative memory (FAM) models can be viewed as (fuzzy) morphological neural networks (MNNs) because they perform an operation of (fuzzy) mathematical morphology at every node, possibly followed by the application of an activation function. The vast majority of these FAMs represent distributive models given by single-layer matrix memories. Although the Kosko subsethood FAM (KS-FAM) can also be classified as a fuzzy morphological associative memory (FMAM), the KS-FAM constitutes a two-layer non-distributive model. In this paper, we prove several theorems concerning the conditions of perfect recall, the absolute storage capacity, and the output patterns produced by the KS-FAM. In addition, we propose a normalization strategy for the training and recall phases of the KS-FAM. We employ this strategy to compare the error correction capabilities of the KS-FAM and other fuzzy and gray-scale associative memories in terms of some experimental results concerning gray-scale image reconstruction. Finally, we apply the KS-FAM to the task of vision-based self-localization in robotics.

A new method for constructing kernel vectors in morphological associative memories of binary patterns

Kernel vectors represent an elegant representation for the retrieval of pattern associations, where the input patterns are corrupted by both erosive and dilative noise. However, their action completely fails when a particular kind of erosive noise, even of very low percentage, corrupts the input pattern. In this paper, a theoretical justification of this fact is given and a new method is proposed for the construction of kernel vectors for binary patterns associations. The new kernels are not binary but ?gray?, because they contain elements with values in the interval [0, 1]. It is shown, both theoretically and experimentally that the new kernel vectors carry the good properties of conventional kernel vectors and, at the same time, they can be easily computed. Moreover, they do not suffer from the particular noise deficiency of the conventional kernel vectors. The recalling result is in general a gray pattern, which in the sequel undergoes a simple thresholding action and passes through a simple Hamming network to produce high recall rates, even in heavily corrupted patterns. Retrieval of pattern associations is very significant for a variety of scientific disciplines including data analysis, signal and image understanding and intelligent control.

Storage and recall capabilities of fuzzy morphological associative memories with adjunction-based learning

We recently employed concepts of mathematical morphology to introduce fuzzy morphological associative memories (FMAMs), a broad class of fuzzy associative memories (FAMs). We observed that many well-known FAM models can be classified as belonging to the class of FMAMs. Moreover, we developed a general learning strategy for FMAMs using the concept of adjunction of mathematical morphology. In this paper, we describe the properties of FMAMs with adjunction-based learning. In particular, we characterize the recall phase of these models. Furthermore, we prove several theorems concerning the storage capacity, noise tolerance, fixed points, and convergence of auto-associative FMAMs. These theorems are corroborated by experimental results concerning the reconstruction of noisy images. Finally, we successfully employ FMAMs with adjunction-based learning in order to implement fuzzy rule-based systems in an application to a time-series prediction problem in industry.

Research on the Framework of Morphological Associative Memories

The morphological associative memories(MAM)are a class of extremely new artificial neural networks.Typical objects of MAM include real MAM(RMAM),complex MAM(CMAM),morphological bidirectional associative memories(MBAM),fuzzy MAM(FMAM),enhanced FMAM(EFMAM),fuzzy MBAM(FMBAM),and so on.They have many attractive advantages and features.However,they have the same morphological theoretical base in essence and it is therefore possible to unify them in a framework of MAM.At the same time,it is one of the most important and difficult researches to construct the unified framework of associative memories.The paper tries to solve the problem.Firstly,in this paper,the algebraic structure in computing of MAM is analyzed in order to establish reliable computing base of the framework.Secondly,the basic operations and the common features in the class of MAM are analyzed,and the essential attributes and methods of MAM are extracted.On this basis,the norms and operators of MAM are defined.And finally,the main theorems of MAM are refined and proved.Thus,a unified theoretical framework of MAM is established.The significance of the framework consists in:(1)The objects of MAM are unified together in mathematics and are therefore better for revealing their peculiarities and the essence of MAM;(2)It can help people find some new methods for morphological associative memories,thereby solving more problems of associative memories,pattern recognition and fuzzy reasoning.

Behavior of morphological associative memories with true-color image patterns

Morphological associative memories (MAMs) are a special type of associative memory which exhibit optimal absolute storage capacity and one-step convergence. This associative model substitutes the additions and multiplications used by other models by computing maximums and minimums. This type of associative model has been applied to different pattern recognition problems including face localization and gray scale image restoration. Despite of his power, MAMs have not been applied in problems that involve true-color patterns. In this paper it is described how a MAM can be applied in problems involving true-color patterns. Furthermore, a complete study of the behavior of this associative model in the restoration of true-color images is performed using a benchmark of 14 400 images altered by different type of noises.

Small-world Network構造を持つ形態学的連想記憶モデルの実現と評価

Small-world Network構造を持つ形態学的連想記憶モデルの実現と評価

Morphological Transform for Image Compression

A new method for image compression based on morphological associative memories (MAMs) is presented. We used the MAM to implement a new image transform and applied it at the transformation stage of image coding, thereby replacing such traditional methods as the discrete cosine transform or the discrete wavelet transform. Autoassociative and heteroassociative MAMs can be considered as a subclass of morphological neural networks. The morphological transform (MT) presented in this paper generates heteroassociative MAMs derived from image subblocks. The MT is applied to individual blocks of the image using some transformation matrix as an input pattern. Depending on this matrix, the image takes a morphological representation, which is used to perform the data compression at the next stages. With respect to traditional methods, the main advantage offered by the MT is the processing speed, whereas the compression rate and the signal-to-noise ratio are competitive to conventional transforms.