Morphological bidirectional associative memories

Ritter, Gerhard X.; Diaz-de-Leon, J. L.; Sussner, Peter

doi:10.1016/s0893-6080(99)00033-7

Cited by 132 publications

(82 citation statements)

References 25 publications

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“…From [10], the conjugate morphological memories, M YX = W * XY and W YX = M * XY , also denoted by W * and M * , perform the feedback scheme for bidirectional recall in a MBAM. The basic association mechanisms for perfect input in the X to Y direction are given by the following one-step procedure without thresholding γ is said to contain random noise.…”

Section: Mbams and The Kernel Methodsmentioning

confidence: 99%

“…The basic association mechanisms for perfect input in the X to Y direction are given by the following one-step procedure without thresholding γ is said to contain random noise. In order to deal efficiently with corrupted versions of exemplar patterns, the kernel method has proven to be useful in the binary case for MAMs [9,13] and MBAMs [10]. Here, we will extend the kernel technique in MBAMs to store and recall non-boolean pattern associations.…”

Section: Mbams and The Kernel Methodsmentioning

confidence: 99%

“…Thus, as many associations as desired can be encoded into the memory; one step convergence and perfect recall of boolean noisy patterns using the idea of kernels were also settled [9]. Furthermore, the theoretical framework for morphological bidirectional associative memories, developed in [10], showed again, that for some binary pattern classes, MBAMs have large storage capacity and superior bidirectional recall than traditional BAM models [5] and also competitive with other feedforward BAM networks [15]. A characterization of kernel vectors for binary patterns that provided for a direct method for kernel computation as well as bounds for the allowable amount of corruption of the exemplar patterns that guarantee perfect recall appeared in [13].…”

Section: Introductionmentioning

confidence: 99%

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Kernel Computation in Morphological Bidirectional Associative Memories

Urcid

Ritter

Iancu

2003

Lecture Notes in Computer Science

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Abstract. Morphological associative memories (MAMs) use a lattice algebra approach to store and recall pattern associations. The lattice matrix operations endow MAMs with properties that are completely different than those of traditional associative memory models. In the present paper, we focus our attention to morphological bidirectional associative memories (MBAMs) capable of storing and recalling non-boolean patterns degraded by random noise. The notions of morphological strong independence (MSI), minimal representations, and kernels are extended to provide the foundation of bidirectional recall when dealing with noisy inputs. For arbitrary pattern associations, we present a practical solution to compute kernels in MBAMs by induced MSI.

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Section: Mbams and The Kernel Methodsmentioning

confidence: 99%

Section: Mbams and The Kernel Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Kernel Computation in Morphological Bidirectional Associative Memories

Urcid

Ritter

Iancu

2003

Lecture Notes in Computer Science

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“…Associative memories have been used for many years for pattern recalling. Refer for example to [1][2][3][4][5][6][7][8][9][10][11][12][13]. Usually, complete unaltered patterns are first used to build a chosen memory model.…”

Section: Introductionmentioning

confidence: 99%

A New Two-Level Associative Memory for Efficient Pattern Restoration

Cruz¹,

Sossa²,

Barron³

2006

Neural Process Lett

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Pattern reconstruction or pattern restoration in the presence of noise is a main problem in pattern recognition. An essential feature of the noise acting on a pattern is its local nature. If a pattern is split into enough sub-patterns, a few of them will be less or more affected by noise, others will remain intact. In this paper, we propose a simple but effective methodology that exploits this fact for the efficient restoration of a pattern. A pattern is restored if enough of its sub-patterns are also restored. Since several patterns can share the same sub-patterns, the final decision is accomplished by means of a voting mechanism. Before deciding if a sub-pattern belongs to a pattern, sub-pattern restoration in the presence of noise is done by an associative memory. Numerical and real examples are given to show the effectiveness of the proposal. Formal conditions under which the proposal guaranties perfect restoration of a pattern from an unaltered or and altered version of it are also given.

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“…A radical change arrived at the end of the 1990s with the so-called morphological associative memories [7,8]. While the classic LA and Hopfield memories found their operation on multiplications and additions, the morphological associative memories do it on the min and max operations well used in Mathematical Morphology.…”

Section: Introductionmentioning

confidence: 99%

Associative Gray Level Pattern Processing using Binary Decomposition and α β Memories

Sossa

Barron

Cuevas

et al. 2005

Neural Process Lett

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In this note we show how a binary memory can be used to recall gray-level patterns. We take as example the αβ associative memories recently proposed in Yáñez, Associative Memories based on order Relations and Binary Operators(In Spanish), PhD Thesis, Center for computing Research, February of 2002, only useful in the binary case. Basically, the idea consists on that given a set of gray-level patterns to be first memorized: (1) Decompose them into their corresponding binary patterns, and (2) Build the corresponding binary associative memory (one memory for each binary layer) with each training pattern set (by layers). A given pattern or a distorted version of it, it is recalled in three steps: (1) Decomposition of the pattern by layers into its binary patterns, (2) Recalling of each one of its binary components, layer by layer also, and (3) Reconstruction of the pattern from the binary patterns already recalled in step 2. The proposed methodology operates at two phases: training and recalling. Conditions for perfect recall of a pattern either from the fundamental set or from a distorted version of one them are also given. Experiments where the efficiency of the proposal is tested are also given.

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Morphological bidirectional associative memories

Cited by 132 publications

References 25 publications

Kernel Computation in Morphological Bidirectional Associative Memories

Kernel Computation in Morphological Bidirectional Associative Memories

A New Two-Level Associative Memory for Efficient Pattern Restoration

Associative Gray Level Pattern Processing using Binary Decomposition and α β Memories

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