An artificial neural network model based on dendritic computation using two lattice metrics is introduced in this paper. A description of the mathematical framework of the proposed model is provided and its corresponding learning algorithm is presented in mathematical pseudocode. Computational experiments are given to demonstrate the effectiveness and performance of the learning algorithm as well as its application to some illustrative pattern recognition problems.

This paper describes a hybrid technique for reducing the number of potential hyperspectral endmembers determined from the min-WXXand max-MXXlattice auto-associative memories. Given a set X of pixel spectra we first compute vector data sets obtained from shifted versions of WXXand MXX. In a second step, application of hard or fuzzy c-means clustering to the column vectors derived from WXXand MXXlowers the number of candidate endmembers and cluster centroids are approximations to final endmembers. Some validation indexes are computed on generated clusters to provide guidance in finding the number of endmembers required to unmix a hyperspectral image. Examples are given to illustrate how our proposed hybrid technique can be applied in the analysis of hyperspectral imagery.

We introduce a methodology for constructing an associative memory that is highly robust in the presence of noisy inputs. The memory is based on dendritic computing employing lattice algebraic operations. A major consequence of this approach is the avoidance of convergence problems during the training phase and rapid association of perfect and nonperfect input patterns with stored associated patterns.

Lattice based neural networks are capable of resolving some difficult non-linear problems and have been successfully employed to solve real-world problems. In this paper a novel model of a lattice neural network (LNN) is presented. This new model generalizes the standard basis lattice neural network (SB-LNN) based on dendritic computing. In particular, we show how each neural dendrite can work on a different orthonormal basis than the other dendrites. We present experimental results that demonstrate superior learning performance of the new Orthonormal Basis Lattice Neural Network (OB-LNN) over SB-LNNs.

Recent discoveries in neuroscience imply that the basic computational elements are the dendrites that make up more than 50% of a cortical neuron's membrane. Neuroscientists now believe that the basic computation units are dendrites, capable of computing simple logic functions. This paper discusses two types of neural networks that take advantage of these new discoveries. The focus of this paper is on some learning algorithms in the two neural networks. Learning is in terms of lattice computations that take place in the dendritic structure as well as in the cell body of the neurons used in this model.

Lattice matrix associative memories have been developed as an alternative way to work with a set of associated pattern pairs for which the storage and retrieval stages are based in the theory of minimax algebra. Several methods have been proposed to cope with the problem of binary or real valued pattern recall from corrupted inputs and recent results on fixed point sets of matrix lattice transforms have provided for an algebraic characterization as well as a geometrical description of the canonical lattice min/max auto-associative memories. Compared to other correlation type associative memory models, the lattice associative memory schemes have shown better performance for both storage and recall capability; however, the computational techniques devised to achieve that purpose are still cumbersome when inputs have undetermined noise bounds. The procedure suggested in this paper uses noise masking to boost the recall performance of either the min or max morphological auto-associative memories. Examples using image patterns show the enhanced recovery of almost correct associations from noisy inputs by a single lattice matrix memory.

This paper presents a model of an artificial neural network whose neurons are endowed with dendritic structures and have a computational framework based on lattice algebra. Such neurons bear closer resemblance to their biological counterpart than other current artificial models. Employing a two-layer dendritic network model, we construct an auto-associative memory which is robust in the presence of random noise. Furthermore, unlike the kernel method, this memory does not require that the original patterns satisfy any conditions of morphological independence.

Autoassociative morphological memories (AMM) are a construct similar to hopfield autoassociatived memories defined on the (R, +, v, /spl and/) lattice algebra. Unlimited storage and perfect recall of noiseless real valued patterns has been proved for AMMs. However AMMs suffer from sensitivity to specific noise models, that can be characterized as erosive and dilative noise. On the other hand, spectral unmixing of hyperspectral images needs the prior definition of a set of endmembers, which correspond to material spectra lying on vertices of the minimum convex region covering the image data. These vertices can be characterized as morphologically independent patterns. We present a procedure based on the AMM noise sensitivity for endmember detection based on this characterization.

Recent advances in neurobiology and the biophysics of neural computation have brought to the foreground the importance of dendritic structures of neurons. These structures are now viewed as the primary basic computational units of the neuron, capable of realizing logical operations. Based on these new biophysical neural models, we develop a new paradigm for single layer perceptrons that incorporates dendritic processes. The basic computational processes in dendrites as well as neurons are based on lattice algebra. The computational capabilities of this new perceptron model is demonstrated by means of several illustrative examples and two theorems.

The development of an artificial neural network in the attempt to model biological brain networks usually emphasizes the role of the neuron as the main processing element. However, recent advances in neurobiology and the biophysics of neural computation have led many researchers to the conclusion that dendrites and their associated spines are equally important. More precisely, they view dendritic structures as the primary basic computational units of the neuron. A neural model that incorporates dendrites; is therefore more faithful to its biophysical counterpart. Based on these biological neural models, we develop a new paradigm of single layer feedforward neural network that includes dendritic processes. A single layer is not a limitation to the capabilities of the model. Dendritic structures function as many functional subunits, each unit being capable of realizing logical operations. The computational framework for processes performed in neurons with dendrites is based on lattice algebra. After describing the proposed model, we demonstrate its computational capabilities by means of three illustrative examples and two theorems.

Recent advances in the biophysics of computation and neurocomputing models have brought to the foreground the importance of dendritic structures in a single neuron cell. Dendritic structures are now viewed as the primary autonomous computational units capable of realizing logical operations. By changing the classic simplified model of a single neuron with a more realistic one that incorporates the dendritic processes, a novel paradigm in artificial neural networks is being established. In this work, we introduce and develop a mathematical model of dendrite computation in a morphological neuron based on lattice algebra. The computational capabilities of this enriched neuron model are demonstrated by means of several illustrative examples and by proving that any single layer morphological perceptron endowed with dendrites and their corresponding input and output synaptic processes is able to approximate any compact region in higher dimensional Euclidean space to within any desired degree of accuracy. Based on this result, we describe a training algorithm for single layer morphological perceptrons and apply it to some well-known nonlinear problems in order to exhibit its performance.

Methods for matrix decomposition have found numerous applications in image processing, in particular for the problem of template decomposition. Since existing matrix decomposition techniques are mainly concerned with the linear domain, we consider it timely to investigate matrix decomposition techniques in the nonlinear domain with applications in image processing. The mathematical basis for these investigations is the new theory of rank within minimax algebra. Thus far, only minimax decompositions of rank 1 and rank 2 matrices into outer product expansions are known to the image processing community. We derive a heuristic algorithm for the decomposition of matrices having arbitrary rank.

Single-layer and multilayer perceptrons are the simplest type of feedforward neural network systems. The first step in computing the next state of a neuron or in performing the next layer neural network computation involves the linear operation of multiplying neural values by their synaptic strengths and adding the results. Application of a nonlinear activation function follows the linear operation in order to provide for nonlinearity of the network and set the next state of the neuron. We introduce a novel class of perceptrons, called morphological perceptrons, in which the operations of multiplication and addition are replaced by addition and maximum (or minimum), respectively. By taking the maximum (or minimum) of sums instead of the sum of products, morphological neuron computation is nonlinear before the application of a nonlinear activation function. As a consequence, the properties of morphological perceptrons are very different to those of traditional feedforward models.

The theory of artificial neural networks has been successfully applied to a wide variety of pattern recognition problems. In this theory, the first step in computing the next state of a neuron or in performing the next layer neural network computation involves the linear operation of multiplying neural values by their synaptic strengths and adding the results. A nonlinear activation function usually follows the linear operation in order to provide for nonlinearity of the network and set the next state of the neuron. In this paper we introduce a novel class of artificial neural networks, called morphological neural networks, in which the operations of multiplication and addition are replaced by addition and maximum (or minimum), respectively. By taking the maximum (or minimum) of sums instead of the sum of products, morphological network computation is nonlinear before possible application of a nonlinear activation function. As a consequence, the properties of morphological neural networks are drastically different than those of traditional neural network models. The main emphasis of the research presented here is on morphological associative memories. We examine the computing and storage capabilities of morphological associative memories and discuss differences between morphological models and traditional semilinear models such as the Hopfield net.

Convolutions are a fundamental tool in image processing. Nonlinear convolutions are used in such operations as the median filter, the medial axis transform, and erosion and dilation as defined in mathematical morphology. For large convolution masks or structuring elements, the computation cost resulting from implementation can be prohibitive. However, in many instances, this cost can be significantly reduced by decomposing the templates representing the masks or structuring elements into a sequence of smaller templates. In addition, such decomposition can often be made architecture specific and, thus, resulting in optimal transform performance. In this paper we provide methods for decomposing morphological templates which are analogous to decomposition methods used in the linear domain. Specifically, we define the notion of the rank of a morphological template which categorizes separable morphological templates as templates of rank one. We establish a necessary and sufficient condition for the decomposability of rank one templates into 3/spl times/3 templates. We then use the invariance of the template rank under certain transformations in order to develop template decomposition techniques for templates of rank two.

The theory of artificial neural networks has been successfully applied to a wide variety of pattern recognition problems. In this paper we introduce a novel class of neural networks, called morphological neural networks, in which the operations of multiplication and addition are replaced by addition and maximum (or minimum), respectively. By taking the maximum (or minimum) of sums instead of the sum of products, morphological network computation is nonlinear before thresholding. As a consequence, the properties of morphological neural networks are drastically different than those of traditional neural network models. In this paper we consider some of these differences and examine the computing capabilities of morphological neural networks. As particular examples of a morphological neural network we discuss morphological associative memories and morphological perceptrons.

A new parallel binary image shrinking algorithm that can be considered as an improvement of Levialdi's (1972) parallel shrinking algorithm and can be used in many image labeling algorithms as a basic operation in order to reduce the storage requirements for local memory and speed up the labeling process is presented. This new parallel shrinking algorithm shrinks an nxn binary image to an image with no black pixels in O(n) parallel steps with a multiplicative constant of 1.5, preserving the 8-connectivity in the shrinking process.

Convolutions and correlations are fundamental operations in computer vision and image processing. The image-template product expresses convolutions and correlations. In this paper, the authors present an efficient algorithm for the image-template product on SIMD mesh connected computers. The image-template product is computed along disjoint convolution paths of the template. For an M /spl times/ N image and a template of T elements, the simple algorithm for the image-template product on an M /spl times/ N mesh connected computer takes O(T) time and requires O(1) local memory per processing element. Compared with the previously proposed algorithms, the algorithm works for both invariant and variant templates without any restrictions on the template shapes. Furthermore, it does not broadcast template weights and does not have partial result movement.>

A new parallel algorithm for image component labeling with local operators on SIMD mesh connected computers is presented, providing a positive answer to the open question posed by several researchers whether there exists an O(n)-time and O(log n)-space local labeling algorithm on SIMD mesh connected computers. The algorithm uses a pipeline mechanism with stack-like data structures to achieve the lower bound of O(n) in time complexity and O(log n) in space complexity. Furthermore, the algorithm has very small multiplicative constants in its complexities.