Median radial basis function neural network,” (1996)

by A G Bors, I Pitas
Venue:IEEE Trans. Neural Networks,
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Face recognition with radial basis function (RBF) neural networks

by Meng Joo Er, Shiqian Wu, Juwei Lu, Student Member, Hock Lye Toh - IEEE Transactions on Neural Networks , 2002
"... Abstract—A general and efficient design approach using a radial basis function (RBF) neural classifier to cope with small training sets of high dimension, which is a problem frequently encountered in face recognition, is presented in this paper. In order to avoid overfitting and reduce the computati ..."
Abstract - Cited by 51 (2 self) - Add to MetaCart
Abstract—A general and efficient design approach using a radial basis function (RBF) neural classifier to cope with small training sets of high dimension, which is a problem frequently encountered in face recognition, is presented in this paper. In order to avoid overfitting and reduce the computational burden, face features are first extracted by the principal component analysis (PCA) method. Then, the resulting features are further processed by the Fisher’s linear discriminant (FLD) technique to acquire lower-dimensional discriminant patterns. A novel paradigm is proposed whereby data information is encapsulated in determining the structure and ini-tial parameters of the RBF neural classifier before learning takes place. A hybrid learning algorithm is used to train the RBF neural networks so that the dimension of the search space is drastically re-duced in the gradient paradigm. Simulation results conducted on the ORL database show that the system achieves excellent perfor-mance both in terms of error rates of classification and learning efficiency. Index Terms—Face recognition, Fisher’s linear discriminant, ORL database, principal component analysis, radial basis function (RBF) neural networks, small training sets of high dimension. I.
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Self-organized fuzzy system generation from training examples

by Ignacio Rojas, Hector Pomares, Julio Ortega, Alberto Prieto - IEEE Trans. Fuzzy Syst , 2000
"... Abstract—In the synthesis of a fuzzy system two steps are generally employed: the identification of a structure and the optimization of the parameters defining it. This paper presents a methodology to automatically perform these two steps in conjunction using a three-phase approach to construct a fu ..."
Abstract - Cited by 33 (10 self) - Add to MetaCart
Abstract—In the synthesis of a fuzzy system two steps are generally employed: the identification of a structure and the optimization of the parameters defining it. This paper presents a methodology to automatically perform these two steps in conjunction using a three-phase approach to construct a fuzzy system from numerical data. Phase 1 outlines the membership functions and system rules for a specific structure, starting from a very simple initial topology. Phase 2 decides a new and more suitable topology with the information received from the previous step; it determines for which variable the number of fuzzy sets used to discretize the domain must be increased and where these new fuzzy sets should be located. This, in turn, decides in a dynamic way in which part of the input space the number of fuzzy rules should be increased. Phase 3 selects from the different structures obtained to construct a fuzzy system the one providing the best compromise between the accuracy of the approximation and the complexity of the rule set. The accuracy and complexity of the fuzzy system derived by the proposed self-organized fuzzy rule generation procedure (SOFRG) are studied for the problem of function approximation. Simulation results are compared with other methodologies such as artificial neural networks, neuro-fuzzy systems, and genetic algorithms. Index Terms—Function approximation, fuzzy system design, generation of membership functions and rules. I.
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Terrain Analysis Using Radar Shape-from-Shading

by Adrian G. Bors, Edwin R. Hancock, Richard C. Wilson - IEEE TRANS. ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE , 2003
"... This paper develops a maximum a posteriori (MAP) probability estimation framework for shape-from-shading (SFS) from synthetic aperture radar (SAR) images. The aim is to use this method to reconstruct surface topography from a single radar image of relatively complex terrain. Our MAP framework make ..."
Abstract - Cited by 25 (14 self) - Add to MetaCart
This paper develops a maximum a posteriori (MAP) probability estimation framework for shape-from-shading (SFS) from synthetic aperture radar (SAR) images. The aim is to use this method to reconstruct surface topography from a single radar image of relatively complex terrain. Our MAP framework makes explicit how the recovery of local surface orientation depends on the whereabouts of terrain edge features and the available radar reflectance information. To apply the resulting process to real world radar data, we require probabilistic models for the appearance of terrain features and the relationship between the orientation of surface normals and the radar reflectance. We show that the SAR data can be modeled using a Rayleigh-Bessel distribution and use this distribution to develop a maximum likelihood algorithm for detecting and labeling terrain edge features. Moreover, we show how robust statistics can be used to estimate the characteristic parameters of this distribution. We also develop an empirical model for the SAR reflectance function. Using the reflectance model, we perform Lambertian correction so that a conventional SFS algorithm can be applied to the radar data. The initial surface normal direction is constrained to point in the direction of the nearest ridge or ravine feature. Each surface normal must fall within a conical envelope whose axis is in the direction of the radar illuminant. The extent of the envelope depends on the corrected radar reflectance and the variance of the radar signal statistics. We explore various ways of smoothing the field of surface normals using robust statistics. Finally, we show how to reconstruct the terrain surface from the smoothed field of surface normal vectors. The proposed algorithm is applied to various SAR da...

Optical Flow Estimation and Moving Object Segmentation Based on Median Radial Basis Function Network

by Adrian G. Bors, Ioannis Pitas - IEEE Trans. on Image Processing , 1998
"... Various approaches have been proposed for simultaneous optical flow estimation and segmentation in image sequences. In this study, the moving scene is decomposed into different regions with respect to their motion, by means of a pattern recognition scheme. The inputs of the proposed scheme are the f ..."
Abstract - Cited by 23 (9 self) - Add to MetaCart
Various approaches have been proposed for simultaneous optical flow estimation and segmentation in image sequences. In this study, the moving scene is decomposed into different regions with respect to their motion, by means of a pattern recognition scheme. The inputs of the proposed scheme are the feature vectors representing still image and motion information. Each class corresponds to a moving object. The classifier employed is the Median Radial Basis Function (MRBF) neural network. An error criterion function derived from the probability estimation theory and expressed as a function of the moving scene model is used as the cost function. Each basis function is activated by a certain image region. Marginal median and median of the absolute deviations (MAD) estimators are employed for estimating the basis function parameters. The image regions associated with the basis functions are merged by the output units in order to identify moving objects. 1 Introduction Motion repres...
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Digital Restoration of Painting Cracks

by Ioannis Giakoumis, Ioannis Pitas - in ISCAS ’98, Proceedings of the IEEE International Symposium on Circuits and Signals, 31 May-3 , 1998
"... In this paper we develop a method for the restoration of cracks on a painting. First, we detect the local minima (they can be either cracks or painting brush strokes), by using a morphological highpass operator, called top-hat transformation. The crack filling procedure must be applied only on the c ..."
Abstract - Cited by 15 (3 self) - Add to MetaCart
In this paper we develop a method for the restoration of cracks on a painting. First, we detect the local minima (they can be either cracks or painting brush strokes), by using a morphological highpass operator, called top-hat transformation. The crack filling procedure must be applied only on the cracks and not on these dark brush strokes, which are also detected. In order to separate these brush strokes from cracks, we use the Hue and Saturation information in the HSV or HSI color space. The separation is obtained by classification through the implementation of the MRBF neural network. Alternatively, a semi-automatic method is described for this separation. The primitive geometric shape-matching property of the morphological opening can be used to separate brush strokes, which have a specific shape. Finally, we propose two crack filling methods, one which is based on order statistics and another one using anisotropic diffusion. The results on painting crack restoration were very good...
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Object Classification in 3-D Images Using Alpha-Trimmed Radial Basis Function Network Mean

by Adrian G. Bors, Ioannis Pitas , 1999
"... We propose a pattern classification based approach for simultaneous 3-D object modeling and segmentation in image volumes. The 3-D objects are described as a set of overlapping ellipsoids. ..."
Abstract - Cited by 10 (2 self) - Add to MetaCart
We propose a pattern classification based approach for simultaneous 3-D object modeling and segmentation in image volumes. The 3-D objects are described as a set of overlapping ellipsoids.

A self-organizing HCMAC neural-network classifier

by Hahn-ming Lee, Chih-ming Chen, Yung-feng Lu - IEEE Transactions on neural networks , 2003
"... Abstract—This paper presents a self-organizing hierarchical cerebellar model arithmetic computer (HCMAC) neural-network classifier, which contains a self-organizing input space module and an HCMAC neural network. The conventional CMAC can be viewed as a basis function network (BFN) with supervised l ..."
Abstract - Cited by 9 (1 self) - Add to MetaCart
Abstract—This paper presents a self-organizing hierarchical cerebellar model arithmetic computer (HCMAC) neural-network classifier, which contains a self-organizing input space module and an HCMAC neural network. The conventional CMAC can be viewed as a basis function network (BFN) with supervised learning, and performs well in terms of its fast learning speed and local generalization capability for approximating nonlinear functions. However, the conventional CMAC has an enormous memory requirement for resolving high-dimensional classification problems, and its performance heavily depends on the approach of input space quantization. To solve these problems, this paper presents a novel supervised HCMAC neural network capable of resolving high-dimensional classification problems well. Also, in order to reduce what is often trial-and-error parameters searching for constructing memory allocation automatically, proposed herein is a self-organizing input space module that uses Shannon’s entropy measure and the golden-section search method to appropriately determine the input space quantization according to the various distributions of training data sets. Experimental results indicate that the self-organizing HCMAC indeed has a fast learning ability and low memory requirement. It is a better performing network than the conventional CMAC for resolving high-dimensional classification problems. Furthermore, the self-organizing HCMAC classifier has a better classification ability than other compared classifiers. Index Terms—Cerebellar model arithmetic computer (CMAC), golden-section search method, self-organizing hierarchical CMAC (HCMAC) classifier, Shannon’s entropy measure. I.
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Prediction and Tracking of Moving Objects in Image Sequences

by Adrian G. Bors, Ioannis Pitas , 2000
"... We employ a prediction model for moving object velocity and location estimation derived from Bayesian theory. The optical flow of a certain moving object depends on the history of its previous values. A joint optical flow estimation and moving object segmentation algorithm is used for the initializa ..."
Abstract - Cited by 8 (2 self) - Add to MetaCart
We employ a prediction model for moving object velocity and location estimation derived from Bayesian theory. The optical flow of a certain moving object depends on the history of its previous values. A joint optical flow estimation and moving object segmentation algorithm is used for the initialization of the tracking algorithm. The segmentation of the moving objects is determined by appropriately classifying the unlabeled and the occluding regions. Segmentation and optical flow tracking is used for predicting future frames.

I.: Minimum Class Variance Support Vector Machines

by Stefanos Zafeiriou, Anastasios Tefas, Ioannis Pitas - IEEE Transactions on Image Processing , 2007
"... Abstract—In this paper, a modified class of support vector machines (SVMs) inspired from the optimization of Fisher’s dis-criminant ratio is presented, the so-called minimum class variance SVMs (MCVSVMs). The MCVSVMs optimization problem is solved in cases in which the training set contains less sam ..."
Abstract - Cited by 7 (4 self) - Add to MetaCart
Abstract—In this paper, a modified class of support vector machines (SVMs) inspired from the optimization of Fisher’s dis-criminant ratio is presented, the so-called minimum class variance SVMs (MCVSVMs). The MCVSVMs optimization problem is solved in cases in which the training set contains less samples that the dimensionality of the training vectors using dimensionality re-duction through principal component analysis (PCA). Afterward, the MCVSVMs are extended in order to find nonlinear decision surfaces by solving the optimization problem in arbitrary Hilbert spaces defined by Mercer’s kernels. In that case, it is shown that, under kernel PCA, the nonlinear optimization problem is transformed into an equivalent linear MCVSVMs problem. The effectiveness of the proposed approach is demonstrated by com-paring it with the standard SVMs and other classifiers, like kernel Fisher discriminant analysis in facial image characterization problems like gender determination, eyeglass, and neutral facial expression detection. Index Terms—Facial images, Fisher’s discriminant analysis, kernel methods, principal component analysis (PCA), support vector machines (SVMs). I.
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Multimodal Decision Level Fusion for Person Authentication

by Vassilios Chatzis, Adrian G. Bors, Ioannis Pitas , 1999
"... In this paper, the use of clustering algorithms for decision level data fusion is proposed. Person authentication results coming from several modalities (e.g. still image, speech), are combined by using fuzzy k-means (FKM) and fuzzy vector quantization (FVQ) algorithms, and median radial basis funct ..."
Abstract - Cited by 6 (0 self) - Add to MetaCart
In this paper, the use of clustering algorithms for decision level data fusion is proposed. Person authentication results coming from several modalities (e.g. still image, speech), are combined by using fuzzy k-means (FKM) and fuzzy vector quantization (FVQ) algorithms, and median radial basis function (MRBF) network. The quality measure of the modalities data is used for fuzzification. Two modifications of the FKM and FVQ algorithms, based on a novel fuzzy vector distance definition, are proposed to handle the fuzzy data and utilize the quality measure. Simulations show that fuzzy clustering algorithms have better performance compared to the classical clustering algorithms and other known fusion algorithms. MRBF has better performance especially when two modalities are combined. Moreover, the use of the quality via the proposed modified algorithms increases the performance of the fusion system.