A.G. Bor and I. Pitas, "Median radial basis function neural network," IEEE Transactions on Neural Net- works, vol. 7, pp. 1351-1364, June 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....For classi cation problems, each local basis function is typically preferentially responsive to a certain class. Based on this obervation, an iterative hybrid learning algorithm was proposed in which the center locations are updated by LVQ while the output weights are updated in the usual way [GC94, BP96]. Another possibility is to select the kernel(s) to be updated in a probabilistic rather than deterministic manner[OF94] In [BP96] ideas from robust statistics were leveraged to determine the center locations and widths using the marginal median and absolution deviations of the (windowed) data ....

.... an iterative hybrid learning algorithm was proposed in which the center locations are updated by LVQ while the output weights are updated in the usual way [GC94, BP96] Another possibility is to select the kernel(s) to be updated in a probabilistic rather than deterministic manner[OF94] In [BP96], ideas from robust statistics were leveraged to determine the center locations and widths using the marginal median and absolution deviations of the (windowed) data points assigned to each kernel. Finally, a subtle link between unsupervised and supervised learning has been shown in [GC94] If the ....

A. G. Bors and I. Pitas. Median radial basis function neural network. IEEE Transactions on Neural Networks, 7(6):1351-1364, November 1996.

....is a two layer feed forward neural network in which various clusters are grouped together in order to describe classes [5] RBF network has very good functional modeling capabilities. The algorithm employed for trakuing the RBF network is based on robust statistics and is called Media RBF (MRBF) [6]. The paper has the following structure. In Section I the problem is described. First, the person authentication problem is described and the methods used are presented in brief. Then, the person authentication fusion system is described and the way that the clustering algorithms are applied as ....

....The output consists of a decision function b(x) 0,1) A very common approach for estimating the parameters of an RBF network consists of an adaptive implementation of the k means clustering algorithm [16] For the covariance matrix estimation, a 2 D extension of this algorithm is employed. In [6] a robust statistics algorithm called Median RBF (MRBF) was proposed for estimating parameters of RBF networks. It was proved that this algorithm provides better parameter estimates when the clusters are overlapping or in the presence of outliers [6] MRBF assigns an incoming data vector to a ....

[Article contains additional citation context not shown here]

A.G. Bor and I. Pitas, "Median radial basis function neural network," IEEE Transactions on Neural Net- works, vol. 7, pp. 1351-1364, June 1996.

....long tailed noise [4] The proposed algorithm is analyzed when estimating the parameters of ideal ellipses. The Hough Transform in spherical coordinates is used in the ellipsoids parameter estimation algorithm. The proposed algorithm contains the classical RBF and Median RBF learning algorithms [5] as particular cases. 2 Segmentation Criterion A classification approach is employed in the 3 D object segmentation. According to the Bayesian classification theory: M p(Ok[ max p(Oj[ff: 1) where M is the total number of objects, Ok is the object to be identified and Y is a volumetric ....

....graylevel similarity criterion. Each voxel in the volumetric image is associated to a certain basis function. Similar regions in the graylevel distribution, are assigned to the same object and they receive the same label. The network output weights ,Xm are calculated using backpropagation as in [5]. 5 Simulation Results The proposed algorithm has been tested on a stack of 60 microscopy images, representing the internal structure of a tooth pulp. Some of the frames are represented in Figure 1 (a) A 3 D view of the stack of images is displayed in Figure 1 (b) We intend to segment the ....

A. G. Bor], I. Pitas, "Median Radial Basis Function neural network," IEEE Trans. on Neural Networks, vol. 7, no. 6, pp. 1351-1364, 1996.

....The classification criterion connects the Gaussian parameters to the set of feature vectors drawn from the image sequence. Each basis function has associated a moving region. The moving regions are connected by the output units in order to model moving objects. We consider the MRBF network [3] for modeling the optical flow and moving object segmentation from the image sequence. The efficiency of the proposed algorithm when compared to the classical learning algorithm in RBF networks has been shown in [3] II. THE CLASSIFICATION CRITERION We consider the video frame partitioned in ....

....by the output units in order to model moving objects. We consider the MRBF network [3] for modeling the optical flow and moving object segmentation from the image sequence. The efficiency of the proposed algorithm when compared to the classical learning algorithm in RBF networks has been shown in [3]. II. THE CLASSIFICATION CRITERION We consider the video frame partitioned in blocks situated on a rectangular grid. We associate a feature vector, describing the local image sequence properties, to each block site. This vector contains a still image feature vec tor Szs and a motion vector Mj: ....

[Article contains additional citation context not shown here]

A.G. Bor, I. Pitas, "Median radial basis function neural networks" IEEE 2'rans. on Neural Networks, vol. 7 no. 6 pp. 1351-1364 Nov. 1996.

....the implementation of training parallelism. In the area of RBF neural networks, a novel on line learning algorithm based on robust estimators has been proposed. The so called Median Radial Basis Functions neural network (MRBF) uses the marginal median LVQ in the estimation of the RBF centers [11, 12]. The Median Absolute Deviation (MAD) has been used in the estimation of the covariance matrix. A fast implementation based on data sample histogram analysis is derived for the MRBF. The properties of the MRBF neural networks and an application of the MRBF neural network in the motion field ....

....estimate has been used: Ylj(n 1) Ylj(n) n) x(n) w(n) T[x(n) w(n) i ]j(n 1) j(n) Vi .IVy(n) 17) We propose a robust statistics based training algorithm. The network resulting from training based on robust statistics is called Median Radial Basis Function (MRBF) neural network [11]. In the first stage we employ the MMLVQ algorithm for evaluating the RBF s centers (5) and the Median of the Absolute Deviations (MAD) 13] for estimating the covariance matrix associated with each Gaussian function. The MAD based estimation of the dispersion parameter is provided by: mad Ix(0) ....

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BOR A. G., and PITAS I., Median radial basis functions neural network, IEEE Trans. on Neural Networks, vol 7, no. 6, Nov. 1996.

.... Variants of this algorithm have been derived in order to increase its efficiency in modeling data distributions [26, 30] An algorithm based on median estimation called Median Radial Basis Function (MRBF) was proved to provide better data classification when compared to the classical algorithm [21]. The classical moment algorithms are sensitive when data are contaminated by noise. In this study we propose a new RBF training algorithm based on the c trimmed Mean statistics. This algorithm orders the data samples associated with a basis function and eliminates a certain percentage of those ....

....rain IiX ill (10) where is the closest center to the incoming data sample X. A robust statistics based algorithm employing the marginal median for Gaussian center estimation and the median of the absolute deviation from the median for width estimation and called Median RBF (MRBF) was proposed in [21]. The theoretical analysis has shown that the bias provided by MRBF is smaller than that of the classical LVQ based RBF algorithm when estimating the parameters of a mixture of overlapping Gaussians. In this study, a new robust statistics based training algorithm which contains the previous two ....

A. G. Bor, I. Pitas, "Median radial basis function neural network," IEEE Trans. on Neural Networks, vol. 7, no. 6, pp. 1351-1364, 1996.

.... filters have been used for tracking in [2, 3, 4] Objects are segmented based on clustering in [3, 5] Simultaneous optical flow estimation and moving object segmentation has been employed in [6] In this approach the moving scene is modeled based on the Median Radial Basis Function (MRBF) network [8]. Each output unit of Adrian G. Borg was with the Dept. of Informatics, University of Thessaloniki, Thessaloniki 540 06, Greece. He is now with the Dept. of Computer Science, University of York, York YO10 5DD, U.K. e maih Adrian. Bors cs.york.ac.uk) lI. Pitas is with the Dept. of Informatics, ....

.... and covariance matrix estimates and WDFD(Jj) repre sents the weighted displaced frame difference (a measure of confidence in the motion estimation algorithm) 6] An unsupervised training algorithm provides the estimates of the MRBF network parameters while modeling the probabilities from (5) [6, 8]. 3 Moving object tracking Let us neglect the dependence on all the frames excepting the previous. In this case we can express each probability in the first product of (4) as an energy function measuring the accuracy of reconstructing the frame f(t 1) from the displaced moving objects which ....

A. G. Borq, I. Pitas, "Median radial basis function neural network," IEEE Trans. on Neural Networks, vol. 7, no. 6, pp. 1351-1364, Nov. 1996.

....from 0 to 0:4. Thus, on the basis of these differences, we can separate a great part of the dark brush strokes from cracks. This separation can be achieved by classification using median radial basis functions (MRBF) neural network, which is a robust version of radial basis functions (RBF) network [6]. The input vectors of the network consist of the hue and saturation values of pixels identified as cracks by the top hat transform. During the recall phase each input is assigned to one of the two available output classes (cracks and thin dark brush strokes) 4.3. Crack filling After ....

A. G. Bors and I. Pitas, "Median Radial Basis Function Neural Network", IEEE Trans. on Neural Networks, vol. 7, no.6, pp. 1351-1364, November 1996.

....object segmentation in the image sequence. This structure is embedded in a two layer feedforward neural network, where each output is assigned to a moving object. A radial basis function (RBF) decomposition is known to be a good functional approximator and has been used in many applications [22] [27]. The first layer units implement Gaussian functions. The classification criterion connects the Gaussian parameters to the set of feature vectors drawn from the image sequence. In the second layer, the moving regions associated to the basis functions are merged in order to model the moving ....

....order to model the moving objects. The mixture of basis functions approximates the probabilities associated to the optical flow estimation and segmentation of the moving objects. The learning algorithm employed for estimating the set of parameters associated to the image sequence has two stages [26, 27]. In the first stage, the basis function center and variance are found based on a clustering approach, similar to the Learning Vector Quantization (LVQ) 28] A robust statistics based algorithm employing the marginal median and median of absolute deviations (MAD) 29, 30] and called MRBF was ....

[Article contains additional citation context not shown here]

A. G. Bors, I. Pitas, "Median radial basis function neural network," IEEE Trans. on Neural Networks, vol. 7, no. 6 , pp. 1351-1364, Nov. 1996.

.... [29] Variants of this algorithm have been derived in order to increase its eciency in modeling data distributions [26, 30] An algorithm based on median estimation called Median Radial Basis Function (MRBF) was proved to provide better data classi cation when compared to the classical algorithm [21]. The classical moment algorithms are sensitive when data are contaminated by noise. In this study we propose a new RBF training algorithm based on the trimmed Mean statistics. This algorithm orders the data samples associated with a basis function and eliminates a certain percentage of those ....

.... i k (10) where k is the closest center to the incoming data sample X. A robust statistics based algorithm employing the marginal median for Gaussian center estimation and the median of the absolute 6 deviation from the median for width estimation and called Median RBF (MRBF) was proposed in [21]. The theoretical analysis has shown that the bias provided by MRBF is smaller than that of the classical LVQ based RBF algorithm when estimating the parameters of a mixture of overlapping Gaussians. In this study, a new robust statistics based training algorithm which contains the previous two ....

A. G. Bors, I. Pitas, \Median radial basis function neural network," IEEE Trans. on Neural Networks, vol. 7, no. 6, pp. 1351-1364, 1996.

.... lters have been used for tracking in [2, 3, 4] Objects are segmented based on clustering in [3, 5] Simultaneous optical ow estimation and moving object segmentation has been employed in [6] In this approach the moving scene is modeled based on the Median Radial Basis Function (MRBF) network [8]. Each output unit of Adrian G. Bor s was with the Dept. of Informatics, University of Thessaloniki, Thessaloniki 540 06, Greece. He is now with the Dept. of Computer Science, University of York, York YO10 5DD, U.K. e mail: Adrian.Bors cs.york.ac.uk) y I. Pitas is with the Dept. of ....

.... and covariance matrix estimates and WDFD( M j ) represents the weighted displaced frame di erence (a measure of con dence in the motion estimation algorithm) 6] An unsupervised training algorithm provides the estimates of the MRBF network parameters while modeling the probabilities from (5) [6, 8]. 3 3 Moving object tracking Let us neglect the dependence on all the frames excepting the previous. In this case we can express each probability in the rst product of (4) as an energy function measuring the accuracy of reconstructing the frame f(t 1) from the displaced moving objects which ....

A. G. Bors, I. Pitas, \Median radial basis function neural network," IEEE Trans. on Neural Networks, vol. 7, no. 6 , pp. 1351-1364, Nov. 1996.

....is a two layer feed forward neural network in which various clusters are grouped together in order to describe classes [5] RBF network has very good functional modeling capabilities. The algorithm employed for training the RBF network is based on robust statistics and is called Median RBF (MRBF) [6]. The paper has the following structure. In Section II the problem is described. First, the person authentication problem is described and the methods used are presented in brief. Then, the person authentication fusion system is described and the way that the clustering algorithms are applied as ....

....The output consists of a decision function (x) 2 (0; 1) A very common approach for estimating the parameters of an RBF network consists of an adaptive implementation of the k means clustering algorithm [16] For the covariance matrix estimation, a 2 D extension of this algorithm is employed. In [6] a robust statistics algorithm called Median RBF (MRBF) was proposed for estimating parameters of RBF networks. It was proved that this algorithm provides better parameter estimates when the clusters are overlapping or in the presence of outliers [6] MRBF assigns an incoming data vector to a ....

[Article contains additional citation context not shown here]

A. G. Bor¸s and I. Pitas, "Median radial basis function neural network," IEEE Transactions on Neural Networks, vol. 7, pp. 1351--1364, June 1996.

....long tailed noise [4] The proposed algorithm is analyzed when estimating the parameters of ideal ellipses. The Hough Transform in spherical coordinates is used in the ellipsoids parameter estimation algorithm. The proposed algorithm contains the classical RBF and Median RBF learning algorithms [5] as particular cases. 2 Segmentation Criterion A classification approach is employed in the 3 D object segmentation. According to the Bayesian classification theory : p(O k jF) M max j=1 p(O j jF) 1) where M is the total number of objects, O k is the object to be identified and F is a ....

....and graylevel similarity criterion. Each voxel in the volumetric image is associated to a certain basis function. Similar regions in the graylevel distribution, are assigned to the same object and they receive the same label. The network output weights mk are calculated using backpropagation as in [5]. 5 Simulation Results The proposed algorithm has been tested on a stack of 60 microscopy images, representing the internal structure of a tooth pulp. Some of the frames are represented in Figure 1 (a) A 3 D view of the stack of images is displayed in Figure 1 (b) We intend to segment the ....

A. G. Bor¸s, I. Pitas, "Median Radial Basis Function neural network," IEEE Trans. on Neural Networks, vol. 7, no. 6, pp. 1351-1364, 1996.

....parameters is analyzed. 1. INTRODUCTION Radial basis function neural network consists of a two layer feed forward structure employed for functional approximation and classification proposes. When used in pattern classification an RBF network successfully approximates the Bayesian classifier [1, 2]. In this case, the underlying probability functions are decomposed in a sum of kernel functions with localized support. The functions, implemented by the hidden units, are usually chosen as Gaussian. The intersection of an Gaussian with an hyperplane is geometrically an ellipsoid. Objects in ....

....quantization [1] This learning algorithm represents the adaptive version of the moments approach, used for estimating the ellipse parameters [4] However, the moments method is likely to provide biased estimates in the case when the ellipses are overlapping or when they are embedded in noise. In [2, 5] marginal median and median of the absolute deviation [6] have been proposed as robust estimators for finding the RBF s hidden unit parameters. In this paper we analyze the ff trimmed mean RBF algorithm. The previous two algorithms are particular cases of the new approach. ff trimmed mean has been ....

[Article contains additional citation context not shown here]

A. G. Bor¸s, I. Pitas, "Median radial basis function neural network," IEEE Trans. on Neural Networks, vol. 7 , no. 6 , pp. 1351-1364 , 1996.

....basis of these differences, we can separate a great part of the dark brush strokes from cracks, which both are detected by the top hat transformation. This separation can be achieved by classification using MRBF neural network, which is a robust version of RBF networks based on median operators [3]. MRBF consists of a two layer neural network, where each hidden unit implements a kernel function. The Gaussian function is usually chosen as kernel function. Each kernel is associated with an activation region from the input space and its output is fed to an output unit. The MRBF algorithm is ....

....neural network, where each hidden unit implements a kernel function. The Gaussian function is usually chosen as kernel function. Each kernel is associated with an activation region from the input space and its output is fed to an output unit. The MRBF algorithm is based on robust estimation [3] of the hidden unit parameters. It employs the marginal median [4] for kernel location estimation and the median of the absolute (a) b) Figure 2: a) A thresholded output containing many brush strokes (hair, number in the left corner) b) The separated brush strokes, after the MRBF application ....

A. Bors, I. Pitas, "Median Radial Basis Function Neural Network, " IEEE Trans. on Neural Networks, vol. 7, no. 6, pp. 1351--1364, November 1996.

....The classification criterion connects the Gaussian parameters to the set of feature vectors drawn from the image sequence. Each basis function has associated a moving region. The moving regions are connected by the output units in order to model moving objects. We consider the MRBF network [3] for modeling the optical flow and moving object segmentation from the image sequence. The efficiency of the proposed algorithm when compared to the classical learning algorithm in RBF networks has been shown in [3] II. The classification criterion We consider the video frame partitioned in ....

....by the output units in order to model moving objects. We consider the MRBF network [3] for modeling the optical flow and moving object segmentation from the image sequence. The efficiency of the proposed algorithm when compared to the classical learning algorithm in RBF networks has been shown in [3]. II. The classification criterion We consider the video frame partitioned in blocks situated on a rectangular grid. We associate a feature vector, describing the local image sequence properties, to each block site. This vector contains a still image feature vector SIJ and a motion vector MIJ ....

[Article contains additional citation context not shown here]

A. G. Bor¸s, I. Pitas, "Median radial basis function neural network," IEEE Trans. on Neural Networks, vol. 7, no. 6, pp. 1351-1364, Nov. 1996.

....voxel coordinates and the graylevel. The parameters of the ellipsoids can be found using the normalized first and second order moments [5] In order to estimate the ellipsoid shape in noise we employ the ff Trimmed Mean algorithm [6] A classical RBF and Median RBF learning algorithms described in [7] are particular cases of the proposed algorithm. The extention of the Hough Transform in 3 D is employed for estimating the centers of the ellipsoids in the context of the ff Trimmed Mean RBF training algorithm. Examples when applying the proposed algorithm in 3 D image segmentation are provided. ....

....center is updated using : k = k 1 N k (X Gamma k ) 11) where N k is the number of data samples associated with the kth basis function. For the covariance matrix, classical estimate can be used : Sigma k = Nk X i=0 (X i Gamma k ) X i Gamma k ) T N k Gamma 1 (12) In [7] the marginal median and median of the absolute deviations from the median estimators were employed for estimating the RBF center and covariance matrix. In this study, after ordering the data samples X (0) X (Nk ) we use the ff Trimmed Mean algorithm : k (t) k (t Gamma 1) c ....

[Article contains additional citation context not shown here]

A. G. Bor¸s, I. Pitas, "Median Radial Basis Function neural network," IEEE Trans. on Neural Networks, vol. 7, no. 6, pp. 1351-1364, 1996.

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A. G. Bor¸s and I. Pitas, "Median radial basis functions neural network", IEEE Trans. on Neural Networks, submitted August 1994.

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