Showing papers on "Bhattacharyya distance published in 2003"
TL;DR: A new approach toward target representation and localization, the central component in visual tracking of nonrigid objects, is proposed, which employs a metric derived from the Bhattacharyya coefficient as similarity measure, and uses the mean shift procedure to perform the optimization.
Abstract: A new approach toward target representation and localization, the central component in visual tracking of nonrigid objects, is proposed. The feature histogram-based target representations are regularized by spatial masking with an isotropic kernel. The masking induces spatially-smooth similarity functions suitable for gradient-based optimization, hence, the target localization problem can be formulated using the basin of attraction of the local maxima. We employ a metric derived from the Bhattacharyya coefficient as similarity measure, and use the mean shift procedure to perform the optimization. In the presented tracking examples, the new method successfully coped with camera motion, partial occlusions, clutter, and target scale variations. Integration with motion filters and data association techniques is also discussed. We describe only a few of the potential applications: exploitation of background information, Kalman tracking using motion models, and face tracking.
4,996 citations
TL;DR: In this paper, an alternative simple form for the distribution is obtained and is shown to be equivalent to that of Chen and Bhattacharyya (1988), which guarantees at least a fixed number of failures in a life testing experiment.
Abstract: Chen and Bhattacharyya (1988,Comm. Statist. Theory Methods,17, 1857–1870) derived the exact distribution of the maximum likelihood estimator of the mean of an exponential distribution and an exact lower confidence bound for the mean based on a hybrid censored sample. In this paper, an alternative simple form for the distribution is obtained and is shown to be equivalent to that of Chen and Bhattacharyya (1988). Noting that this scheme, which would guarantee the experiment to terminate by a fixed timeT, may result in few failures, we propose a new hybrid censoring scheme which guarantees at least a fixed number of failures in a life testing experiment. The exact distribution of the MLE as well as an exact lower confidence bound for the mean is also obtained for this case. Finally, three examples are presented to illustrate all the results developed here.
283 citations
TL;DR: A feature extraction method is presented by utilizing an error estimation equation based on the Bhattacharyya distance to use classification errors in the transformed feature space, which are estimated using the error estimation equations, as a criterion for feature extraction.
248 citations
01 Jan 2003
TL;DR: A new class of kernels between distributions that permits discriminative estimation via, for instance, support vector machines, while exploiting the properties, assumptions, and invariances inherent in the choice of generative model are introduced.
Abstract: We introduce a new class of kernels between distributions. These induce a kernel on the input space between data points by associating to each datum a generative model fit to the data point individually. The kernel is then computed by integrating the product of the two generative models corresponding to two data points. This kernel permits discriminative estimation via, for instance, support vector machines, while exploiting the properties, assumptions, and invariances inherent in the choice of generative model. It satisfies Mercer’s condition and can be computed in closed form for a large class of models, including exponential family models, mixtures, hidden Markov models and Bayesian networks. For other models the kernel can be approximated by sampling methods. Experiments are shown for multinomial models in text classification and for hidden Markov models for protein sequence classification.
127 citations
13 Oct 2003
TL;DR: A novel method for tracking objects by combining density matching with shape priors is presented; a variational approach allows for a natural, parametrization-independent shape term to be derived.
Abstract: We present a novel method for tracking objects by combining density matching with shape priors. Density matching is a tracking method which operates by maximizing the Bhattacharyya similarity measure between the photometric distribution from an estimated image region and a model photometric distribution. Such trackers can be expressed as PDE-based curve evolutions, which can be implemented using level sets. Shape priors can be combined with this level-set implementation of density matching by representing the shape priors as a series of level sets; a variational approach allows for a natural, parametrization-independent shape term to be derived. Experimental results on real image sequences are shown.
103 citations
TL;DR: A novel representation scheme for view-based motion analysis using just the change in the relational statistics among the detected image features, without the need for object models, perfect segmentation, or part-level tracking is offered.
Abstract: We offer a novel representation scheme for view-based motion analysis using just the change in the relational statistics among the detected image features, without the need for object models, perfect segmentation, or part-level tracking. We model the relational statistics using the probability that a random group of features in an image would exhibit a particular relation. To reduce the representational combinatorics of these relational distributions, we represent them in a Space of Probability Functions (SoPF), where the Euclidean distance is related to the Bhattacharya distance between probability functions. Different motion types sweep out different traces in this space. We demonstrate and evaluate the effectiveness of this representation in the context of recognizing persons from gait. In particular, on outdoor sequences: (1) we demonstrate the possibility of recognizing persons from not only walking gait, but running and jogging gaits as well; (2) we study recognition robustness with respect to view-point variation; and (3) we benchmark the recognition performance on a database of 71 subjects walking on soft grass surface, where we achieve around 90 percent recognition rates in the presence of viewpoint variation.
62 citations
01 Jan 2003
TL;DR: In this article, the Dempster-Shafer theory of evidence is applied to fuse the information from three different sources for the same image, and the results prove the potential of the method for real images starting from the three RGB bands only.
Abstract: We present a new method for the segmentation of color images for extracting information from terrestrial, aerial or satellite images. It is a supervised method for solving a part of the automatic extraction problem. The basic technique consists in fusing information coming from three different sources for the same image. The first source uses the information stored in each pixel, by means of the Mahalanobis distance. The second uses the multidimensional distribution of the three bands in a window centred in each pixel, using the Bhattacharyya distance. The last source also uses the Bhattacharyya distance, in this case coocurrence matrices are compared over the cube texture built around each pixel. Each source represent a different order of statistic. The Dempster - Shafer theory of evidence is applied in order to fuse the information from these three sources. This method shows the importance of applying context and textural properties for the extraction process. The results prove the potential of the method for real images starting from the three RGB bands only. Finally, some examples about the extraction of linear cartographic features, specially roads, are shown.
33 citations
24 Nov 2003
TL;DR: A new registration method for ultrasound volumes relying on on a statistical texture-based similarity measure, derived from Bhattacharyya coefficient, is investigated and parametric ultrasound image registration is stated as a robust minimization issue.
Abstract: A new registration method for ultrasound volumes relying on on a statistical texture-based similarity measure is investigated. Texture information is given by spatial Gabor filters and represented by statistical kernel-based distributions. The registration similarity measure is then defined as a probabilistic distance, derived from Bhattacharyya coefficient, between two statistical distributions. Given this similarity measure, parametric ultrasound image registration is stated as a robust minimization issue. We also exploit frequency properties of spatial Gabor filters to propose a multiresolution approach to perform this minimization. We provide a preliminary evaluation of the new registration technique on clinical data.
31 citations
20 Jul 2003
TL;DR: This work develops a texture classification strategy by a sub-band filtering technique similar to a Gabor decomposition that is readily and cheaply extended to 3D that reduces the number of features required for classification by selecting a set of discriminant features conditioned on a set training texture samples.
Abstract: This paper considers the problem of classification of Magnetic Resonance Images using 2D and 3D texture measures. Joint statistics such as co-occurrence matrices are common for analysing texture in 2D since they are simple and effective to implement. However, the computational complexity can be prohibitive especially in 3D. In this work, we develop a texture classification strategy by a sub-band filtering technique that can be extended to 3D. We further propose a feature selection technique based on the Bhattacharyya distance measure that reduces the number of features required for the classification by selecting a set of discriminant features conditioned on a set training texture samples. We describe and illustrate the methodology by quantitatively analysing a series of images: 2D synthetic phantom, 2D natural textures, and MRI of human knees.
30 citations
TL;DR: Bhattacharyya and Soejoeti as discussed by the authors proved that the maximum likelihood estimate of the shape parameters is unique for the Weibull distribution in a multiple step-stress accelerated life test.
Abstract: Bhattacharyya and Soejoeti (Bhattacharyya, G. K., Soejoeti, Z. A. (1989). Tampered failure rate model for step-stress accelerated life test. Commun. Statist.—Theory Meth. 18(5):1627–1643.) pro- posed the TFR model for step-stress accelerated life tests. Under the TFR model, this article proves that the maximum likelihood estimate of the shape parameters is unique for the Weibull distribution in a multiple step-stress accelerated life test, and investigates the accuracy of the maximum likelihood estimate using the Monte-Carlo simulation.
26 citations
04 Jun 2003
TL;DR: It is shown, that the accuracy of the Bayes document classifier can be improved by the proposed model in comparison with theBayes classifiers based on the multivariate Bernoulli model, the multinomial model as well as the mult variables mixture model.
Abstract: The goal of text document classification is to assign a new document into one class from the predefined classes based on its contents. In this paper, a mixture of multinomial distributions is proposed as a model for class-conditional distributions in document classification task. A bag-of-words approach to vector document representation is employed. It is shown, that the accuracy of the Bayes document classifier can be improved by the proposed model in comparison with the Bayes classifiers based on the multivariate Bernoulli model, the multinomial model as well as the multivariate Bernoulli mixture model. Experimental results on the Reuters and the Newsgroups data sets indicate the effectiveness of the multinomial mixture model. Furthermore, an increase in classification accuracy is achieved for small training data sets, when multiclass Bhattacharyya distance is used instead of average mutual information as a feature selection criterion.
Journal Article•
TL;DR: Some inequalities for the and applications for the Kullback-Leibler, , Hellinger and Bhattacharyya distances in Information Theory are given.
Abstract: Some inequalities for the and applications for the Kullback-Leibler, , Hellinger and Bhattacharyya distances in Information Theory are given.
TL;DR: It is demonstrated that, unlike the Fisher ratio, the Bhattacharyya distance is an efficient figure of merit when one uses detection algorithms based on the generalized likelihood ratio test for realistic situations when the target and the background mean values are unknown.
Abstract: We analyze the optimization of low-flux coherent active imagery systems for target detection. We demonstrate that, unlike the Fisher ratio, the Bhattacharyya distance is an efficient figure of merit when one uses detection algorithms based on the generalized likelihood ratio test for realistic situations when the target and the background mean values are unknown. For example, we show that detection capabilities can be better if the pulse energy is divided into four shots, whereas using more than ten shots does not significantly improve the results.
23 Sep 2003
TL;DR: In this article, a comparison of spectral bands recommended through employment of different data separation measures and the reliability and robustness of these measures was performed on artificially generated target and background IR radiance data sets.
Abstract: A comparison of the spectral bands recommended through employment of different data separation measures and the reliability and robustness of these measures was performed on artificially generated target and background IR radiance data sets. The Mahalanobis distance, Signal to Clutter Ratio, Bhattacharya distance and Informational Difference criteria were employed in order to obtain the best single and paired spectral bands for data separation between two data classes of 'targets' and 'backgrounds' in day and night conditions. The results show that for conditions in which there is a distinct temperature difference between the two data classes, all the criteria perform similarly, with only small differences in the recommended spectral bands and general performance. However, in daylight conditions with multiple types of backgrounds and targets, criteria based on the assumption of concentrated data classes (SCR, Mahalanobis) tend to provide contradictory results, while those based on general statistical principles (Bhattacharya, Informational Difference) produce unequivocal results that are relatively unaffected by data set complexity.
07 Jul 2003
TL;DR: It is shown that a parameter quantifying the contrast between the object of interest and the background can be defined from the Bhattacharyya distance, which applies to several different noise statistics which belong to the exponential family.
Abstract: We address the problem of the characterization of segmentation performance of Minimum Description Length snake techniques in function of the noise which affects the image. It is shown that a parameter quantifying the contrast between the object of interest and the background can be defined from the Bhattacharyya distance. This contrast parameter is very general since it applies to several different noise statistics which belong to the exponential family. We illustrate its relevancy with a segmentation application using a polygonal snake descriptor.
TL;DR: In this paper, a family of distributions for which an unbiased estimator of a functiong(θ) of a real parameter θ can attain the second order Bhattacharyya lower bound is derived.
Abstract: A family of distributions for which an unbiased estimator of a functiong(θ) of a real parameter θ can attain the second order Bhattacharyya lower bound is derived. Indeed, we obtain a necessary and sufficient condition for the attainment of the second order Bhattacharyya bound for a family of mixtures of distributions which belong to the exponential family. Furthermore, we give an example which does not satisfy this condition, but where the Bhattacharyya bound is attainable for a non-exponential family of distributions.
TL;DR: The algorithm based on centroid neural network with Bhattacharyya distance is evaluated in the context of speech recognition and the results show that it can reduce the Gaussian mixtures by almost 60% over the k-means algorithm.
Abstract: An unsupervised competitive neural network algorithm for clustering mixtures of Gaussian probability density functions is proposed. The algorithm based on centroid neural network with Bhattacharyya distance is evaluated in the context of speech recognition and the results show that it can reduce the Gaussian mixtures by almost 60% over the k-means algorithm.
TL;DR: This work shows that for normally distributed features the Bhattacharyya distance is a particular case of the Jensen-Shannon divergence, and thus evaluation of this distance is equivalent to a statistical test about the similarity of the two populations.
16 Sep 2003
TL;DR: The problem of classification of radar targets when both phases and amplitudes are used under diverse angles of polarization ellipse and ellipticity is considered and it is shown that target separations and classification performances are, consistently, on the order of magnitudes better for the case of joint amplitude and phase case than the traditionally used amplitude-only signatures.
Abstract: In this paper I report new results in an ongoing study to address the problem of classification of radar targets when both phases and amplitudes are used under diverse angles of polarization ellipse and ellipticity is considered in this paper. Rayleigh quotient, Bhattacharyya, Divergence, Kolmogorov, Matusta, Kullback-Leibler distances, Bayesian Probability of Error, Divergence distance-based probability of error, Bhattacharyya distance-based probability of error and Receiver Operating Characteristic curves are derived for both amplitude-only and joint amplitude and phase on real synthetic
aperture radar target signatures and shown that target separations and classification performances are, consistently, on the order of magnitudes better for the case of joint amplitude and phase case than the traditionally used amplitude-only signatures.
01 Jan 2003
13 Mar 2003
TL;DR: This paper presents a comparative study of different unsupervised feature extraction mechanisms and shows their effects on unsuper supervised detection and classification.
Abstract: Feature extraction, implemented as a linear projection from a higher dimensional space to a lower dimensional subspace, is a very important issue in hyperspectral data analysis. The projection must be done in a matter that minimizes the redundancy, maintaining the information content. In hyperspectral data analysis, a relevant objective of feature extraction is to reduce the dimensionality of the data maintaining the capability of discriminating object of interest from the cluttered background. This paper presents a comparative study of different unsupervised feature extraction mechanisms and shows their effects on unsupervised detection and classification. The mechanisms implemented and compared are an unsupervised SVD based band subset selection mechanism, Projection Pursuit, and Principal Component Analysis. For purposes of validating the unsupervised methods, supervised mechanisms as Discriminant Analysis and a supervised band subset selection using Bhattacharyya distance were implemented and its results were compared with the unsupervised methods. Unsupervised band subset selection based on SVD chooses automatically the most independent set of bands. Projection Pursuit based feature extraction algorithm automatically searches for projections that optimize a projection index. The projection index we optimized is one that measures the information divergence between the probability density function of the projected data and the Gaussian probability density function. This produces a projection where the probability density function of the whole data set is multi-modal, instead of a Gaussian uni-modal distribution. This augments the separability of the unknown clusters in the lower dimensional space. Finally they were compared with well-known and used Principal Component Analysis. The methods were tested using synthetic as well as remotely sensed data obtained from AVIRIS and LANDSAT. They were compared using unsupervised classification methods in a known ground truth area.
01 Jan 2003
TL;DR: This work develops a texture classification strategy by a sub-band filtering technique that can be extended to 3D and proposes a feature selection technique based on the Bhattacharyya distance measure that reduces the number of features required for the classification.
Abstract: This paper considers the problem of classification of Magnetic Resonance Images using 2D and 3D texture measures. Joint statistics such as co-occurrence matrices are common for analysing texture in 2D since they are simple and effective to implement. However, the computational complexity can be prohibitive especially in 3D. In this work, we develop a texture classification strategy by a sub-band filtering technique that can be extended to 3D. We further propose a feature selection technique based on the Bhattacharyya distance measure that reduces the number of features required for the classification by selecting a set of discriminant features conditioned on a set training texture samples. We describe and illustrate the methodology by quantitatively analysing a series of images: 2D synthetic phantom, 2D natural textures, and MRI of human knees.
Patent•
29 Apr 2003
TL;DR: In this paper, a plurality of phonemes are arranged using Bhattacharyya's distance manner, and the phoneme from a phoneme having the greatest degree of similarity, one by one, are integrated to perform an integrated layer clustering.
Abstract: Disclosed is a method for reducing computational quantity amount utterance verification using an anti-phoneme model in order to reduce a scenario error due to a wrong recognition in a speech recognition application system. In the method, a plurality of phonemes are arranged. Distances between the phonemes are measured using, a Bhattacharyya’s distance manner. The phonemes are integrated from a phoneme having the greatest degree of similarity, one by one, to perform an integrated layer clustering. Anti-phoneme model aggregates are classified into nine classes by the integrated layer clustering. Each of the nine classes has a similar phoneme. A degree of similarity with respect to an uttered phoneme based on the anti-phoneme model aggregates which are classified into the nine classes is calculated during an utterance verification.
01 Jan 2003
TL;DR: This paper derives probability densities that are least discriminable in the Bhattacharyya metric.
Abstract: In a variety of detection applications, robust techniques are used to cope with the uncertainty in the statistical model assumed for the data. Traditional methods using /spl epsiv/-contamination classes are often too restrictive. Other techniques require that the nominal densities be Gaussian. This paper proposes Bhattacharyya balls around arbitrary nominal distributions as a flexible yet realistic alternative in uncertainty modeling. We derive probability densities that are least discriminable in the Bhattacharyya metric.
01 Aug 2003
TL;DR: The Bhattacharyya distance functional invariance classifier design method (BDFICDM) reaches an excellent tradeoff between the accuracy performance of nearly 100% and the time performance as much as there is available computational resources for parallelism.
Abstract: The Bhattacharyya distance functional invariance classifier design method (BDFICDM) reaches an excellent tradeoff between the accuracy performance of nearly 100% and the time performance as much as there is available computational resources for parallelism. A serial implementation of the method is applied to an image composed of two synthetic and two Bradatz textures preserving its characteristics of being highly suitable to a parallel implementation. This implementation characterizes the pattern by composing independent cells of magnitudes evaluated through the interaction of spatially distributed elementary piece of information (EPI) using the Bhatacharyya distance similarity measure. The localized representation, EPI is composed of shifted frames sampled by a sequential process over a direction in order to preserve the pattern topological information. The representational extension of the functional pattern representation is its reduction focusing only on those EPI best candidates for generating invariance locations and using the graph structures for their representation. The BDF sample is classified within a Bayesian approach by comparing it to only those reduced pattern states of invariance, decreasing abruptly the number of needed interactions and comparisons. The procedure comprises the multiple frame, resolution, hypothesis and class approaches and the image representation used as input in the training and classification processes at the frame decomposition instance, is reduced through the use of the KL transform.