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Bhattacharyya distance

About: Bhattacharyya distance is a(n) research topic. Over the lifetime, 1340 publication(s) have been published within this topic receiving 31623 citation(s). The topic is also known as: Bhattacharyya coefficient.
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Journal ArticleDOI
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.

4,901 citations


Proceedings ArticleDOI
14 Feb 2000-
TL;DR: The theoretical analysis of the approach shows that it relates to the Bayesian framework while providing a practical, fast and efficient solution for real time tracking of non-rigid objects seen from a moving camera.
Abstract: A new method for real time tracking of non-rigid objects seen from a moving camera is proposed. The central computational module is based on the mean shift iterations and finds the most probable target position in the current frame. The dissimilarity between the target model (its color distribution) and the target candidates is expressed by a metric derived from the Bhattacharyya coefficient. The theoretical analysis of the approach shows that it relates to the Bayesian framework while providing a practical, fast and efficient solution. The capability of the tracker to handle in real time partial occlusions, significant clutter, and target scale variations, is demonstrated for several image sequences.

3,295 citations


Journal ArticleDOI
Thomas Kailath1
TL;DR: This partly tutorial paper compares the properties of an often used measure, the divergence, with a new measure that is often easier to evaluate, called the Bhattacharyya distance, which gives results that are at least as good and often better than those given by the divergence.
Abstract: Minimization of the error probability to determine optimum signals is often difficult to carry out. Consequently, several suboptimum performance measures that are easier than the error probability to evaluate and manipulate have been studied. In this partly tutorial paper, we compare the properties of an often used measure, the divergence, with a new measure that we have called the Bhattacharyya distance. This new distance measure is often easier to evaluate than the divergence. In the problems we have worked, it gives results that are at least as good as, and are often better, than those given by the divergence.

1,783 citations


Journal ArticleDOI
TL;DR: The Mahalanobis distance, in the original and principal component (PC) space, will be examined and interpreted in relation with the Euclidean distance (ED).
Abstract: The theory of many multivariate chemometrical methods is based on the measurement of distances. The Mahalanobis distance (MD), in the original and principal component (PC) space, will be examined and interpreted in relation with the Euclidean distance (ED). Techniques based on the MD and applied in different fields of chemometrics such as in multivariate calibration, pattern recognition and process control are explained and discussed.

1,516 citations


Journal ArticleDOI
Abstract: This paper, mostly expository in nature, surveys four measures of distinguishability for quantum-mechanical states. This is done from the point of view of the cryptographer with a particular eye on applications in quantum cryptography. Each of the measures considered is rooted in an analogous classical measure of distinguishability for probability distributions: namely, the probability of an identification error, the Kolmogorov distance, the Bhattacharyya coefficient, and the Shannon (1948) distinguishability (as defined through mutual information). These measures have a long history of use in statistical pattern recognition and classical cryptography. We obtain several inequalities that relate the quantum distinguishability measures to each other, one of which may be crucial for proving the security of quantum cryptographic key distribution. In another vein, these measures and their connecting inequalities are used to define a single notion of cryptographic exponential indistinguishability for two families of quantum states. This is a tool that may prove useful in the analysis of various quantum-cryptographic protocols.

701 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20222
202146
202053
201969
201873
201763

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Topic's top 5 most impactful authors

Ismail Ben Ayed

10 papers, 291 citations

Lochandaka Ranathunga

5 papers, 25 citations

Farid Melgani

4 papers, 142 citations

Simone Calderara

4 papers, 152 citations

Benoit Huet

4 papers, 44 citations