On the Mahalanobis Distance Classification Criterion for Multidimensional Normal Distributions

Gallego Bonet, Guillermo and Cuevas Rodríguez, Carlos and Mohedano del Pozo, Raúl and García Santos, Narciso (2013). On the Mahalanobis Distance Classification Criterion for Multidimensional Normal Distributions. "IEEE Transactions on Signal Processing", v. 61 (n. 17); pp. 4387-4396. ISSN 1053-587X. https://doi.org/10.1109/TSP.2013.2269047.

Description

Title: On the Mahalanobis Distance Classification Criterion for Multidimensional Normal Distributions
Author/s:
  • Gallego Bonet, Guillermo
  • Cuevas Rodríguez, Carlos
  • Mohedano del Pozo, Raúl
  • García Santos, Narciso
Item Type: Article
Título de Revista/Publicación: IEEE Transactions on Signal Processing
Date: 1 September 2013
ISSN: 1053-587X
Volume: 61
Subjects:
Freetext Keywords: multidimensional signal processing, uncertainty, classification algorithms, Gaussian distribution, Chi-squared distribution, Mahalanobis distance.
Faculty: E.T.S.I. Telecomunicación (UPM)
Department: Señales, Sistemas y Radiocomunicaciones
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

Many existing engineering works model the statistical characteristics of the entities under study as normal distributions. These models are eventually used for decision making, requiring in practice the definition of the classification region corresponding to the desired confidence level. Surprisingly enough, however, a great amount of computer vision works using multidimensional normal models leave unspecified or fail to establish correct confidence regions due to misconceptions on the features of Gaussian functions or to wrong analogies with the unidimensional case. The resulting regions incur in deviations that can be unacceptable in high-dimensional models. Here we provide a comprehensive derivation of the optimal confidence regions for multivariate normal distributions of arbitrary dimensionality. To this end, firstly we derive the condition for region optimality of general continuous multidimensional distributions, and then we apply it to the widespread case of the normal probability density function. The obtained results are used to analyze the confidence error incurred by previous works related to vision research, showing that deviations caused by wrong regions may turn into unacceptable as dimensionality increases. To support the theoretical analysis, a quantitative example in the context of moving object detection by means of background modeling is given.

More information

Item ID: 19074
DC Identifier: http://oa.upm.es/19074/
OAI Identifier: oai:oa.upm.es:19074
DOI: 10.1109/TSP.2013.2269047
Deposited by: Dr Guillermo Gallego Bonet
Deposited on: 28 Aug 2013 08:31
Last Modified: 21 Apr 2016 17:19
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