Abstract
We propose a modified classifier that is based on the maximum a posteriori probability principle that is applied to images having the matrix normal distributions. These distributions have a special covariance structure, which is interpretable and easier to estimate than general covariance matrices. The modification is applicable when the estimated covariance matrices are still not well-conditioned. The proposed classifier is tested on synthetic images and on images of gas burner flames. The results of comparisons with other classifiers are also provided.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Baringhaus, L., Henze, N.: A consistent test for multivariate normality based on the empirical characteristic function. Metrika 35(1), 339–348 (1988)
Devroye, L., Gyorfi, L., Lugosi, G.: A Probabilistic Theory of Pattern Recognition. Springer, Berlin (2013)
Haykin, S.S., et al.: Neural Networks and Learning Machines. Pearson, Upper Saddle River (2009)
Krzysko, M., Skorzybut, M., Wolynski ,W.: Classifiers for doubly multivariate data. Discussiones Mathematicae: Probability & Statistics, p. 31 (2011)
Li, S.Z.: Markov Random Field Modeling in Image Analysis. Springer, Berlin (2009). https://doi.org/10.1007/978-1-84800-279-1
Manceur, A.M., Dutilleul, P.: Maximum likelihood estimation for the tensor normal distribution: algorithm, minimum sample size, and empirical bias and dispersion. J. Comput. Appl. Math. 239, 37–49 (2013)
Ohlson, M., Ahmad, M.R., Von Rosen, D.: The multilinear normal distribution: Introduction and some basic properties. J. Multivar. Anal. 113, 37–47 (2013)
Rafajłowicz, E.: Data structures for pattern and image recognition with application to quality control Acta Polytechnica Hungarica, Informatics (under review)
Rafajłowicz, E., Pawlak-Kruczek, H., Rafajłowicz, W.: Statistical classifier with ordered decisions as an image based controller with application to gas burners. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014. LNCS (LNAI), vol. 8467, pp. 586–597. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-07173-2_50
Rafajłowicz, E., Rafajłowicz, W.: Image-driven decision making with application to control gas burners. In: Saeed, K., Homenda, W., Chaki, R. (eds.) CISIM 2017. LNCS, vol. 10244, pp. 436–446. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59105-6_37
Skubalska-Rafajłowicz, E.: Sparse random projections of camera images for monitoring of a combustion process in a gas burner. In: Saeed, K., Homenda, W., Chaki, R. (eds.) CISIM 2017. LNCS, vol. 10244, pp. 447–456. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59105-6_38
Werner, K., Jansson, M., Stoica, P.: On estimation of covariance matrices with Kronecker product structure. IEEE Trans. Sig. Process. 56(2), 478–491 (2008)
Wójcik, W., Kotyra, A.: Combustion diagnosis by image processing. Photonics Lett. Pol. 1(1), 40–42 (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Rafajłowicz, E. (2018). Classifiers for Matrix Normal Images: Derivation and Testing. In: Rutkowski, L., Scherer, R., Korytkowski, M., Pedrycz, W., Tadeusiewicz, R., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2018. Lecture Notes in Computer Science(), vol 10841. Springer, Cham. https://doi.org/10.1007/978-3-319-91253-0_62
Download citation
DOI: https://doi.org/10.1007/978-3-319-91253-0_62
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-91252-3
Online ISBN: 978-3-319-91253-0
eBook Packages: Computer ScienceComputer Science (R0)