This paper addresses the problem of estimating the model parameters of a piecewise multi-linear (PML) approximation to a probability density function (PDF). In an earlier paper, we already introduced the PML model and discussed its use for the purpose of designing Bayesian pattern classifiers. The estimation of the unknown model parameters was based on a least squares minimisation of the difference between the estimated PDF and the estimating PML function. Here, we show how a Maximum Likelihood (ML) approach can be used to estimate the unknown parameters and discuss the advantages of this approach. Subsequently, we briefly introduce its application in a new approach to histogram matching in digital subtraction radiography.
Nyssen, E, Naik, N & Truyen, B 2002, Piecewise multi-linear PDF modelling using an ML approach. in T Caelli, A Amin, RPW Duin, D de Ridder & M Kamel (eds), Structural, Syntactic, and Statistical Pattern Recognition: Proceedings SSPR/SPR 2002, Joint IAPR International Workshops on Statistical Techniques in Pattern Recognition (SPR) and Structural and Syntactic Pattern Recognition (SSPR). vol. 2396, Lecture Notes in Computer Science, Springer-Verlag Berlin Heidelberg, Berlin, Germany, pp. 752-760, SSPR/SPR 2002, Joint IAPR International Workshops on Statistical Techniques in Pattern Recognition (SPR) and Structural and Syntactic Pattern Recognition (SSPR), Windsor, Ontario, Canada, 6/08/02. https://doi.org/10.1007/3-540-70659-3_79
Nyssen, E., Naik, N., & Truyen, B. (2002). Piecewise multi-linear PDF modelling using an ML approach. In T. Caelli, A. Amin, R. P. W. Duin, D. de Ridder, & M. Kamel (Eds.), Structural, Syntactic, and Statistical Pattern Recognition: Proceedings SSPR/SPR 2002, Joint IAPR International Workshops on Statistical Techniques in Pattern Recognition (SPR) and Structural and Syntactic Pattern Recognition (SSPR) (Vol. 2396, pp. 752-760). (Lecture Notes in Computer Science). Springer-Verlag Berlin Heidelberg. https://doi.org/10.1007/3-540-70659-3_79
@inproceedings{a01f97f3f5544374a87a66fe2c847b7e,
title = "Piecewise multi-linear PDF modelling using an ML approach",
abstract = "This paper addresses the problem of estimating the model parameters of a piecewise multi-linear (PML) approximation to a probability density function (PDF). In an earlier paper, we already introduced the PML model and discussed its use for the purpose of designing Bayesian pattern classifiers. The estimation of the unknown model parameters was based on a least squares minimisation of the difference between the estimated PDF and the estimating PML function. Here, we show how a Maximum Likelihood (ML) approach can be used to estimate the unknown parameters and discuss the advantages of this approach. Subsequently, we briefly introduce its application in a new approach to histogram matching in digital subtraction radiography.",
keywords = "probability density function, piecewise multi-linear approximation, Bayesian pattern classifiers, digital subtraction radiography",
author = "Edgard Nyssen and Naren Naik and Bart Truyen",
year = "2002",
doi = "10.1007/3-540-70659-3_79",
language = "English",
isbn = "978-3-540-44011-6",
volume = "2396",
series = "Lecture Notes in Computer Science",
publisher = "Springer-Verlag Berlin Heidelberg",
pages = "752--760",
editor = "Terry Caelli and Adnan Amin and Duin, {Robert P. W.} and {de Ridder}, Dick and Mohamed Kamel",
booktitle = "Structural, Syntactic, and Statistical Pattern Recognition",
note = "SSPR/SPR 2002, Joint IAPR International Workshops on Statistical Techniques in Pattern Recognition (SPR) and Structural and Syntactic Pattern Recognition (SSPR) ; Conference date: 06-08-2002 Through 08-08-2002",
}