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, Truyen, B & Sahli, H 2003, Energy minimisation methods for static and dynamic curve matching. in D Chen & X Cheng (eds), Pattern Recognition and String Matching. vol. 13, Combinatorial Optimization Series, Springer, Boston, MA, Boston, MA, pp. 545-564, Joint IAPR International Workshops SSPR 2002 and SPR 2002, Windsor, Ontario, Canada, 6/08/02. https://doi.org/10.1007/978-1-4613-0231-5_22
Nyssen, E., Truyen, B., & Sahli, H. (2003). Energy minimisation methods for static and dynamic curve matching. In D. Chen, & X. Cheng (Eds.), Pattern Recognition and String Matching (Vol. 13, pp. 545-564). (Combinatorial Optimization Series). Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0231-5_22
@inbook{4662d85be3dd41b09fc7f14708413492,
title = "Energy minimisation methods for static and dynamic curve matching",
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 = "curve matching, probability density function, PDF, piecewise multi-linear approximation, PML, Bayesian pattern classifiers",
author = "Edgard Nyssen and Bart Truyen and Hichem Sahli",
year = "2003",
doi = "10.1007/978-1-4613-0231-5_22",
language = "English",
isbn = "978-1-4613-7952-2",
volume = "13",
series = "Combinatorial Optimization Series",
publisher = "Springer, Boston, MA",
pages = "545--564",
editor = "Dechang Chen and Xiuzhen Cheng",
booktitle = "Pattern Recognition and String Matching",
note = "Joint IAPR International Workshops SSPR 2002 and SPR 2002 ; Conference date: 06-08-2002 Through 09-08-2002",
}