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Unformatted text preview: PATTERN RECOGNITION Professor Aly A. Farag Computer Vision and Image Processing Laboratory University of Louisville URL: www.cvip.uofl.edu ; Email: aly.farag@louisville.edu Planned for ECE 620 and ECE 655  Summer 2011 TA/Grader: Melih Aslan; CVIP Lab Rm 6, msaslan01@lousiville.edu Lecture 7: Parameter Estimation for Gaussian Classification MaximumLikelihood & Bayesian Parameter Estimation Introduction MaximumLikelihood Estimation Example of a Specific Case The Gaussian Case: unknown and Bias Appendix: ML Problem Statement Introduction Data availability in a Bayesian framework We could design an optimal classifier if we knew: P( i ) (priors) P(x  i ) (classconditional densities) Unfortunately, we rarely have this complete information! Design a classifier from a training sample Priors estimation is usually easy to accomplish Samples are often too small for classconditional estimation (large dimension of feature space!) Pattern Classification, Chapter 3 2 Gaussian Case: P(x  i ) is normal; i.e., P(x  i ) ~ N( i , i ) Characterized by 2 parameters i , i Estimation techniques MaximumLikelihood (ML) and the Bayesian estimations Results are nearly identical, but the approaches are different Pattern Classification, Chapter 3 3 Parameters in ML estimation Parameters are fixed but unknown! Parameters are fixed but unknown!...
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 Summer '08
 Staff
 Image processing

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