Statistical Classifiers in Computer Vision

Abstract: This paper introduces a unified Bayesian approach to 3–D computer visionusing segmented image features. The theoretical part summarizes the basic require-ments of statistical object recognition systems. Non–standard types of models are intro-duced using parametric probability density functions, which allow the implementationof Bayesian classifiers for object recognition purposes. The importance of model den-sities is demonstrated by concrete examples. Normally distributed features are used forautomatic learning, localization, and classification. The contribution concludes with theexperimental evaluation of the presented theoretical approach.1 IntroductionClassification in computer vision is commonly dominated by geometrical, model–based approaches (Faugeras (1993)). Heuristics for many algorithms in imageprocessing restricted to the given problem domain and motivated by associatedapplications are reported in the literature. Herein, model–based image analysisprovides the scientific framework for matching algorithms and for understandingthe information process. The comprehensive goal is to describe the intrinsiccharacter of images in a symbolic or parametric manner.Bayesian methods have provided solutions to various classical problems in patternrecognition. Especially the progress in the field of speech processing is substan-tially based on the application of statistical methods. The general use of Bayesianclassifiers is motivated by several aspects: they show optimality in a decisiontheoretic sense under a 0–1 cost function (Duda and Hart (1973)). Furthermore,statistical methods can deal with uncertainty in a natural manner, have a wellelaborated mathematical theory, and provide a unified framework within whichmany different tasks can be considered. For that reason, we favor model–basedcomputer vision algorithms which apply statistical discriminants or, at least, closeapproximations of Bayesian classifiers.In this paper, we present a probabilistic framework for 3–D vision: statisticalmethods for object modeling, algorithms for the automatic estimation of modelparameters — even in the presence of incomplete and disturbed training data —,classification rules, and localization methods for 3–D objects using 2–D views.The introduced model densities show several degrees of freedom, and standardhidden Markov models or mixtures of densities can be derived by specialization.The experiments prove that the classification and pose estimation task for 3–Dobjects using real image data can be treated statistically