Towards a coherent statistical framework for dense deformable template estimation

• Published in: Journal of the Royal Statistical Society. Series B, Statistical methodology Vol. 69; no. 1; pp. 3 - 29
• Main Authors: Allassonnière, S, Amit, Y, Trouvé, A
• Format: Journal Article
• Language: English
• Published: Oxford, UK Oxford, UK : Blackwell Publishing Ltd 01.02.2007; Blackwell Publishing Ltd; Blackwell Publishers; Blackwell; Royal Statistical Society; Oxford University Press
• Series: Journal of the Royal Statistical Society Series B
• Subjects: Algorithms; Applied sciences; Approximation; Artificial intelligence; Bayesian analysis; Bayesian estimation; Computer based modeling; Computer science; control theory; systems; Consistent estimators; Covariance; Covariance matrices; Deformable templates; Deformation; Distribution theory; Error rates; Estimating techniques; Exact sciences and technology; Expectation-maximization algorithm; Geometric shapes; Mathematics; Methodology; Mixture models; Object recognition; Parametric inference; Parametric models; Pattern recognition. Digital image processing. Computational geometry; Pixels; Probability; Probability and statistics; Probability theory and stochastic processes; Research methods; Sciences and techniques of general use; Standard deviation; Statistical methods; Statistical variance; Statistics; Studies; Bayes estimation; Computer vision; Bayesian estimation; Expectation-maximization algorithm; Iterative method; Statistical estimation; Object recognition; Asymptotic convergence; Template; Statistical method; Deformable templates; Algorithm performance; Mixed model; Statistical model; Classification; A posteriori estimation; Mixture models; Probabilistic model; Maximum likelihood; EM algorithm; Computing method
• ISSN: 1369-7412; 1467-9868
• DOI: 10.1111/j.1467-9868.2007.00574.x

The problem of estimating probabilistic deformable template models in the field of computer vision or of probabilistic atlases in the field of computational anatomy has not yet received a coherent statistical formulation and remains a challenge. We provide a careful definition and analysis of a well-defined statistical model based on dense deformable templates for grey level images of deformable objects. We propose a rigorous Bayesian framework for which we prove asymptotic consistency of the maximum a posteriori estimate and which leads to an effective iterative estimation algorithm of the geometric and photometric parameters in the small sample setting. The model is extended to mixtures of finite numbers of such components leading to a fine description of the photometric and geometric variations of an object class. We illustrate some of the ideas with images of handwritten digits and apply the estimated models to classification through maximum likelihood.