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Learning sparse spline-based shape models

Abstract : In many contexts it is important to be able to find compact representations of the collective morphological properties of a set of objects. This is the case of autonomous robotic platforms operating in natural environments that must use the perceptual properties of the objects present in their workspace to execute their mission. This thesis is a contribution to the definition of formalisms and methods for automatic identification of such models. The shapes we want to characterize are closed curves corresponding to contours of objects detected in the scene. We begin with the formal definition of the notion of shape as classes of equivalence with respect to groups of basic geometric operators, introducing two distinct approaches that have been used in the literature: discrete and continuous. The discrete theory, admitting the existence of a finite number of recognizable landmarks, provides in an obvious manner a compact representation but is sensible to their selection. The continuous theory of shapes provides a more fundamental approach, but leads to shape spaces of infinite dimension, lacking the parsimony of the discrete representation. We thus combine in our work the advantages of both approaches representing shapes of curves with splines: piece-wise continuous polynomials defined by sets of knots and control points. We first study the problem of fitting free-knots splines of varying complexity to a single observed curve. The trade-off between the parsimony of the representation and its fidelity to the observations is a well known characteristic of model identification using nested families of increasing dimension. After presenting an overview of methods previously proposed in the literature, we single out a two-step approach which is formally sound and matches our specific requirements. It splits the identification, simulating a reversible jump Markov chain to select the complexity of the model followed by a simulated annealing algorithm to estimate its parameters. We investigate the link between Kendall's shape space and spline representations when we take the spline control points as landmarks. We consider now the more complex problem of modeling a set of objects with similar morphological characteristics. We equate the problem to finding the statistical distribution of the parameters of the spline representation, modeling the knots and control points as unobserved variables. The identified distribution is the maximizer of a marginal likelihood criterion, and we propose a new Expectation-Maximization algorithm to optimize it. Because we may want to treat a large number of curves observed sequentially, we adapt an iterative (on-line) version of the EM algorithm recently proposed in the literature. For the choice of statistical distributions that we consider, both the expectation and the maximization steps must resort to numerical approximations, leading to a stochastic/on-line variant of the EM algorithm that, as far as we know, is implemented here for the first time.
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Contributor : Laure Amate <>
Submitted on : Monday, February 15, 2010 - 4:02:02 PM
Last modification on : Monday, October 12, 2020 - 10:30:32 AM
Long-term archiving on: : Friday, June 18, 2010 - 6:38:05 PM


  • HAL Id : tel-00456612, version 1



Laure Amate. Learning sparse spline-based shape models. Signal and Image processing. Université Nice Sophia Antipolis, 2009. English. ⟨tel-00456612⟩



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