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A consistent framework for a statistical analysis of surfaces based on generalized stochastic processes

Abstract : The statistical analysis of surfaces is an important issue of Image Analysis, especially in Computational Anatomy. In 2005, Glaunès and Vaillant proposed to handle surfaces through some mathematical currents defined as linear forms on a space of mappings from R 3 into itself. In this paper, we extend this deterministic representation of surfaces using some random linear forms inspired from generalized stochastic processes. Then, we set an observation model where observed surfaces are viewed as random variations of a mean representative of a population (called the template). This observation model accounts not only for the variability of surfaces within an homogeneous population but also for errors due to acquisition. Within this model, we construct an estimate of the template and establish its consistency.
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Submitted on : Tuesday, August 28, 2018 - 12:10:48 PM
Last modification on : Saturday, November 28, 2020 - 3:09:12 AM
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Benjamin Coulaud, Frédéric Richard. A consistent framework for a statistical analysis of surfaces based on generalized stochastic processes. Far East Journal of Theoretical Statistics, 2020, 59 (2), pp.97-120. ⟨10.17654/TS059020097⟩. ⟨hal-01863312⟩

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