%0 Book Section
%T A Consistent Statistical Framework for Current-Based Representations of Surfaces
%+ Institut de Mathématiques de Marseille (I2M)
%A Coulaud, Benjamin
%A Richard, Frédéric, Jp
%@ 978-3-319-22803-7
%B Curves and Surfaces
%E J.-D. Boissonat et al.
%V 9213
%P 151-159
%8 2015
%D 2015
%Z Engineering Sciences [physics]/Signal and Image processing
%Z Statistics [stat]/Methodology [stat.ME]
%Z Statistics [stat]/Applications [stat.AP]Book sections
%X In this paper, we deal with the statistical analysis of surfaces. To address this issue, we extend to a stochastic setting a surface representation by currents (Glaunès and Vaillant, 2005). This extension is inspired from the theory of generalized stochastic processes due to It\^o (1954) and Gelfand and Vilenkin (1964). It consists of random linear forms defined on a space of vector fields. Upon this representation, we build a probabilistic model that allows us to describe the random variability of current-based representations of surfaces. For this model, we then propose estimators of a mean representant of a surface population, and the population variance. Finally, we establish the consistency of these estimators.
%G English
%L hal-01270046
%U https://hal.science/hal-01270046
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ I2M
%~ I2M-2014-