A Consistent Statistical Framework for Current-Based Representations of Surfaces

Benjamin Coulaud (1) , Frédéric Jp Richard (1)

1 I2M - Institut de Mathématiques de Marseille

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.

Domaines: Traitement du signal et de l'image [eess.SP]; Méthodologie [stat.ME]; Applications [stat.AP]

Benjamin Coulaud, Frédéric Jp Richard. A Consistent Statistical Framework for Current-Based Representations of Surfaces. J.-D. Boissonat et al. Curves and Surfaces, 9213, , pp.151-159, 2015, 978-3-319-22803-7. ⟨hal-01270046⟩