Statistical Analysis of Functions on Surfaces, With an Application to Medical Imaging

Abstract

Abstract–In functional data analysis, data are commonly assumed to be smooth functions on a fixed interval of the real line. In this work, we introduce a comprehensive framework for the analysis of functional data, whose domain is a two-dimensional manifold and the domain itself is subject to variability from sample to sample. We formulate a statistical model for such data, here called functions on surfaces, which enables a joint representation of the geometric and functional aspects, and propose an associated estimation framework. We assess the validity of the framework by performing a simulation study and we finally apply it to the analysis of neuroimaging data of cortical thickness, acquired from the brains of different subjects, and thus lying on domains with different geometries. Supplementary materials for this article are available online.

KEYWORDS:

• Functional data
• Geometric statistics
• Neuroimaging
• Registration

Acknowledgments

The authors greatly appreciate the really useful comments of the AE and two referees, which helped considerably strengthen the article.

Additional information

Funding

JA was supported by the Engineering and Physical Sciences Research Council (EP/K021672/2 and EP/N014588/1). EL was supported by the EPSRC grant EP/L016516/1