# Statistical Analysis of Functions on Surfaces, with an application to Medical Imaging

arXiv: https://arxiv.org/abs/1707.00453 · HTML: https://mlsanity.com/paper/1707.00453/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jul 2017.

## Built on by (most cited first, 1 of 1)

- [Energy Trees: Regression and Classification With Structured and Mixed-Type Covariates](https://mlsanity.com/paper/2207.04430/) (2022)

## Abstract (arXiv)

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.