Motivation for Function and Shape Analysis

Abstract

This textbook is dedicated to the study of functional data analysis and shape analysis of curves in Euclidean spaces. In the first item, one develops tools for statistical analysis of real-valued functional data on fixed intervals. While function data analysis is a broad topic area, worthy of a textbook in itself, we will focus heavily on a specific aspect that deals with alignment or registration of functional data. In the second item, one studies shapes formed by curves in 2D, 3D, and higher dimensions, with a goal of performing statistical inferences. Since these curves are also functions, albeit vector valued, and the issue of registration is of prime importance in their shape analysis, we will cover these topics under a broad umbrella of elastic functional and shape data analysis!