A1523
Title: A fully functional approach for statistical shape analysis
Authors: Issam-Ali Moindjie - University of Quebec in Montreal (Canada) [presenting]
Marie-Helene Descary - University of Quebec in Montreal (Canada)
Cedric Beaulac - Universite Du Quebec a Montreal (Canada)
Abstract: The shape $\tilde{\bf X}$ of a random planar curve, $\mathbf{X}$, is what remains when the deformation variables (scaling, rotation, translation, and parametrization) are removed. Previous studies in statistical shape analysis have focused on analyzing $\tilde{\bf X}$ through discrete observations of ${\bf X}$. While this approach has some computational advantages, it overlooks the continuous nature of variables: $\tilde{\bf X}$, ${\bf X}$, and it ignores the potential dependence of deformation variables on each other and $\tilde{ \bf X}$, which results in a loss of information in the data structure. The approach uses functional data analysis to introduce a new framework for studying $\bf X$. Basis expansion techniques are employed to find analytic solutions for deformation variables such as rotation and parametrization deformations. Then, the generative model of $\bf X$ is investigated using a joint-principal component analysis approach. Numerical experiments on synthetic data and the $\textit{2dshapesstructures}$ datasets demonstrate how this new approach performs better at analyzing random planar curves than traditional functional data methods.
