A functional data approach for statistical shapes analysis
Issam Moindjié · Oct 11, 2024
Date: 2024-10-11
Time: 15:30-16:30 (Montreal time)
Location: In person, Burnside 1104
https://mcgill.zoom.us/j/87824357176
Meeting ID: 878 2435 7176
Passcode: None
Abstract:
The shape $\tilde{\mathbf{X}}$ of a random planar curve, $\mathbf{X}$, is what remains when the deformation variables (scaling, rotation, translation, and reparametrization) 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. I will introduce a new framework for studying $\bf X$ based on functional data analysis in this presentation. 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 and real datasets demonstrate how this new approach performs better at analyzing random planar curves than traditional functional data methods.