English

A Hierarchical Geodesic Model for Longitudinal Analysis on Manifolds

Methodology 2022-03-07 v3 Differential Geometry Metric Geometry Optimization and Control Applications

Abstract

In many applications, geodesic hierarchical models are adequate for the study of temporal observations. We employ such a model derived for manifold-valued data to Kendall's shape space. In particular, instead of the Sasaki metric, we adapt a functional-based metric, which increases the computational efficiency and does not require the implementation of the curvature tensor. We propose the corresponding variational time discretization of geodesics and employ the approach for longitudinal analysis of 2D rat skulls shapes as well as 3D shapes derived from an imaging study on osteoarthritis. Particularly, we perform hypothesis test and estimate the mean trends.

Keywords

Cite

@article{arxiv.2111.15371,
  title  = {A Hierarchical Geodesic Model for Longitudinal Analysis on Manifolds},
  author = {Esfandiar Nava-Yazdani and Hans-Christian Hege and Christoph von Tycowicz},
  journal= {arXiv preprint arXiv:2111.15371},
  year   = {2022}
}

Comments

This is a preprint version of an article submitted to the Journal of Mathematical Imaging and Vision c\c{opyright}Springer

R2 v1 2026-06-24T07:57:41.031Z