  The root is an important organ of a plant since it is responsible for water
and nutrient uptake. Analyzing and modelling variabilities in the geometry and
topology of roots can help in assessing the plant's health, understanding its
growth patterns, and modeling relations between plant species and between
plants and their environment. In this article, we develop a framework for the
statistical analysis and modeling of the geometry and topology of plant roots.
We represent root structures as points in a tree-shape space equipped with a
metric that quantifies geometric and topological differences between pairs of
roots. We then use these building blocks to compute geodesics, i.e., optimal
deformations under the metric between root structures, and to perform
statistical analysis on root populations. We demonstrate the utility of the
proposed framework through an application to a dataset of wheat roots grown in
different environmental conditions. We also show that the framework can be used
in various applications including classification and regression.
