# Statistical Analysis and Modeling of the Geometry and Topology of Plant Roots

## TL;DR

This paper introduces a statistical framework for analyzing and modeling the geometry and topology of plant roots, aiding in understanding growth patterns and environmental effects.

## Contribution

The authors develop a novel tree-shape space representation and metric for root structures, enabling statistical analysis, geodesic computation, and applications like classification.

## Key findings

- Framework effectively captures root variability
- Application to wheat roots demonstrates environmental influence
- Framework supports classification and regression tasks

## Abstract

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.