Statistical shape analysis of wheat root systems

The roots of a plant play a vital role in its growth and development, but due to practical difficulties of observing underground roots, the study of their shape has long been neglected. Recent advances in CT imaging technology have allowed for accurate non-destructive imaging of root systems in soil. This technique has formed the basis of the FutureRoots project. The main challenge with analysing the shape of a plant root system is that they have varying topological structure, so traditional shape analysis methods cannot be applied. In this thesis, we develop three approaches for analysing wheat root systems. The first approach involves measuring a set of pre-chosen root traits, and analysing this set using conventional statistical methods. This approach is effective but may miss potentially important shape information and the large number of measurable traits reduces the potential power of statistical tests. The second approach is to perform pairwise comparisons based on the Hausdorff Metric and use Multidimensional scaling to reduce a large set of pairwise comparisons to a dataset which can be analysed with conventional statistical methods. This approach can detect and test for overall shape differences but can fail to detect subtle differences. The third approach is to apply the Persistent Homology technique from Topological Data Analysis, which is designed to find underlying topological differences between two shapes. This method successfully finds differences but it is difficult to interpret the results. We will apply these three techniques to simulated data and a real life dataset. In addition, because of experimental considerations, the wheat roots had to be unnaturally constrained to a small area so we have developed a method to estimate how they would have grown unconstrained