Taking shape: The data science of elastic shape analysis with practical applications

Abstract

A mathematical curve can represent many different objects, both physical and abstract, from the outline curve of an artefact in an image to the weight of growing animal to the set of frequencies used in a sound. Regardless of these variations, the curves can almost always vary non-linearly. One way to study shapes and their potential variations is elastic shape analysis, a rich theory of which has developed over the past twenty years. However, methods of elastic shape analysis are seldom utilized in practical applications on real-world data, especially outside of the mathematical shape analysis community.

Our aim in this thesis is to explore some practical applications of elastic shape analysis. To do this, we work with various types of shape data, the majority of which are based on image datasets. As our focus is on two-dimensional curves, it is important to be able to robustly extract contours from images, before we can apply elastic shape analysis tools. In order to analyse the shapes in a dataset, we turn to methods of machine learning, to investigate the applications of elastic shape analysis in classification.

In this thesis, we introduce an anthology of projects, in order to emphasise and under- stand the potential of elastic shape analysis in practical applications. There are four main

projects in this thesis: (i) Classification of objects using outlines and the comparisons between methods of elastic shape analysis, geometric morphometrics, and human experts,

with a focus on ancient Greek vases, (ii) Mussel species identification and a demonstra- tion that shape may not be enough in some applications, (iii) A novel tool to monitor

the development of k ̄ak ̄ap ̄o chicks, and (iv) Classifying individual kiwi based on acoustic data from their calls.

By combining tools from computer vision and machine learning with methods of elastic shape analysis, we introduce a practical framework for the application of elastic shape analysis, through a data science lens.