1 Introduction

1.1 Definition and motivation

Objects are everywhere, natural and man-made. Geometrical data from objects are routinely collected all around us, from sophisticated medical scans in hospitals to ubiquitous smart-phone camera images. Decisions about objects are often made using their sizes and shapes in geometrical data, for example disease diagnosis, face recognition and protein identification. Hence, developing methods for the analysis of size and shape is of wide, growing importance. Locating points on objects is often straightforward and we initially consider analysing such data, before extending to curved outlines, smooth surfaces and full volumes.

Size and shape analysis is of great interest in a wide variety of disciplines. Some specific applications follow in Section 1.4 from biology, chemistry, medicine, image analysis, archaeology, bioinformatics, geology, particle science, genetics, geography, law, pharmacy and physiotherapy. As many of the earliest applications of shape analysis were in biology we concentrate initially on biological examples and terminology, but the domain of applications is in fact very broad indeed.

The word ‘shape’ is very commonly used in everyday language, usually referring to the appearance of an object. Following Kendall (1977) the definition of shape that we consider is intuitive.

Definition 1.1 Shape is all the geometrical information that remains when location, scale and rotational effects are removed from an object.

An object’s ...

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