Since the publication of the first edition of this book (Dryden and Mardia 1998) there have been numerous exciting novel developments in the field of statistical shape analysis. Although a book length treatment of the new developments is certainly merited, much of the work that we discussed in the first edition still forms the foundations of new methodology. The shear volume of applications of the methodology has multiplied significantly, and we are frequently amazed by the breadth of applications of the field.

The first edition of the book primarily discussed the topic of landmark shape analysis, which is still the core material of the field. We have updated the material, with a new focus on illustrating the methodology with examples based on the shapes package (Dryden 2015) in R (R Development Core Team 2015). This new focus on R applications and an extension of the material has resulted in the new title ‘Statistical Shape Analysis, with Applications in R’ for this second edition. There is more emphasis on the joint analysis of size and shape (form) in this edition, treatment of unlabelled size-and-shape and shape analysis, more three-dimensional applications and more discussion of general Riemannian manifolds, providing more context in our discussion of geometry of size and shape spaces. All chapters contain a good deal of new material and we have rearranged some of the ordering of topics for a more coherent treatment. Chapters 6, 13, 14, 16 and 18 are almost entirely new. We have updated the references and give brief descriptions of many of the new and ongoing developments, and we have included some exercises at the end of the book which should be useful when using the book as a class text.

In Chapter 1 we provide an introduction and describe some example datasets that are used in later chapters. Chapter 2 introduces some basic size and shape coordinates, which we feel is an accessible way to understand some of the more elementary ideas. Chapter 3 provides a general informal introduction to Riemannian manifolds to help illustrate some of the geometrical concepts. In Chapter 4 we concentrate on Kendall’s shape space and shape distances, and in Chapter 5 the size-and-shape (form) space and distance.

After having provided the geometrical framework in Chapters 2--5, statistical inference is then considered with a focus on the estimation of mean shape or size-and-shape in Chapter 6. Chapter 7 provides a detailed discussion of Procrustes analysis, which is the main technique for registering landmark data. Chapter 8 contains specific two-dimensional methods which exploit the algebraic structure of complex numbers, where rotation and scaling are carried out via multiplication and translation by addition. Chapter 9 contains the main practical inferential methods, based on tangent space approximations. Chapter 10 introduces some shape distributions, primarily for two-dimensional data. Chapter 11 contains shortened material on offset normal shape distributions compared with the first edition, retaining the main results and referring to our original papers for specific details. Chapter 12 discusses size and shape deformations, with a particular focus on thin-plate splines as in the first edition.

In Chapter 13 we have introduced many recent developments in non-parametric shape analysis, with discussion of limit theorems and the bootstrap. Chapter 14 introduces unlabelled shape, where the correspondence between landmarks is unknown and must be estimated, and the topic is of particularly strong interest in bioinformatics. Chapter 15 lays out some distance-based measures, and some techniques based on multidimensional scaling. Chapter 16 provides a brief summary of some recent work on analysing curves, surfaces and volumes. Although this area is extensive in terms of applications and methods, many of the basic concepts are extensions of the simpler methods for landmark data analysis. Chapter 17 is a more minor update of shapes in images, which is a long-standing application area, particularly Bayesian image analysis using deformable templates. Chapter 18 completes the material with discussion of a wide variety of recent methods, including statistics on other manifolds and the broad field of Object Data Analysis.

There are many other books on the topic of shape analysis which complement our own including Bookstein (1991); Stoyan and Stoyan (1994); Stoyan et al. (1995); Small (1996); Kendall et al. (1999); Lele and Richtsmeier (2001); Grenander and Miller (2007); Bhattacharya and Bhattacharya (2008); Claude (2008); Davies et al. (2008b); da Fontoura Costa and Marcondes Cesar J. (2009); Younes (2010); Zelditch et al. (2012); Brombin and Salmaso (2013); Bookstein (2014) and Patrangenaru and Ellingson (2015). A brief discussion of other books and reviews is given in Section 18.7.

Our own work has been influenced by the long-running series of Leeds Annual Statistical Research (LASR) Workshops, which have now been taking place for 40 years (Mardia et al. 2015). A strong theme since the 1990s has been statistical shape analysis, and a particularly influential meeting in 1995 had talks by both Kendall and Bookstein among many others (Mardia and Gill 1995), and the proceedings volume was dedicated to both David Kendall and Fred Bookstein.

We are very grateful for the help of numerous colleagues in our work, notably at the University of Leeds and The University of Nottingham. We give our special thanks to Fred Bookstein and John Kent who provided many very insightful comments on the first edition and we are grateful for Fred Bookstein's comments on the current edition. Their challenging comments have always been very helpful indeed. Also, support of a Royal Society Wolfson Research Merit Award WM110140 and EPSRC grant EP/K022547/1 is gratefully acknowledged.

We would be pleased to hear about any typographical or other errors in the text.

Ian Dryden and Kanti Mardia
Nottingham, Leeds and Oxford,
January 2016