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Shape Analysis Proceedings in CURRENT ISSUES IN STATISTICAL SHAPE ANALYSIS Edited by KVMardia, C.A.GU1 After AlbrechtDurer, 1524 Leeds University Press Proceedings in Current Issues in Statistical Shape Analysis International Conference, held in Leeds, UK, 5-7 April, 1995, incorporating The 15th Leeds Statistics Research Workshop co-sponsored by the Centre of Medical Imaging Research (CoMIR) Edited by K.V.Mardia, C.A.Gill Department of Statistics, University of Leeds, Leeds LS2 9JT. Leeds University Press Front cover: After AlbrechtDurer, 1524 (Reproduced from "D'Arcy Thompson On Growth and Form" (abridged edition) edited by J.T. Bonner, Cambridge University Press, 1961, with permission). Copyright ©K.V. Mardia, C.A. Gill, Department of Statistics, University of Leeds. ISBN 0 85316 161 5 Conference Committee I.L. Dryden J.T. Kent K.V. Mardia Department of Statistics University of Leeds Leeds, LS2 9JT, UK Conference Organisers C.A. Gill K.V. Mardia Session Chairs Session I: Procrustes and Mathematical Statistics Issues J.T. Kent Department of Statistics, University of Leeds, Leeds LS2 9JT, UK. Session II: Overview and Shape Geometry Fred L. Bookstein Centre for Human Growth & Development, University of Michigan, Ann Arbor, Michigan 48109, USA. Session III: Image Analysis and Computer Vision D.C. Hogg School of Computer Studies, University of Leeds, Leeds LS2 9JT, UK. Session IV: Morphometrics and Shape Geometry K.V. Mardia Department of Statistics, University of Leeds, Leeds LS2 9JT, UK. To David Kendall & Fred Bookstein for their pioneering work on SHAPE PREFACE The annual Leeds Research Workshop by the Department of Statistics began informally (i.e. without numbering!) as far back as 1975. We have had a number of preceding work­ shops with the underlying theme of Shape Analysis, Image Analysis and Medical Imaging. Over the years, key speakers have included Julian Besag, Fred Bookstein, Colin Goodall, John Gower, Chris Jennison, Wilfrid Kendall, Stephen Pizer and Brian Ripley among others. Recently, the Centre of Medical Imaging Research, Leeds has been co-sponsoring the event and it has strengthened the medical imaging applications. It was agreed at our last Research Workshop to have a session on Mathematical Aspects of Shape Analysis. The idea of the conference on "Current Statistical Issues on Shape Analysis" crystalized with Fred Bookstein when various statistical issues were openly discussed on Morphmet last July-August. I am delighted that various key researchers in this field have agreed to participate in the Conference and to contribute to the Proceedings at a very tight timescale. I am also grateful to the authors who gave their cooperation in carrying out my editorial instructions. It is an added advantage of this Conference that the Proceed­ ings are being published and will be available before the Conference albeit at the expense of not too thorough proof-reading. This Conference is in a way reminiscent of many of the Wilks' Workshops organized by Colin Goodall and Geof Watson on Shape Analysis in Princeton. I very much hope that it will have the same success in stimulating new ideas as we had with Princeton's Workshops. To get a flavour of the papers in the Proceedings, the reader is recommended to use the overview prepared by Dr I.L. Dryden. I am grateful to the Conference Committee for their untiring help in acting as refer­ ees at short notice, in particular, to John Kent for helping me take editorial decisions and to lan Dryden for preparing an overview. Christine Gill, the co-editor, has helped me in organizing the Leeds Research Workshop for several years with great enthusiasm and ef­ ficiency. That it has grown into an international event is in no small way due to her efforts. Finally, I should comment on one of the special features of the Proceedings. There are various articles which not only review important topics but also highlight possible future directions. I very much hope that the Proceedings and the Conference prove successful in stimulating these developments. If these speculations become reality, we can look forward to subsequent conferences as a regular event in Shape Analysis! Kanti Mardia 15-3-1995 CONTENTS Overview: Proceedings of CISSA lan Dryden PART I: PAPERS Opening Address Looking at geodesies in E| David G. Kendall 6 SESSION I: Procrustes and Mathematical Statistics Issues 9 Distance Geometry and Shape John C. Gower 11 Procrustes Methods in the Statistical Analysis of Shape Revisited Colin Goodall 18 The Mean Shape and the Shape of the Means Huiling Le 34 Investigating Regularity in Spatial Point Patterns using Shape Analysis lan Dryden, Mohammad Faghihi, Charles Taylor 40 Euclidean Distance Matrix Analysis: a Statistical Review Subhash Lele, Timothy M. Cole, III 49 SESSION II: Overview and Shape Geometry 55 Shape Advances and Future Perspectives Kanti Mardia 57 Construction of a Markov Process on UjtS^ *° Model a Process Arising in Vision Burzin Bhavnagri 76 Abstract Landmarks and their Applications fly a S. Molchanov 82 Shape Metrics and Frobenius Norms Christopher G. Small, Michael E. Lewis 88 Vlll SESSION III: Image Analysis and Computer Vision 97 Reversible Jump MCMC Computation and High Level Image Analysis Peter J. Green 99 A Compartmented Snake for Model-based Boundary Location J.A. Merchant, CM. Onyango, R.D. Tillett 100 Active Shape Models: A Review of Recent Work T.F. Cootes, C.J. Taylor 108 2-D Shape Recognition by Sequential Test Procedures Jens D. Andersen, Klaus Hansen 115 Generating Spatiotemporal Models from Examples Adam Baumberg, David Hogg 122 Bayesian Inference in Computer Vision: Binocular Stereo from Axioms to Algorithm Mads Nielsen 128 SESSION IV: Morphometrics and Shape Geometry 137 Metrics and Symmetries of the Morphometric Synthesis Fred L. Bookstein 139 Multivariate Analysis of Shape Using Partial-warp Scores F. James Rohlf 154 Eigenshape Analysis of the Left Ventricle Paul D. Sampson 159 A Simple Construction of Triangle Shape Space W.D.K. Green 160 Concluding Address Current Issues for Statistical Inference in Shape Analysis John T. Kent 167 ix PART II: POSTERS 177 I: Procrustes and Mathematical Statistics Issues 177 Euclidean Shape Tensor Analysis William Cooper, Colin Goodall, Shailaja Suryawanshi, Hensiong Tan 179 Shape Analysis of Outlines Through Fourier Methods Using Curvature Measures S. Renaud 181 A Transformation Invariant Neural Net for Landmark Data Harry Southworth 183 II: Overview and Shape Geometry 185 Connected Components of the Space of Simple, Closed Non-degenerate Polygons Burzin Bhavnagri 187 Optimal Positions of Star-shaped Sets Anilkoemar Mancham 189 III: Image Analysis and Computer Vision 191 A Unified Shape and Grey-value Model for Biomedical Images Analysis Rocio Aguilar-Chongtay and Richard Baldock 193 Flexible Colour Point Distribution Models CM. Onyango and J.A. Marchant 195 IV: Morphometrics and Shape Geometry 199 Shape Comparisons of Samples of the Fossorial Rodent, Spalax ehrenbergi, from Middle Eastern Localities Marco Corti, Leslie F. Marcus and Carlo Fadda 201 Homology: Selection of Landmarks, Space Curves, and Psuedolandmarks in the Creation of Deformable Templates David Dean, Andre Gueziec and Court B. Cutting 203 Shape Coordinates and Random Walk: Morphological Evolution in the Late Cretaceous Contusotruncana contusa Lineage. (Planktonic Foraminifera) Michal Kucera 206 Analysis of the Skull Shape Changes in Apes, using 3D Procrustes Superimposition Xavier Penin and Michel Baylac 208 The Use of Articular Surface Shape to Match the Components of the H. habilis (OH 8/35) Talocrural Joint C.G. Wood, B.A. Wood, C.A. Key and L.C. Aiello 111 Address List of Authors 213 Author Index 217 OVERVIEW: PROCEEDINGS OF CISSA I.L. Dryden, Department of Statistics, University of Leeds, Leeds, LS2 9JT, UK. Introduction and Opening Address Statistical shape analysis is concerned with all aspects of analyzing objects where location, orientation and possibly scale information can be ignored. The subject has flourished since the pioneering work of D.G. Kendall (1984) and EL. Bookstein (1986), both of whom we are privileged to have speaking at the confer­ ence. Interest in the area is widespread, as can be seen from this collection of papers - from theoretical issues in mathematical statistics, probability and differential geometry to practical issues in computer vision, med­ ical imaging and biology. The papers have been collected in the order of presentation at the conference, with the poster abstracts at the end. Taken as a whole the papers contain a comprehensive survey of the theory and application of the current state of the art in shape analysis. As well as the presentation of some new results, many important discussion points and directions for further work are included. The opening address of the conference is given by D.G. Kendall, whose seminal paper in 1984 laid the mathematical foundations for the subject. His shape space ££, and its differential geometric properties (in­ cluding the Procrustes distance) provide the environment for die work hi most of the proceeding papers. Session I: Procrustes and Mathematical Statistics Issues Procrustes analysis has proved to be a popular method of shape analysis. The generalized Procrustes pro­ cedure was developed by Gower (1975) and has been adapted for shape analysis by Goodall (1991). These two speakers open our first session and offer new thoughts on shape analysis. J.C. Gower considers shape analysis based on Euclidean Distance Matrices and offers geometrical insights into this multidimensional scaling type of approach. C.R. Goodall considers a review of Procrustes methods in shape, including some new developments and updates since his 1991 read paper, particularly with reference to consistency, like­ lihood and estimation of covariance parameters. Further, he proceeds to describe Euclidean Shape Tensor Analysis - an approach to shape analysis based on subsets of landmarks. A special case of this procedure is Euclidean Distance Matrix Analysis (EDMA). To conclude the session further mathematical statistical issues are considered. H. Le considers a gen­ eral notion of mean shape - the Karcher mean shape - and obtains such a mean under Bookstein's (1986) independent isotropic Gaussian model.
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