AUCL University College London Department of Computer Science Calculating the Curvature Shape Characteristics of the Human Body from 3D Scanner Data by: Ioannis Douros a thesis submitted for the degree of Doctor of Philosophy in Computer Science University of London June 2004 UMI Number: U602665 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Dissertation Publishing UMI U602665 Published by ProQuest LLC 2014. Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code. ProQuest LLC 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346 ABSTRACT In the recent years, there have been significant advances in the development and manufacturing of 3D scanners capable of capturing detailed (external) images of whole human bodies. Such hardware offers the opportunity to collect information that could be used to describe, interpret and analyse die shape of the human body for a variety of applications where shape information plays a vital role (e.g. apparel sizing and customisation; medical research in fields such as nutrition, obesity/anorexia and perceptive psychology; ergonomics for vehicle and furniture design). However, the representations delivered by such hardware typically consist of unstructured or partially structured point clouds, whereas it would be desirable to have models that allow shape-related information to be more immediately accessible. This thesis describes a method of extracting the differential geometry properties of the body surface from unorganized point cloud datasets. In effect, this is a way of constructing curvature maps that allows the detection on the surface of features that are deformable (such as ridges) rather thanreformable under certain transformations. Such features could subsequently be used to interpret the topology of a human body and to enable classification according to its shape, rather than itssize (as is currently the standard practice for many of the applications concerned). The background, motivation and significance of this research are presented in chapter one. Chapter two is a literature review describing the previous and current attempts to model 3D objects in general and human bodies in particular, as well as the mathematical and technical issues associated with the modelling. Chapter three presents an overview of: the methodology employed throughout the research; die assumptions regarding the data to be processed; and the strategy for evaluating the results for each stage of the methodology. Chapter four describes an algorithm (and some variations) for approximating the local surface geometry around a given point of the input data set by means of a least-squares minimization. The output of such an algorithm is a surface patch described in an analytic (implicit) form. This is necessary for the next step described below. The case is made for using implicit surfaces rather than more popular 3D surface representations such as parametric forms or height functions. Chapter five describes the processing needed for calculating curvature-related characteristics for each point of the input surface. This utilises the implicit surface patches generated by the algorithm described in the previous chapter, and enables the construction of a “curvature map” of the original surface, which incorporates rich information such as the principal curvatures, shape indices and curvature directions. Chapter six describes a family of algorithms for calculating features such as ridges and umbilic points on the surface from the curvature map, in a manner that bypasses the problem of separating a vector field (i.e. the principal curvature directions) across the entire surface of an object. An alternative approach, using the focal surface information, is also considered briefly in comparison. The concluding chapter summarises the results from all steps of the processing and evaluates them in relation to die requirements set in chapter one. Directions for further research are also proposed. 1 Acknowledgements I would like to thank my supervisor Professor Bernard Buxton for his help, support, enthusiasm and meticulous feedback, without which this work would be impossible to complete. I would also like to thank Professor Philip Treleaven for enabling me to do this work and supporting me throughout, and my assessor, Professor Simon Arridge for his detailed and constructive remarks that have been essential in determining the directions of the research (especially the comment that “real world data is not all that it is cracked up to be”). Special thanks are due to Dr. Laura Dekker, whose human body modelling work at UCL has been the inspiration and starting point for my research; to Dr. Ian Porteous, whose help and support provided valuable and essential insight into the world of 3D surfaces and their features; and to Hamamatsu Photonics for providing the hardware that made this work possible. I gratefully acknowledge the help and expertise of many other people: Jeni Bougourd, Jon Wells, Avy Tahan, Tim Hutton, Conny Ruiz, Bernhard Spanlang, Tzvetomir Vassilev, Joao Oliveira, George Kartsounis, Kostas Leftheriotis, Nikolaos Sapidis, Hein Daanen and Yiorgos Chrysanthou. Finally, I would like to thank Sue Baggett (for reasons that are too many to list), all my colleagues at UCL, my family and friends for their encouragement and support, and all the anonymous volunteers who offered to have their bodies scanned for this research. 2 TABLE OF CONTENTS ABSTRACT......................................................................................................................... 1 Acknowledgements .... .........................................................................................................2 Index of Figures.................................................................................................................. 6 Index of Tables .................................................................................... 10 1 Introduction .................................................................... 11 1.1 Background.......................... 11 1.2 Motivation .............................................................. 12 13 Significance of the Research .................................................................................. 13 1.4 Hypothesis ............................................................................... 16 1.5 Objectives...............................................................................................................16 1.6 Definitions of Basic Concepts ................................................................................. 17 1.7 Contributions.........................................................................................................19 1.8 Structure of the Thesis............................................ 21 2 Existing Work..............................................................................................................22 2.1 Application Domains .................................................................... 22 2.2 Human Body Scanning Systems ............................... 25 23 Human Body Modelling Work .............................................................................. 26 2.4 Surface Reconstruction and Parameterisation ......................................................27 2.5 Curvature Estimation ........................ 31 2.6 Local Surface Fitting ........................................... 32 2.7 Feature Detection .......................................... 33 2.8 Matching and Registration .................................... 34 2.9 Deformable Shape Modelling and Analysis .............. 35 2.10 Multiple Levels of Detail ........................................................................ 39 3 Design and Methodology.............................................................................................40 3.1 Local Surface Reconstruction ................................................................................ 40 3.2 Issues to be Addressed ............................................................................................42 33 Evaluation of the Results .............................. 49 4 Local Surface Reconstruction................................................................................... 55 4.1 Approximation of the Local Surface Shape ............................................................55 4.2 Minimization Problem... ......................................................................................... 62 43 Closest point selection ................................................................ 66 4.4 Results .....................................................................................................................69 4.5 Conclusions ..................................... 81 5 Calculation of Curvature Characteristics................................................... 82 5.1 Principal Curvatures and their Directions .............. 82 5.2 Gaussian and Mean Curvature .............................................................................. 89 53 Curvedness and Shape Index ..................................................................................91