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Statistics and Analysis of Shapes

  • Textbook
  • © 2006

Overview

Editors:
  1. Hamid Krim

    1. Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Anthony Yezzi

    1. School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, USA

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    You can also search for this editor in PubMed   Google Scholar

  • Practical applications: shape analysis is used in statistics, biomedical applications (Magnetic Resonance Imaging), and many other related disciplines
  • Contributions from some of the leading experts and pioneers in the field
  • Self-contained, unified volume is the first comprehensive treatment of theory, methods, algorithms, and programs available in a single resource
  • Extensive illustrations throughout help the reader overcome the sometimes terse technical details of the geometric and probabilistic formalism.
  • Knowledge of advanced calculus, basic statistics and probability theory are the only prerequisites for the reader
  • May be used as a textbook for a graduate-level special topics course in statistics and signal/image analysis, or for an intensive short course on shape analysis and modeling

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Medial Axis Computation and Evolution

    • Sylvain Bouix, Kaleem Siddiqi, Allen Tannenbaum, Steven W. Zucker
    Pages 1-28

  3. Shape Variation of Medial Axis Representations via Principal Geodesic Analysis on Symmetric Spaces

    • P. Thomas Fletcher, Stephen M. Pizer, Sarang C. Joshi
    Pages 29-59

  4. 2D Shape Modeling using Skeletal Graphs in a Morse Theoretic Framework

    • Sajjad Hussain Baloch, Hamid Krim
    Pages 61-80

  5. Matching with Shape Contexts

    • Serge Belongie, Greg Mori, Jitendra Malik
    Pages 81-105

  6. Shape Recognition Based on an a Contrario Methodology

    • Pablo Musé, Frédéric Sur, Frédéric Cao, Yann Gousseau, Jean-Michel Morel
    Pages 107-136

  7. Integral Invariants and Shape Matching

    • Siddharth Manay, Daniel Cremers, Byung-Woo Hong, Anthony Yezzi Jr., Stefano Soatto
    Pages 137-166

  8. On the Representation of Shapes Using Implicit Functions

    • N. Paragios, M. Taron, X. Huang, M. Rousson, D. Metaxas
    Pages 167-199

  9. Computing with Point Cloud Data

    • Facundo Mémoli, Guillermo Sapiro
    Pages 201-229

  10. Determining Intrinsic Dimension and Entropy of High-Dimensional Shape Spaces

    • Jose A. Costa, Alfred O. Hero III
    Pages 231-252

  11. Object-Image Metrics for Generalized Weak Perspective Projection

    • Gregory Arnold, Peter F. Stiller, Kirk Sturtz
    Pages 253-279

  12. Wulff Shapes at Zero Temperature for Some Models Used in Image Processing

    • Xavier Descombes, Eugène Pechersky
    Pages 281-301

  13. Curve Shortening and Interacting Particle Systems

    • Sigurd Angenent, Allen Tannenbaum, Anthony Yezzi Jr., Ofer Zeitouni
    Pages 303-311

  14. Riemannian Structures on Shape Spaces: A Framework for Statistical Inferences

    • Shantanu Joshi, David Kaziska, Anuj Srivastava, Washington Mio
    Pages 313-333

  15. Modeling Planar Shape Variation via Hamiltonian Flows of Curves

    • Joan Glaunès, Alain Trouvé, Laurent Younes
    Pages 335-361

  16. Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics

    • Guillaume Charpiat, Olivier Faugeras, Renaud Keriven, Pierre Maurel
    Pages 363-395
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Keywords

About this book

Shapes have been among man’s fascinations from thestoneage to thespace age. The scienti?c study of shapes may indeed be traced back to D’Arcy Thompson in his pioneering book On Growth and Form where shape was shown to be dependent on functionality [6]. Numerous de?nitions of a notion of a shape have been proposed in the past, each and every one highlighting aspects relevant to a particular application of interest. The advent of digital imagery, together with the ubiquitous exploitation of its characteristics in a variety of applications, have triggered a renewed and keen interest in further re?ning and possibly unifying the notion ofshape. The present contributed book is, to a large extent, motivated by this upsurge in activity and by the need for an update on recent accomplishments and trends. Theresearchactivityinshapeanalysisisdistinguishedbytwomainschools of thought: — The?rstapproximatesshapesbya?nite-dimensionalrepresentation(a set of landmarks), which is then subjected to various transformations to account for variability and to subsequently derive models. — The second, on the other hand, interprets shapes as closed contours in an in?nite-dimensional space, which, when subjected to transformations, morph into other shapes, thereby yielding a notion of similarity in the space of shapes. 1 Landmark-BasedShapeRepresentation Shapeisaboutscale,orientation,andrelationshipamongtheso-calledchar- teristic points/landmarks of an object-delineating contour. Such information about a data set better de?nes a shape. Equivalently, when such information is taken out of two data sets, the resulting shapes may be compared.

Reviews

From the reviews:

"This edited volume is a state-of-the-art collection of papers in digital image processing and analysis. … The book is intellectually stimulating and written for researchers in electrical engineering, computer science, computational statistics, or applied mathematics. It will be useful for presentations in research seminars or in journal clubs in these areas." (Victor Patrangenaru, Journal of the American Statistical Association, Vol. 103 (484), December, 2008)

Editors and Affiliations

  • Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, USA

    Hamid Krim

  • School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, USA

    Anthony Yezzi

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