Statistics and Analysis of Shapes

1. Front Matter

   Pages i-xi

   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

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.

• Computerassistierte Detektion
• Graph
• Master Patient Index
• Probability theory
• algorithm
• algorithms
• calculus
• cognition
• databases
• image analysis
• image processing
• learning
• linear optimization
• modeling
• statistics

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)

• 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

Policies and ethics