Statistics and Analysis of Shapes

ISBN-13: 9780817643768 / Angielski / Twarda / 2006 / 396 str.

Hamid Krim; Anthony Yezzi Jr

Opis

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.

Recenzje

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)

Spis treści

Introduction S. Bouix, K. Siddiqi, A. Tannenbaum, and S.W. Zucker: Medial Axis Computation and Evolution P.T. Fletcher, S.M. Pizer, adn S.C. Joshi: Shape Variation of Medial Axis Representations via Principal Geodesic Analysis of Symmetric Spaces S.H. Balloch and H. Krim: 2D Shape Modeling Using Skeletal Graphs in a Morse Theoretic Framework S. Belongie, G. Mori, and J. Malik: Matching with Shape Contexts P. Musé, F. Sur, F. Cao, Y. Gousseau, and J.-M. Morel: Shape Recognition Based on a Contrario Methodology S. Manay, D. Cremers, B.-W. Hong, A. Yezzi, Jr., and S. Soatto: Integral Invariants and Shape Matching N. Paragios, M. Taron, X. Huang, M. Rousson, and D. Metaxas: On the Representation of Shapes Using Implicit Functions F. Mémoli and G. Sapiro: Computing with Point Cloud Data J.A. Costa and A.O. Hero III: Determining Intrinsic Dimension and Entropy of High-Dimensional Shape Spaces G. Arnold, P.F. Stiller, and K. Sturtz: Object-Image Metrics for Generalized Weak Perspective Projection X. Descombes and E. Pechersky: Wulff Shapes at Zero Temperature for Some Models Used in Image Processing S. Angenent, A. Tannenbaum, A. Yezzi, Jr., and O. Zeitouni: Curve Shortening and Interacting Particle Systems S. Joshi, D. Kaziska, A. Srivastava, and W. Mio: Riemannian Structures on Shape Spaces: A Framework for Statistical Inferences J. Glaunès, A. Trouvé, and L. Younes: Modeling Planar Shape Variation via Hamiltonian Flows of Curves G. Charpiat, O. Faugeras, R. Keriven, and P. Maurel: Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics

Blurb

The subject of pattern analysis and recognition pervades many aspects of our daily lives, including user authentication in banking, object retrieval from databases in the consumer sector, and the omnipresent surveillance and security measures around sensitive areas. Shape analysis, a fundamental building block in many approaches to these applications, is also used in statistics, biomedical applications (Magnetic Resonance Imaging), and many other related disciplines.

 

With contributions from some of the leading experts and pioneers in the field, this self-contained, unified volume is the first comprehensive treatment of theory, methods, and algorithms, available in a single resource, without the typical quagmire of vast information scattered over a wide body of literature. Developments are discussed from a rapidly increasing number of research papers in diverse fields, including the mathematical and physical sciences, engineering, and medicine.

 

The initial chapters explore the statistical modeling of landmarks while subsequent chapters address the probabilistic modeling of entire shapes. The latter part of the book, with the exception of the last two chapters, concentrates on case studies as well as implementational and practical challenges in real systems. Extensive illustrations throughout help readers overcome the sometimes terse technical details of the geometric and probabilistic formalism. Knowledge of advanced calculus and basic statistics and probability theory are the only prerequisites for the reader.

 

Statistics and Analysis of Shapes will be an essential learning kit for statistical researchers, engineers, scientists, medical researchers, and students seeking a rapid introduction to the field. It 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. The state-of-the-art techniques presented will also be useful for experienced researchers and practitioners in academia and industry.