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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.
List of contents
Medial Axis Computation and Evolution.- Shape Variation of Medial Axis Representations via Principal Geodesic Analysis on Symmetric Spaces.- 2D Shape Modeling using Skeletal Graphs in a Morse Theoretic Framework.- Matching with Shape Contexts.- Shape Recognition Based on an a Contrario Methodology.- Integral Invariants and Shape Matching.- On the Representation of Shapes Using Implicit Functions.- Computing with Point Cloud Data.- Determining Intrinsic Dimension and Entropy of High-Dimensional Shape Spaces.- Object-Image Metrics for Generalized Weak Perspective Projection.- Wulff Shapes at Zero Temperature for Some Models Used in Image Processing.- Curve Shortening and Interacting Particle Systems.- Riemannian Structures on Shape Spaces: A Framework for Statistical Inferences.- Modeling Planar Shape Variation via Hamiltonian Flows of Curves.- Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics.
Summary
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.
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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)
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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)
