Statistics and Analysis of Shapes (eBook)

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. 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.

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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.