vbid/9780817644819

Description

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.Typham this is the title: Statistics and Analysis of Shapes 1st Edition