Elastic Shape Models for Face Analysis Using Curvilinear Coordinates

International audienceThis paper studies the problem of analyzing variability in shapes of facial surfaces using a Rie- mannian framework, a fundamental approach that allows for joint matchings, comparisons, and deformations of faces under a chosen metric. The starting point is to impose a curvilinear coordinate system, named the Darcyan coordinate system, on facial surfaces; it is based on the level curves of the surface distance function measured from the tip of the nose. Each facial surface is now represented as an indexed collection of these level curves. The task of finding optimal deformations, or geodesic paths, between facial surfaces reduces to that of finding geodesics between level curves, which is accomplished using the theory of elastic shape analy- sis of 3D curves. Elastic framework allows for nonlinear matching between curves and between points across curves. The resulting geodesics provide optimal elastic deformations between faces and an elastic metric for comparing facial shapes. We demonstrate this idea using examples from FSU face databas

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Proton Dissociative

The electroproduction of ae mesons with proton diffractive dissociation for Q 2 ? 7 GeV 2 and the elastic electroproduction of OE mesons for Q 2 ? 6 GeV 2 are studied in e + p collisions at HERA with the H1 detector, for an integrated luminosity of 2.8 pb \Gamma1 . The dependence of the cross sections on P 2 t and Q 2 is measured, and the vector meson polarisation obtained. The cross section ratio between proton dissociative and elastic production of ae mesons is measured and discussed in the framework of the factorisation hypothesis of diffractive vertices. The ratio of the elastic cross section for OE and ae meson production is investigated as a function of Q 2 . C. Adloff 35 , S. Aid 13 , M. Anderson 23 , V. Andreev 26 , B. Andrieu 29 , V. Arkadov 36 , C. Arndt 11 , I. Ayyaz 30 , A. Babaev 25 , J. Bahr 36 , J. B'an 18 , P. Baranov 26 , E. Barrelet 30 , R. Barschke 11 , W. Bartel 11 , U. Bassler 30 , H.P. Beck 38 , M. Beck 14 ,..