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dc.contributor.authorCohen, Laurent D.
dc.date.accessioned2011-05-03T07:24:56Z
dc.date.available2011-05-03T07:24:56Z
dc.date.issued1996
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/6144
dc.language.isoenen
dc.subjectdeformable models and templatesen
dc.subjectdistance mapen
dc.subjectenergy minimizationen
dc.subjectfeature extractionen
dc.subjectpattern matchingen
dc.subjectshape extraction and regularizationen
dc.subjectspline functionsen
dc.subjectsurface and curve reconstructionen
dc.subject.ddc519en
dc.titleAuxiliary variables and two-step iterative algorithms in computer vision problemsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe present a new mathematical formulation of some curve and surface reconstruction algorithms by the introduction of auxiliary variables. For deformable models and templates, the extraction of a shape is obtained through the minimization of an energy composed of an internal regularization term (not necessary in the case of parametric models) and an external attraction potential. Two-step iterative algorithms have been often used where, at each iteration, the model is first locally deformed according to the potential data attraction and then globally smoothed (or fitted in the parametric case). We show how these approaches can be interpreted as the introduction of auxiliary variables and the minimization of a two-variables energy. The first variable corresponds to the original model we are looking for, while the second variable represents an auxiliary shape close to the first one. This permits to transform an implicit data constraint defined by a non convex potential into an explicit convex reconstruction problem. This approach is much simpler since each iteration is composed of two simple to solve steps. Our formulation permits a more precise setting of parameters in the iterative scheme to ensure convergence to a minimum. We show some mathematical properties and results on this new auxiliary problem, in particular when the potential is a function of the distance to the closest feature point. We then illustrate our approach for some deformable models and templates.en
dc.relation.isversionofjnlnameJournal of Mathematical Imaging and Vision
dc.relation.isversionofjnlvol6en
dc.relation.isversionofjnlissue1en
dc.relation.isversionofjnldate1996
dc.relation.isversionofjnlpages59-83en
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/BF00127375en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSpringeren
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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