A Unified Framework for Detecting Groups and Appli

Authors: Frédéric Cao Julie Delon Agnès Desolneux Pablo Musé Frédéric Sur

Publish Date: 2006/09/21

Volume: 27, Issue: 2, Pages: 91-119

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Abstract

A unified a contrario detection method is proposed to solve three classical problems in clustering analysis The first one is to evaluate the validity of a cluster candidate The second problem is that meaningful clusters can contain or be contained in other meaningful clusters A rule is needed to define locally optimal clusters by inclusion The third problem is the definition of a correct merging rule between meaningful clusters permitting to decide whether they should stay separate or unite The motivation of this theory is shape recognition Matching algorithms usually compute correspondences between more or less local features called shape elements between images to be compared Each pair of matching shape elements leads to a unique transformation similarity or affine map The present theory is used to group these shape elements into shapes by detecting clusters in the transformation spaceFrédéric Cao graduated from the Ecole Polytechnique in 1995 and obtained a PhD in applied mathematics in Ecole Normale Supérieure de Cachan in 2000 He defended his “Habilitation à diriger des recherches in 2004 His research interests include partial differential equations for image and shape filtering but also statistical approaches to shape recognition and data analysis or motion analysisJulie Delon was born in France in 1978 During the period 1997–2001 she has studied applied mathematics at the Ecole Normale Supérieure de Cachan From 2001 to 2004 she prepared a PhD thesis in image analysis at the CMLA Cachan France and defended it in December 2004 She is currently a research scientist with CNRS at Télécom ParisAgnès Desolneux was born in France in 1974 She defended her PhD thesis in applied mathematics in 2000 under the direction of JeanMichel Morel at the ENS Cachan She is currently CNRS researcher at the MAP5 University Paris 5 She is working on statistical methods in image analysis Web page http//wwwmathinfounivparis5fr/~desolneux/Pablo Musé was born in Montevideo Uruguay in 1975 He received the Electrical Engineer degree from the Universidad de la República Uruguay in 1999 and the DEA in Mathematics Vision and Learning from the Ecole Normale Supérieure de Cachan France in 2001 In 2004 he obtained his PhD in Applied Mathematics also from ENS Cachan where he had a researcher position until May 2005 Since then he has been with Cognitech Inc Pasadena CA USAFrédéric Sur was born in 1976 He is a former student of École Normale Supérieure de Cachan France In 2004 he received his PhD degree in applied mathematics and image analysis from Université Paris Dauphine He is now an assistant professor at École des Mines de Nancy France and with Loria laboratory

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