Table des matières 1
نویسندگان
چکیده
In this thesis, we propose a set of tools for the statistical quanti cation and com-parison of asymmetry within a population or between two populations of structuresrepresented by 3D point sets. These tools are designed in a coherent framework relyingon a modeling of the point sets as mixtures of probability density functions dependingon parameters describing for example a re ection or a 3D deformation. The estima-tion of the parameters best superposing the mixtures is performed with variants of theExpectation-Maximisation algorithm. Particularly, we propose algorithms allowing i)the estimation of a symmetry plane of a point set, ii) the estimation of a symmetrysurface of a point set, iii) the estimation of a non-linear deformation best superposing 2point sets and iv) the building of statistical shape models from a set of point sets. Then,we show how to combine these methods to build statistical asymmetry maps (mean,standard deviation, signi cant asymmetries, signi cant di erences, etc) and global mea-surements characterising the asymmetry of the populations under study. Finally, we useour tools to compare the cortical asymmetries of 2 Situs Inversus subjects (congenitalcondition in which the major visceral organs are mirrored from their normal positions)with those of a control population.tel-00684994,version1-3Apr2012
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.......................................................................................................... v Notations et acronymes ............................................................................... vii Table des matières ......................................................................................... ix Table des figures ......................................................
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............................................................................................................v Table des matières ...............................................................................................vii Liste des figures ....................................................................................................xi Liste des tableaux.................................
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