Docteur de l'université Automatic Segmentation and Shape Analysis ...

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106 Chapter 4 Statistical shape model of Hippocampus (a) β = 0 (b) β = 0.2 (c) β = 0.5 (d) β = 1 Figure 4.14: An example of regularization on symmetric shape parameter estimation. (a) RMS 0.188mm, Hausdorff distance 0.970mm (b) β = 0.2, RMS 0.186mm, Hausdorff distance 0.963mm. (c) RMS 0.220mm, Hausdorff distance 1.16mm. (d) RMS 0.253mm, Hausdorff distance 1.30mm.
Chapter 4 Statistical shape model of Hippocampus 107 4.4 Summary In this chapter, we described the building of SSMs from the training shape data. The shape surfaces are first parameterized on a unit sphere by area-preserving mapping. The spherical parameterization of surfaces are then flattend to the shape image representation, which are re-parameterized to eliminate the spurious correspondences by groupwise optimization. The re-parameterization on the shape image is analogous to the non-rigid deformation in image registration, which is computed with fluid regularization. A fast algorithm solving fluid velocity using discrete sine transform is applied to regularize the shape reparameterization. The result SSM based on the correspondence in the parameter space is evaluated in terms of its compactness, generalization ability and specificity. Once the SSM is built, it is used to estimate the shape parameters of unseen surfaces or point sets. An EM algorithm is used to estimate the transformation and the deformation of the model to fit the data with correspondence as the hidden variable. The data term to be optimized is symmetric between the model and the surface data in order to impose the consistency of the estimation. The SSM also provide the shape prior for the MAP estimator which includes a regularization term. The consistent symmetric estimation is shown to improve the details and the precision of the reconstruction of the shape surface from the model, and the shape prior regularization is necessary to avoid the problem of overfitting. With the presence of noises, mismatches, and disappearance of the correspondence, the regularized MAP gives more accurate estimation of shape parameters.
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UNIVERSITE DE BOURGOGNE U.F.R. SCIE
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Résumé L’objectif de cette thè
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Abstract The aim of this thesis is
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TABLE DES MATIÈRES Acknowledgement
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