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112 Chapter 5 Quantitative shape analysis of hippocampus in AD on their discrimination ability against the control group and the correlation with measures of cognition. The coefficients of modes describing the shape variations are used as features for disease classification, and the evaluation of the subregional models are based on the performance of the classifiers. . Centered. surfaces XC = {Xi} . Selected subregional landmarks {P(Xi; L) : Xi ∈ XC} . Procrustes aligned subregional landmarks M = { ˜ . Procrustes alignment II Xi} . . Masking at . threshold α . Shape descriptors bi PCA . . . Procrustes alignment I Procrustes aligned landmarks L . Hotelling’s T 2 test Significance map {p s (L)} . Localization step . Shape modeling step Figure 5.1: The pipeline of local shape descriptor extraction. The shape surfaces are first centered and aligned via Procrustes alignment I. A Hotelling’s T 2 test is performed on each landmark of the aligned surfaces to obtain a significance mask, which is used to threshold the previously centered shape surfaces. The selected landmarks are aligned by Procrustes alignment II, and a Principal Component Analysis (PCA) is performed to extract the shape descriptors.
Chapter 5 Quantitative shape analysis of hippocampus in AD 113 5.2 Shape analysis using SSM The SSM for hippocampus is built upon a training set of hippocampal surfaces, in which the k landmarks on the surface of hippocampus are reparameterized to avoid the false variation induced by incorrect correspondences. This correspondence problem can be solved by a groupwise optimization and fluid regularization on the shape image (Davies et al., 2008b) as described in the §4.1. Once the correspondence is established, the surfaces can be aligned by using Pro- crustes analysis, either through rigid-body or similarity transformations. The volume information is preserved after rigid body transformations. Procrustes analysis aligns the training data via rigid-body transformations to the size-and-shape space SΣ k 3 in which the variation among the data would be driven by the change in both the size and the shape of hippocampus. If the training samples are aligned via isotropic similarity transformations, the surfaces will be rescaled to normalize the hippocampal volume. Thus we have the training set in the shape space Σ k 3. As shape is defined as the remaining information ‘when the differences which can be attributed to translations, rotations, and dilations have been quotiented out’ (Kendall, 1984), the normalization of the volume by similarity transform enables the SSM to be more specific to the change in shape rather than incorporating variations in the sizes of hippocampi. The SSMs used are built on both rigid-body and similarity aligned surfaces. For a set of hippocampal landmarks {X1, X2, · · · , Xn} consisting of n samples with established correspondence, each sample is represented by the coordinates of its k landmarks concatenated as a 3k-vector Xi = ( x 1 i , y 1 i , z 1 i , x 2 i , y 2 i , z 2 i , · · · , x k i , y k i , z k ) T i ∈ R 3k , (5.1) where p s i = (x s i , y s i , z s i ) T ∈ Xi is the position of the s-th sampled landmark point on the Xi. If the surfaces in {Xi, i = 1, · · · , n} are aligned using Procrustes analysis, either rigidly or via isotropic similarity transformations, a PCA can be performed
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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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LISTE DES FIGURES 1.1 Cortical atro
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Page 164 and 165: 146 BIBLIOGRAPHY Alzheimer, A. (191
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BIBLIOGRAPHY 163 Heckemann, R. A.,
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BIBLIOGRAPHY 165 R. C. (2003). MRI
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BIBLIOGRAPHY 167 Konrad, C., Ukas,
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BIBLIOGRAPHY 169 Mahony, R. and Man
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BIBLIOGRAPHY 171 disease, mild cogn
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BIBLIOGRAPHY 173 Petersen, R. C., S
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BIBLIOGRAPHY 175 Rorden, C. and Bre
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BIBLIOGRAPHY 177 Shen, K., Bourgeat
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BIBLIOGRAPHY 179 Barillot, C., Hayn
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BIBLIOGRAPHY 181 Tzourio-Mazoyer, N
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BIBLIOGRAPHY 183 Vos, F. M., de Bru
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BIBLIOGRAPHY 185 Woolrich, M. W., J
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