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88 Chapter 4 Statistical shape model of Hippocampus . . . . . . . (a) . (b) . (c) . (d) . (e) . (f) Figure 4.7: Six possible choices of reorientation and unfolding of the octahedron. The octahedron is cut in the manner of Figure 4.4. Left column: 6 re-orientations; right column: the unfolding. The faces unfolded are color coded.
Chapter 4 Statistical shape model of Hippocampus 89 Algorithm 9 Groupwise optimization with fluid regularization. Adapted and modified from Davies et al. (2008b). 1: Initialize with ui ← 0, vi ← 0, i = 1, · · · , n. 2: while u not converging do 3: for all shapes images Si, i = 1, · · · , n do 4: Compute Fi given ui (eq. 4.37) 5: Compute vi given Fi (eq. 4.41, Cahill et al., 2007) 6: Update ui: ← ui + τ(vi − (vi · ∇)ui) (eq. 4.45) 7: end for 8: if the minimum Jacobian of any ui is below threshold then 9: for all shapes images Si, i = 1, · · · , n do 10: Si(x) ← Si(x − ui) (eq. 4.46) 11: ui ← 0, vi ← 0 12: end for 13: end if 14: if reorientation required then 15: for all shapes images Si, i = 1, · · · , n do 16: Si(x) ← Si(x − ui) (eq. 4.46) 17: reorient the octahedron unfolding gi 18: update Si 19: ui ← 0, vi ← 0 20: end for 21: end if 22: end while where (x s i , y s i , z s i ) T = fi ◦ γi(θs, φs) = Si ◦ ψi(ıs, js), s = 1, 2, · · · , k (4.48) are the sampled points. For sampling on subdivided octahedron k = 4N 2 +2. The mean gives the data matrix ¯X = 1 n n∑ Xi, (4.49) i=1 X = (X1 − ¯ X, X2 − ¯ X, · · · , Xn − ¯ X). (4.50) A PCA is performed such that each shape can be approximated by a subspace spanned by the eigenvectors of the larger covariance matrix X = ¯ X + Wb, (4.51)
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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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TABLE DES MATIÈRES xi 4.1.4.3 Spec
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LISTE DES FIGURES 1.1 Cortical atro
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LISTE DES FIGURES xvii 5.6 The accu
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144 LIST OF PUBLICATIONS using dive
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146 BIBLIOGRAPHY Alzheimer, A. (191
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148 BIBLIOGRAPHY Baillard, C., Hell
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150 BIBLIOGRAPHY of post mortem mag
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152 BIBLIOGRAPHY B. (2008). Three-d
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154 BIBLIOGRAPHY Cootes, T. F., Tay
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156 BIBLIOGRAPHY head in MR images
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