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60 Chapter 3 Hippocampal segmentation using multiple atlases such that each of its column sj · Ij ◦ Tj(Ω) is a |Ω| dimensional vector representing the signed atlas image sk · Ik ◦ Tk of |Ω| voxels. With |A | ≥ 2, the LAR algorithm for atlas selection is listed in Algorithm 4. Algorithm 4 Atlas selection by LAR (Efron et al., 2004) 1: while |A | ≤ the number of atlases to be selected do 2: for all k, update the correlation ĉk ← C(Ik ◦ Tk, I − ÎA ) 3: Ĉ ← maxk{ĉk} 4: for all k do 5: sk ← sign(ĉk) 6: end for 7: XA ← (sk · Ik ◦ Tk) , k ∈ A 8: GA ← X T 9: A XA AA ← ( 1T A G −1 A 1A ) 1 − 2 , where 1A is a one-vector of length |A | 10: compute the least-angle image UA Tk such that C(Ik ◦ Tk, UA ) = C(Ik ′ ◦ ′, UA ), ∀k, k ′ ∈ A 11: for all k do 12: ak ← C(Ik ◦ Tk, UA ) 13: end for 14: ˆγ ← min + { Ĉ−ĉk k /∈A AA −ak , only positive components 15: select the atlas ˆ k ← arg min + { Ĉ−ĉk k /∈A AA −ak , 16: A ← A ∪ { ˆ k} 17: update ÎA ← ÎA + ˆγUA 18: end while } Ĉ+ĉk , where min AA +ak + indicates the minimum takes } Ĉ+ĉk AA +ak Analysis of computational complexity shows that LAR is efficient. When n < |Ω|, the computational complexity of entire LAR sequence will be O(n 3 +|Ω|·n 2 ) which is linear to the number of voxels |Ω| (Efron et al., 2004). 3.4 Results and discussion In the experiments, we constructed an population specific set of atlases from the elderly population enrolled in the Australian Imaging, Biomarker & Lifestyle Flag- ship Study of Ageing (AIBL) study, using our proposed supervised method, ini- tialized with the generic IBSR atlases. In total 40 atlases of elderly subjects are produced and evaluated in terms of their agreement propagated on the larger elderly population.
Chapter 3 Hippocampal segmentation using multiple atlases 61 For the test of atlas selection strategies, we used a larger atlas set provided by Alzheimer’s Disease Neuroimaging Initiative (ADNI). A leave-one-out cross- validation is performed on two set of atlases. One consists of NC subjects (n = 138), and the other consists of AD patients (n = 99). The performance of different atlas selection criteria on large atlas sets (n ∼ 100) is tested. 3.4.1 Supervised atlas construction 3.4.1.1 Materials . . .0.0 .0.5 .1.0 Figure 3.4: Probability images Pl of hippocampus of an NC subject in AIBL data, with the white colour indicating unanimous agreement. Top: T1-weighted MR images of hippocampus; middle: the probability images fusing 9 propagated atlases from IBSR, selected according to image similarity; bottom: the probability images fusing 9 atlases propagated from population specific atlases, selected according to image similarity.
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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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Chapter 6 Conclusions 139 Given the
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Chapter 6 Conclusions 141 6.2.3 Sha
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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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158 BIBLIOGRAPHY Evans, A. C., Coll
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BIBLIOGRAPHY 161 Ghanei, A., Soltan
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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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