Maximum a posteriori estimation of linear shape variation with application to vertebra and cartilage modeling
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Maximum a posteriori estimation of linear shape variation with application to vertebra and cartilage modeling. / Crimi, Alessandro; Lillholm, Martin; Nielsen, Mads; Ghosh, Anarta; de Bruijne, Marleen; Dam, Erik B.; Sporring, Jon.
I: IEEE Transactions on Medical Imaging, Bind 30, Nr. 8, 2011, s. 1514-1526.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › fagfællebedømt
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TY - JOUR
T1 - Maximum a posteriori estimation of linear shape variation with application to vertebra and cartilage modeling
AU - Crimi, Alessandro
AU - Lillholm, Martin
AU - Nielsen, Mads
AU - Ghosh, Anarta
AU - de Bruijne, Marleen
AU - Dam, Erik B.
AU - Sporring, Jon
PY - 2011
Y1 - 2011
N2 - The estimation of covariance matrices is a crucial step in several statistical tasks. Especially when using few samples of a high dimensional representation of shapes, the standard maximum likelihood estimation (ML) of the covariance matrix can be far from the truth, is often rank deficient, and may lead to unreliable results. In this paper, we discuss regularization by prior knowledge using maximum a posteriori (MAP) estimates. We compare ML to MAP using a number of priors and to Tikhonov regularization. We evaluate the covariance estimates on both synthetic and real data, and we analyze the estimates' influence on a missing-data reconstruction task, where high resolution vertebra and cartilage models are reconstructed from incomplete and lower dimensional representations. Our results demonstrate that our methods outperform the traditional ML method and Tikhonov regularization.
AB - The estimation of covariance matrices is a crucial step in several statistical tasks. Especially when using few samples of a high dimensional representation of shapes, the standard maximum likelihood estimation (ML) of the covariance matrix can be far from the truth, is often rank deficient, and may lead to unreliable results. In this paper, we discuss regularization by prior knowledge using maximum a posteriori (MAP) estimates. We compare ML to MAP using a number of priors and to Tikhonov regularization. We evaluate the covariance estimates on both synthetic and real data, and we analyze the estimates' influence on a missing-data reconstruction task, where high resolution vertebra and cartilage models are reconstructed from incomplete and lower dimensional representations. Our results demonstrate that our methods outperform the traditional ML method and Tikhonov regularization.
U2 - 10.1109/TMI.2011.2131150
DO - 10.1109/TMI.2011.2131150
M3 - Journal article
C2 - 21427019
VL - 30
SP - 1514
EP - 1526
JO - I E E E Transactions on Medical Imaging
JF - I E E E Transactions on Medical Imaging
SN - 0278-0062
IS - 8
ER -
ID: 33949906