Maximum a posteriori estimation of linear shape variation with application to vertebra and cartilage modeling

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Alessandro Crimi, Martin Lillholm, Mads Nielsen, Anarta Ghosh, Marleen de Bruijne, Erik B. Dam, Jon Sporring

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.

OriginalsprogEngelsk
TidsskriftIEEE transactions on medical imaging
Vol/bind30
Udgave nummer8
Sider (fra-til)1514-1526
Antal sider13
ISSN1558-254X
DOI
StatusUdgivet - 2011

ID: 33949906