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

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 - 2011/8

Y1 - 2011/8

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

SN - 1558-254X

VL - 30

SP - 1514

EP - 1526

JO - IEEE Transactions on Medical Imaging

JF - IEEE Transactions on Medical Imaging

IS - 8

ER -