title: Maximum a posteriori estimation of linear shape variation with application to vertebra and cartilage modeling.
abstract: 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.
authors.affiliation: Department of Computer Science (DIKU), University of Copenhagen, Copenhagen, Denmark. alecrimi@diku.dk
authors.forename: Alessandro
authors.initials: A
authors.lastname: Crimi
authors.forename: Martin
authors.initials: M
authors.lastname: Lillholm
authors.forename: Mads
authors.initials: M
authors.lastname: Nielsen
authors.forename: Anarta
authors.initials: A
authors.lastname: Ghosh
authors.forename: Marleen
authors.initials: M
authors.lastname: de Bruijne
authors.forename: Erik B
authors.initials: EB
authors.lastname: Dam
authors.forename: Jon
authors.initials: J
authors.lastname: Sporring
mesh_terms: D000328:Adult; D000368:Aged; D000465:Algorithms; D001499:Bayes Theorem; D002358:Cartilage, Articular / Q000000981:diagnostic imaging*; D003198:Computer Simulation; D005260:Female; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D007719:Knee Joint / Q000000981:diagnostic imaging; D008159:Lumbar Vertebrae / Q000033:anatomy & histology*; D008279:Magnetic Resonance Imaging / Q000379:methods; D008297:Male; D008875:Middle Aged; D008953:Models, Anatomic; D025341:Principal Component Analysis; D011859:Radiography / Q000379:methods