Gooya, A, Lekadir, K, Castro-Mateos, I et al. (2 more authors) (2018) Mixture of Probabilistic Principal Component Analyzers for Shapes from Point Sets. IEEE Transactions on Pattern Analysis and Machine Intelligence, 40 (4). pp. 891-904. ISSN 0162-8828
Abstract
Inferring a probability density function (pdf) for shape from a population of point sets is a challenging problem. The lack of point-to-point correspondences and the non-linearity of the shape spaces undermine the linear models. Methods based on manifolds model the shape variations naturally, however, statistics are often limited to a single geodesic mean and an arbitrary number of variation modes. We relax the manifold assumption and consider a piece-wise linear form, implementing a mixture of distinctive shape classes. The pdf for point sets is defined hierarchically, modeling a mixture of Probabilistic Principal Component Analyzers (PPCA) in higher dimension. A Variational Bayesian approach is designed for unsupervised learning of the posteriors of point set labels, local variation modes, and point correspondences. By maximizing the model evidence, the numbers of clusters, modes of variations, and points on the mean models are automatically selected. Using the predictive distribution, we project a test shape to the spaces spanned by the local PPCA's. The method is applied to point sets from: i) synthetic data, ii) healthy versus pathological heart morphologies, and iii) lumbar vertebrae. The proposed method selects models with expected numbers of clusters and variation modes, achieving lower generalization-specificity errors compared to state-of-the-art.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | (c) 2017, IEEE. This is an author produced version of a paper published in IEEE Transactions on Pattern Analysis and Machine Intelligence. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Shape, Principal component analysis, Sociology, Manifolds, Data models, Probability density function; Generative modeling, variational Bayes, model selection, graphical models, statistical shape models |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 31 Aug 2018 09:15 |
Last Modified: | 19 Aug 2019 16:04 |
Status: | Published |
Publisher: | IEEE |
Identification Number: | 10.1109/TPAMI.2017.2700276 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:135010 |