Active shape models—their training and application
Computer Vision and Image Understanding
Probabilistic Visual Learning for Object Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Hierarchical Latent Variable Model for Data Visualization
IEEE Transactions on Pattern Analysis and Machine Intelligence
An introduction to variational methods for graphical models
Learning in graphical models
Mixtures of probabilistic principal component analyzers
Neural Computation
Proceedings of the 1998 conference on Advances in neural information processing systems II
SMEM algorithm for mixture models
Proceedings of the 1998 conference on Advances in neural information processing systems II
Nonlinear manifold learning for visual speech recognition
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Principal Manifolds and Bayesian Subspaces for Visual Recognition
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Transformed Component Analysis: Joint Estimation of Spatial Transformations and Image Components
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Wormholes in Shape Space: Tracking through Discontinuous Changes in Shape
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Journal of Cognitive Neuroscience
Inferring parameters and structure of latent variable models by variational bayes
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Principal Component Analysis over Continuous Subspaces and Intersection of Half-Spaces
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
EigenSegments: A Spatio-Temporal Decomposition of an Ensemble of Images
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
Multimodal Data Representations with Parameterized Local Structures
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Video-based face recognition using probabilistic appearance manifolds
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
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In recent years several techniques have been proposed for modelling the low-dimensional manifolds, or 'subspaces', of natural images. Examples include principal component analysis (as used for instance in 'eigen-faces'), independent component analysis, and auto-encoder neural networks. Such methods suffer from a number of restrictions such as the limitation to linear manifolds or the absence of a probablistic representation. In this paper we exploit recent developments in the fields of variational inference and latent variable models to develop a novel and tractable probabilistic approach to modelling manifolds which can handle complex non-linearities. Our framework comprises a mixture of sub-space components in which both the number of components and the effective dimensionality of the subspaces are determined automatically as part of the Bayesian inference procedure. We illustrate our approach using two classical problems: modelling the manifold of face images and modelling the manifolds of hand-written digits.