An introduction to hidden Markov models and Bayesian networks
Hidden Markov models
Transformation-Invariant Clustering Using the EM Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Modeling Visual Patterns by Integrating Descriptive and Generative Methods
International Journal of Computer Vision
On Affine Invariant Clustering and Automatic Cast Listing in Movies
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part IV
Non-linear Bayesian Image Modelling
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part I
Determining Correspondences for Statistical Models of Appearance
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part I
Multimodal Data Representations with Parameterized Local Structures
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Discrete Applied Mathematics - The 2001 international workshop on combinatorial image analysis (IWCIA 2001)
Automatic Construction of Active Appearance Models as an Image Coding Problem
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision - Special Issue on Texture Analysis and Synthesis
A Comparison of Algorithms for Inference and Learning in Probabilistic Graphical Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Data Driven Image Models through Continuous Joint Alignment
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Transformation-Invariant Component Analysis
International Journal of Computer Vision
Ubiquitously supervised subspace learning
IEEE Transactions on Image Processing
Learning explicit and implicit visual manifolds by information projection
Pattern Recognition Letters
Learning appearance and transparency manifolds of occluded objects in layers
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Learning graphical models of images, videos and their spatial transformations
UAI'00 Proceedings of the Sixteenth conference on Uncertainty in artificial intelligence
TILT: Transform Invariant Low-Rank Textures
International Journal of Computer Vision
Learning deformations with parallel transport
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part II
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A simple, effective way to model images is to represent each input pattern by a linear combination of "component" vectors, where the amplitudes of the vectors are modulated to match the input. This approach includes principal component analysis, independent component analysis and factor analysis. In practice, images are subjected to randomly selected transformations of a known nature, such as translation and rotation. Direct use of the above methods will lead to severely blurred components that tend to ignore the more interesting and useful structure. In previous work, we introduced a clustering algorithm that is invariant to transformations [1].In this paper, we propose a method called transformed component analysis, which incorporates a discrete, hidden variable that accounts for transformations and uses the expectation maximization algorithm to jointly extract components and normalize for transformations. We illustrate the algorithm using a shading problem, facial expression modeling and written digit recognition.