Brendan J. Frey and Nebojsa Jojic 1999.
Transformed component analysis: Joint estimation of spatial transformations and image components.
In Proceedings of the IEEE International Conference on Computer Vision 1999,
Kerkyra, Greece, Sep 20-25.
IEEE Computer Society Press: Los Alamitos, CA.
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, rotation and scale. Direct
application of the above methods will lead to severely blurred
components and even to components that only account for
the transformations and ignore the more interesting and useful structure.
We propose a method called transformed component analysis,
which incorporates a discrete, hidden variable that accounts
for transformations and uses a linear-time expectation maximization algorithm
to jointly extract components and normalize for transformations.
We illustrate the algorithm using a shading problem,
facial expression modeling and handwritten digit recognition.
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