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Abstract:
One of the most important problems in visual perception is
that of visual invariance: how are objects perceived to be the same
despite undergoing transformations such as translations, rotations
or scaling? In this paper, we describe a Bayesian method for
learning invariances based on Lie group theory. We show that
previous approaches based on first-order Taylor series expansions
of inputs can be regarded as special cases of the Lie group
approach, the latter being capable of handling in principle
arbitrarily large transformations. Using a matrix-exponential based
generative model of images, we derive an unsupervised algorithm for
learning Lie group operators from input data containing
infinitesimal transformations. The on-line unsupervised learning
algorithm maximizes the posterior probability of generating the
training data. We provide experimental results suggesting that the
proposed method can learn Lie group operators for handling
reasonably large 1-D translations and 2-D rotations.
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