Learning Lie Groups for Invariant Visual Perception
Rajesh P. N. Rao, Daniel Ruderman · 1998
One of the most important problems in visual perception is that of visual in-variance: how are objects perceived to be the same despite undergoing transfor-mations 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 ca-pable of handling in principle arbitrarily large transfonnations. Using a matrix-exponential based generative model of images, we derive an unsupervised al-gorithm for learning Lie group operators from input data containing infinites-imal transfonnations. The on-line unsupervised learning algorithm maximizes the posterior probability of generating the training data. We provide experimen-tal results suggesting that the proposed method can learn Lie group operators for handling reasonably large I-D translations and 2-D rotations. 1