Learning Lie Groups for Invariant Visual Perception

Part of Advances in Neural Information Processing Systems 11 (NIPS 1998)

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Rajesh Rao, Daniel Ruderman


One of the most important problems in visual perception is that of visual in(cid:173) variance: how are objects perceived to be the same despite undergoing transfor(cid:173) 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(cid:173) pable of handling in principle arbitrarily large transfonnations. Using a matrix(cid:173) exponential based generative model of images, we derive an unsupervised al(cid:173) gorithm for learning Lie group operators from input data containing infinites(cid:173) imal transfonnations. The on-line unsupervised learning algorithm maximizes the posterior probability of generating the training data. We provide experimen(cid:173) tal results suggesting that the proposed method can learn Lie group operators for handling reasonably large I-D translations and 2-D rotations.