Learning Lie Groups for Invariant Visual Perception

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 transfonnations. Using a matrixexponential based generative model of images, we derive an unsupervised algorithm for learning Lie group operators from input data containing infinitesimal transfonnations.