Learning translation invariant recognition in massively parallel networks
Volume I: Parallel architectures on PARLE: Parallel Architectures and Languages Europe
Introduction to Shannon sampling and interpolation theory
Introduction to Shannon sampling and interpolation theory
Learning invariance from transformation sequences
Neural Computation
Learning Lie groups for invariant visual perception
Proceedings of the 1998 conference on Advances in neural information processing systems II
Slow feature analysis: unsupervised learning of invariances
Neural Computation
Contour Tracking by Stochastic Propagation of Conditional Density
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume I - Volume I
EigenTracking: Robust Matching and Tracking of Articulated Objects Using a View-Based Representation
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume I - Volume I
Multilinear Analysis of Image Ensembles: TensorFaces
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Efficient Pattern Recognition Using a New Transformation Distance
Advances in Neural Information Processing Systems 5, [NIPS Conference]
Bilinear Sparse Coding for Invariant Vision
Neural Computation
Separating Style and Content with Bilinear Models
Neural Computation
A multiresolution manifold distance for invariant image similarity
IEEE Transactions on Multimedia
Learning image transformations without training examples
ISVC'11 Proceedings of the 7th international conference on Advances in visual computing - Volume Part II
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A fundamental problem in biological and machine vision is visual invariance: How are objects perceived to be the same despite transformations such as translations, rotations, and scaling? In this letter, we describe a new, unsupervised approach to learning invariances based on Lie group theory. Unlike traditional approaches that sacrifice information about transformations to achieve invariance, the Lie group approach explicitly models the effects of transformations in images. As a result, estimates of transformations are available for other purposes, such as pose estimation and visuomotor control. Previous approaches based on first-order Taylor series expansions of images can be regarded as special cases of the Lie group approach, which utilizes a matrix-exponential-based generative model of images and can handle arbitrarily large transformations. We present an unsupervised expectation-maximization algorithm for learning Lie transformation operators directly from image data containing examples of transformations. Our experimental results show that the Lie operators learned by the algorithm from an artificial data set containing six types of affine transformations closely match the analytically predicted affine operators. We then demonstrate that the algorithm can also recover novel transformation operators from natural image sequences. We conclude by showing that the learned operators can be used to both generate and estimate transformations in images, thereby providing a basis for achieving visual invariance.