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When a three-dimensional object moves relative to an observer, a change occurs on the observer's image plane and in the visual representation computed by a learned model.
Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra, 1959
Wigner, E. P · 1959
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Group Theoretical Methods in Image Understanding
Kanatani, K · 1990
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Unitary Representations and Harmonic Analysis
Sugiura, Mitsuo · 1990
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Learning Lie groups for invariant visual perception
Rao, R. P. N. and Ruderman, D. L · 1999
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Rotation invariant spherical harmonic representation of 3D shape descriptors
Kazhdan, Michael, Funkhouser, Thomas, and Rusinkiewicz, Szymon · 2003
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Learning methods for generic object recognition with invariance to pose and lighting
LeCun, Y. and Bottou, L · 2004
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Learning the Lie groups of visual invariance
Miao, X. and Rao, R. P. N · 2007
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Rotation matrices for real spherical harmonics: general rotations of atomic orbitals in space-fixed axes
Pinchon, Didier and Hoggan, Philip E · 2007
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Fast computation of 3d spherical fourier harmonic descriptors - a complete orthonormal basis for a rotational invariant representation of three-dimensional objects
Skibbe, Henrik, Wang, Qing, and Reisert, Marco · 2009
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Theano: A CPU and GPU math compiler in Python
Bergstra, J., Breuleux, O., Bastien, F., Lamblin, P., Pascanu, R., Desjardins, G., Turian, J., Warde-Farley, D., and Bengio, Y · 2010
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An unsupervised algorithm for learning lie group transformations
Sohl-Dickstein, J., Wang, J. C., and Olshausen, B. A · 2010
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Adaptive Subgradient Methods for Online Learning and Stochastic Optimization
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Transforming auto-encoders
Hinton, GE, Krizhevsky, A, and Wang, SD · 2011
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Lie Group Transformation Models for Predictive Video Coding
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Invariant scattering convolution networks
Bruna, Joan and Mallat, Stéphane · 2012
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Steps Toward a Theory of Visual Information: Active Perception, Signal-to-Symbol Conversion and the Interplay Between Sensing and Control
Soatto, Stefano · 2012
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Representation Learning: A Review and New Perspectives
Bengio, Y., Courville, A., and Vincent, P · 2013
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Learning Stable Group Invariant Representations with Convolutional Networks
Bruna, Joan, Szlam, Arthur, and LeCun, Yann · 2013
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Unsupervised learning of invariant representations with low sample complexity: the magic of sensory cortex or a new framework for machine learning?
Anselmi, Fabio, Leibo, Joel Z, Rosasco, Lorenzo, Mutch, Jim, Tacchetti, Andrea, and Poggio, Tomaso · 2014
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Learning the Irreducible Representations of Commutative Lie Groups
Cohen, T. and Welling, M · 2014
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Group Invariant Scattering
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