Learning Transformational Invariants from Natural Movies

We describe a hierarchical, probabilistic model that learns to extract complex motion from movies of the natural environment. The model consists of two hidden layers: the first layer produces a sparse representation of the image that is expressed in terms of local amplitude and phase variables. The second layer learns the higher-order structure among the time-varying phase variables. After training on natural movies, the top layer units discover the structure of phase-shifts within the first layer. We show that the top layer units encode transformational invariants: they are selective for the speed and direction of a moving pattern, but are invariant to its spatial structure (orientation/spatial-frequency). The diversity of units in both the intermediate and top layers of the model provides a set of testable predictions for representations that might be found in VI and MT. In addition, the model demonstrates how feedback from higher levels can influence representations at lower levels as a by-product of inference in a graphical model.

[1]  E. Adelson,et al.  The analysis of moving visual patterns , 1985 .

[2]  E H Adelson,et al.  Spatiotemporal energy models for the perception of motion. , 1985, Journal of the Optical Society of America. A, Optics and image science.

[3]  Peter Földiák,et al.  Learning Invariance from Transformation Sequences , 1991, Neural Comput..

[4]  Kechen Zhang,et al.  Emergence of Position-Independent Detectors of Sense of Rotation and Dilation with Hebbian Learning: An Analysis , 1993, Neural Computation.

[5]  T. Sejnowski,et al.  A selection model for motion processing in area MT of primates , 1995, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[6]  David J. Field,et al.  Sparse coding with an overcomplete basis set: A strategy employed by V1? , 1997, Vision Research.

[7]  E. Rolls,et al.  INVARIANT FACE AND OBJECT RECOGNITION IN THE VISUAL SYSTEM , 1997, Progress in neurobiology.

[8]  Terrence J. Sejnowski,et al.  The “independent components” of natural scenes are edge filters , 1997, Vision Research.

[9]  Eero P. Simoncelli,et al.  A model of neuronal responses in visual area MT , 1998, Vision Research.

[10]  Gerhard Krieger,et al.  The atoms of vision: Cartesian or polar? , 1999 .

[11]  Aapo Hyvärinen,et al.  Emergence of Phase- and Shift-Invariant Features by Decomposition of Natural Images into Independent Feature Subspaces , 2000, Neural Computation.

[12]  Christoph Kayser,et al.  Learning the invariance properties of complex cells from their responses to natural stimuli , 2002, The European journal of neuroscience.

[13]  Terrence J. Sejnowski,et al.  Slow Feature Analysis: Unsupervised Learning of Invariances , 2002, Neural Computation.

[14]  Tai Sing Lee,et al.  Hierarchical Bayesian inference in the visual cortex. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[15]  Aapo Hyvärinen,et al.  Bubbles: a unifying framework for low-level statistical properties of natural image sequences. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[16]  David J. Fleet,et al.  Computation of component image velocity from local phase information , 1990, International Journal of Computer Vision.

[17]  Y. LeCun,et al.  Learning methods for generic object recognition with invariance to pose and lighting , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[18]  Rajesh P. N. Rao,et al.  Bilinear Sparse Coding for Invariant Vision , 2005, Neural Computation.

[19]  Michael S. Lewicki,et al.  A Hierarchical Bayesian Model for Learning Nonlinear Statistical Regularities in Nonstationary Natural Signals , 2005, Neural Computation.

[20]  Thomas Serre,et al.  Robust Object Recognition with Cortex-Like Mechanisms , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[21]  Edmund T. Rolls,et al.  Invariant Global Motion Recognition in the Dorsal Visual System: A Unifying Theory , 2007, Neural Computation.