Learning Nonlinear Statistical Regularities in Natural Images by Modeling the Outer Product of Image Intensities

It is well known that there exist nonlinear statistical regularities in natural images. Existing approaches for capturing such regularities always model the image intensities by assuming a parameterized distribution for the intensities and learn the parameters. In the letter, we propose to model the outer product of image intensities by assuming a gaussian distribution for it. A two-layer structure is presented, where the first layer is nonlinear and the second layer is linear. Trained on natural images, the first-layer bases resemble the receptive fields of simple cells in the primary visual cortex (V1), while the second-layer units exhibit some properties of the complex cells in V1, including phase invariance and masking effect. The model can be seen as an approximation of the covariance model proposed in Karklin and Lewicki (2009) but has more robust and efficient learning algorithms.

[1]  Terrence J. Sejnowski,et al.  Soft Mixer Assignment in a Hierarchical Generative Model of Natural Scene Statistics , 2006, Neural Computation.

[2]  Aapo Hyvärinen,et al.  Topographic Independent Component Analysis , 2001, Neural Computation.

[3]  A. Sillito,et al.  Spatial organization and magnitude of orientation contrast interactions in primate V1. , 2002, Journal of neurophysiology.

[4]  Aapo Hyv.  A Two-Layer Model of Natural Stimuli Estimated with Score Matching , 2010 .

[5]  RussLL L. Ds Vnlos,et al.  SPATIAL FREQUENCY SELECTIVITY OF CELLS IN MACAQUE VISUAL CORTEX , 2022 .

[6]  Eero P. Simoncelli,et al.  Natural signal statistics and sensory gain control , 2001, Nature Neuroscience.

[7]  J. Movshon,et al.  Spatial summation in the receptive fields of simple cells in the cat's striate cortex. , 1978, The Journal of physiology.

[8]  David J. Field,et al.  Emergence of simple-cell receptive field properties by learning a sparse code for natural images , 1996, Nature.

[9]  Jiawei Han,et al.  SRDA: An Efficient Algorithm for Large-Scale Discriminant Analysis , 2008, IEEE Transactions on Knowledge and Data Engineering.

[10]  Xuelong Li,et al.  Principal Component 2-D Long Short-Term Memory for Font Recognition on Single Chinese Characters , 2016, IEEE Transactions on Cybernetics.

[11]  J. H. Hateren,et al.  Independent component filters of natural images compared with simple cells in primary visual cortex , 1998 .

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

[13]  Rajat Raina,et al.  Efficient sparse coding algorithms , 2006, NIPS.

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

[15]  Terrence J. Sejnowski,et al.  Spatiochromatic Receptive Field Properties Derived from Information-Theoretic Analyses of Cone Mosaic Responses to Natural Scenes , 2003, Neural Computation.

[16]  Honglak Lee,et al.  An Analysis of Single-Layer Networks in Unsupervised Feature Learning , 2011, AISTATS.

[17]  A. B. Bonds.  Role of Inhibition in the Specification of Orientation Selectivity of Cells in the Cat Striate Cortex , 1989, Visual Neuroscience.

[18]  Honglak Lee,et al.  Sparse deep belief net model for visual area V2 , 2007, NIPS.

[19]  Michael S. Lewicki,et al.  Emergence of complex cell properties by learning to generalize in natural scenes , 2009, Nature.

[20]  Aapo Hyvärinen,et al.  A Two-Layer Model of Natural Stimuli Estimated with Score Matching , 2010, Neural Computation.

[21]  Geoffrey E. Hinton,et al.  Modeling pixel means and covariances using factorized third-order boltzmann machines , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[22]  J. V. van Hateren,et al.  Independent component filters of natural images compared with simple cells in primary visual cortex , 1998, Proceedings of the Royal Society of London. Series B: Biological Sciences.