Hierarchical model of natural images and the origin of scale invariance

The study of natural images and how our brain processes them has been an area of intense research in neuroscience, psychology, and computer science. We introduced a unique approach to studying natural images by decomposing images into a hierarchy of layers at different logarithmic intensity scales and mapping them to a quasi-2D magnet. The layers were in different phases: “cold” and ordered at large-intensity scales, “hot” and disordered at small-intensity scales, and going through a second-order phase transition at intermediate scales. There was a single “critical” layer in the hierarchy that exhibited long-range correlation similar to that found in the 2D Ising model of ferromagnetism at the critical temperature. We also determined the interactions between layers mapped from natural images and found mutual inhibition that generated locally “frustrated” antiferromagnetic states. Almost all information in natural images was concentrated in a few layers near the phase transition, which has biological implications and also points to the hierarchical origin of scale invariance in natural images.

[1]  Geoffrey E. Hinton,et al.  Reducing the Dimensionality of Data with Neural Networks , 2006, Science.

[2]  William Bialek,et al.  Statistics of Natural Images: Scaling in the Woods , 1993, NIPS.

[3]  G. Tkačik,et al.  Local statistics in natural scenes predict the saliency of synthetic textures , 2010, Proceedings of the National Academy of Sciences.

[4]  H. B. Barlow,et al.  Possible Principles Underlying the Transformations of Sensory Messages , 2012 .

[5]  L. Landau,et al.  statistical-physics-part-1 , 1958 .

[6]  K. Wilson.  Problems in Physics with many Scales of Length , 1979 .

[7]  D J Field,et al.  Relations between the statistics of natural images and the response properties of cortical cells. , 1987, Journal of the Optical Society of America. A, Optics and image science.

[8]  J. H. van Hateren,et al.  Modelling the Power Spectra of Natural Images: Statistics and Information , 1996, Vision Research.

[9]  Russell D. Fernald,et al.  Casting a Genetic Light on the Evolution of Eyes , 2006, Science.

[10]  W. Bialek,et al.  Statistical thermodynamics of natural images. , 2008, Physical review letters.

[11]  Michael J. Berry,et al.  Spin glass models for a network of real neurons , 2009, 0912.5409.

[12]  Yoshua. Bengio,et al.  Learning Deep Architectures for AI , 2007, Found. Trends Mach. Learn..

[13]  Henricus J.W. Zandvliet,et al.  The 2D Ising square lattice with nearest- and next-nearest-neighbor interactions , 2006 .

[14]  Jascha Sohl-Dickstein,et al.  Minimum Probability Flow Learning , 2009, ICML.

[15]  Eero P. Simoncelli,et al.  Natural image statistics and neural representation. , 2001, Annual review of neuroscience.

[16]  B. Kedem,et al.  Spectral analysis and discrimination by zero-crossings , 1986, Proceedings of the IEEE.

[17]  Geoffrey E. Hinton,et al.  A Learning Algorithm for Boltzmann Machines , 1985, Cogn. Sci..

[18]  Geoffrey E. Hinton,et al.  Generating more realistic images using gated MRF's , 2010, NIPS.

[19]  Wolfhard Janke,et al.  Interface tension of the square lattice Ising model with next-nearest-neighbour interactions , 2007 .

[20]  D. Baylor,et al.  Spectral sensitivity of cones of the monkey Macaca fascicularis. , 1987, The Journal of physiology.

[21]  R. Masland.  The fundamental plan of the retina , 2001, Nature Neuroscience.

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