Local image statistics: maximum-entropy constructions and perceptual salience.

The space of visual signals is high-dimensional and natural visual images have a highly complex statistical structure. While many studies suggest that only a limited number of image statistics are used for perceptual judgments, a full understanding of visual function requires analysis not only of the impact of individual image statistics, but also, how they interact. In natural images, these statistical elements (luminance distributions, correlations of low and high order, edges, occlusions, etc.) are intermixed, and their effects are difficult to disentangle. Thus, there is a need for construction of stimuli in which one or more statistical elements are introduced in a controlled fashion, so that their individual and joint contributions can be analyzed. With this as motivation, we present algorithms to construct synthetic images in which local image statistics--including luminance distributions, pair-wise correlations, and higher-order correlations--are explicitly specified and all other statistics are determined implicitly by maximum-entropy. We then apply this approach to measure the sensitivity of the human visual system to local image statistics and to sample their interactions.

[1]  Mary M. Conte,et al.  Interaction of luminance and higher-order statistics in texture discrimination , 2005, Vision Research.

[2]  Gerhard Krieger,et al.  Nonlinear mechanisms and higher-order statistics in biological vision and electronic image processing: review and perspectives , 2001, J. Electronic Imaging.

[3]  W. Geisler.  Visual perception and the statistical properties of natural scenes. , 2008, Annual review of psychology.

[4]  J. Gallant,et al.  Predicting neuronal responses during natural vision , 2005, Network.

[5]  W A Richards,et al.  Lightness scale from image intensity distributions. , 1981, Applied optics.

[6]  Yves Goussard,et al.  Stationary Markov Random Fields on a Finite Rectangular Lattice , 1998, IEEE Trans. Inf. Theory.

[7]  I. Good,et al.  The Maximum Entropy Formalism. , 1979 .

[8]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[9]  B. Julesz.  Textons, the elements of texture perception, and their interactions , 1981, Nature.

[10]  B. Julesz,et al.  Visual discrimination of textures with identical third-order statistics , 1978, Biological Cybernetics.

[11]  Antonio Torralba,et al.  Statistics of natural image categories , 2003, Network.

[12]  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.

[13]  Song-Chun Zhu,et al.  Filters, Random Fields and Maximum Entropy (FRAME): Towards a Unified Theory for Texture Modeling , 1998, International Journal of Computer Vision.

[14]  Gasper Tkacik,et al.  Local statistics in natural scenes predict the saliency of synthetic textures , 2010, Proceedings of the National Academy of Sciences.

[15]  Matthias Bethge,et al.  Hierarchical Modeling of Local Image Features through $L_p$-Nested Symmetric Distributions , 2009, NIPS.

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

[17]  M. Landy,et al.  A visual mechanism tuned to black , 2004, Vision Research.

[18]  Jonathan D. Victor,et al.  Isodiscrimination contours in a three-parameter texture space , 2010 .

[19]  Mary M. Conte,et al.  Spatial organization of nonlinear interactions in form perception , 1991, Vision Research.

[20]  Eero P. Simoncelli,et al.  Nonlinear Extraction of Independent Components of Natural Images Using Radial Gaussianization , 2009, Neural Computation.

[21]  D. K. Pickard,et al.  Unilateral Markov fields , 1980, Advances in Applied Probability.

[22]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[23]  Jonathon Shlens,et al.  The Structure of Multi-Neuron Firing Patterns in Primate Retina , 2006, The Journal of Neuroscience.

[24]  B. Wandell,et al.  Surface characterizations of color thresholds. , 1990, Journal of the Optical Society of America. A, Optics and image science.

[25]  Michael J. Berry,et al.  Weak pairwise correlations imply strongly correlated network states in a neural population , 2005, Nature.

[26]  Jonathan D Victor,et al.  Analyzing the activity of large populations of neurons: how tractable is the problem? , 2007, Current Opinion in Neurobiology.

[27]  Eero P. Simoncelli,et al.  A Parametric Texture Model Based on Joint Statistics of Complex Wavelet Coefficients , 2000, International Journal of Computer Vision.

[28]  Shun-ichi Amari,et al.  Information geometry on hierarchy of probability distributions , 2001, IEEE Trans. Inf. Theory.