Frontiers in Computational Neuroscience 2 Methods 2.1 Visual Stimuli and Task

Signals in the environment are rarely specified exactly: our visual system may know what to look for (e.g., a specific face), but not its exact configuration (e.g., where in the room, or in what orientation). Uncertainty, and the ability to deal with it, is a fundamental aspect of visual processing. The MAX model is the current gold standard for describing how human vision handles uncertainty: of all possible configurations for the signal, the observer chooses the one corresponding to the template associated with the largest response. We propose an alternative model in which the MAX operation, which is a dynamic non-linearity (depends on multiple inputs from several stimulus locations) and happens after the input stimulus has been matched to the possible templates, is replaced by an early static non-linearity (depends only on one input corresponding to one stimulus location) which is applied before template matching. By exploiting an integrated set of analytical and experimental tools, we show that this model is able to account for a number of empirical observations otherwise unaccounted for by the MAX model, and is more robust with respect to the realistic limitations imposed by the available neural hardware. We then discuss how these results, currently restricted to a simple visual detection task, may extend to a wider range of problems in sensory processing.

[1]  J Nachmias,et al.  Letter: Grating contrast: discrimination may be better than detection. , 1974, Vision research.

[2]  M. J. Korenberg,et al.  The identification of nonlinear biological systems: Wiener and Hammerstein cascade models , 1986, Biological Cybernetics.

[3]  A. Watson,et al.  A standard model for foveal detection of spatial contrast. , 2005, Journal of vision.

[4]  M J Morgan,et al.  The Combination of Filters in Early Spatial Vision: A Retrospective Analysis of the Mirage Model , 1997, Perception.

[5]  N. Issa,et al.  Subcortical Representation of Non-Fourier Image Features , 2010, The Journal of Neuroscience.

[6]  M P Eckstein,et al.  Visual signal detection in structured backgrounds. II. Effects of contrast gain control, background variations, and white noise. , 1997, Journal of the Optical Society of America. A, Optics, image science, and vision.

[7]  G. Rhodes,et al.  Caricature Effects, Distinctiveness, and Identification: Testing the Face-Space Framework , 2000, Psychological science.

[8]  Dennis M Levi,et al.  What limits performance in the amblyopic visual system: seeing signals in noise with an amblyopic brain. , 2008, Journal of vision.

[9]  R. Hess,et al.  Size matters, but not for everyone: individual differences for contrast discrimination. , 2005, Journal of vision.

[10]  Dennis M Levi,et al.  Stochastic model for detection of signals in noise. , 2009, Journal of the Optical Society of America. A, Optics, image science, and vision.

[11]  A. Ahumada Classification image weights and internal noise level estimation. , 2002, Journal of vision.

[12]  D. Levi,et al.  Receptive versus perceptive fields from the reverse-correlation viewpoint , 2006, Vision Research.

[13]  T. Cohn,et al.  Effect of large spatial uncertainty on foveal luminance increment detectability. , 1985, Journal of the Optical Society of America. A, Optics and image science.

[14]  C. Tyler,et al.  Signal detection theory in the 2AFC paradigm: attention, channel uncertainty and probability summation , 2000, Vision Research.

[15]  Robert Shapley,et al.  Linear and nonlinear systems analysis of the visual system: Why does it seem so linear? A review dedicated to the memory of Henk Spekreijse , 2009, Vision Research.

[16]  Miguel P Eckstein,et al.  Classification image analysis: estimation and statistical inference for two-alternative forced-choice experiments. , 2002, Journal of vision.

[17]  S. Fomin,et al.  Elements of the Theory of Functions and Functional Analysis , 1961 .

[18]  H Ghandeharian,et al.  Visual signal detection. I. Ability to use phase information. , 1984, Journal of the Optical Society of America. A, Optics and image science.

[19]  D. Pelli,et al.  Display Characterization , 1998 .

[20]  Dennis M Levi,et al.  Classification images for detection and position discrimination in the fovea and parafovea. , 2002, Journal of vision.

[21]  J. Solomon The history of dipper functions , 2009, Attention, perception & psychophysics.

[22]  Theodore E. Cohn,et al.  Coincidence-enhanced stochastic resonance: Experimental evidence challenges the psychophysical theory behind stochastic resonance , 2007, Neuroscience Letters.

[23]  M. Carandini,et al.  A Synaptic Explanation of Suppression in Visual Cortex , 2002, The Journal of Neuroscience.

[24]  H. B. Barlow,et al.  The precision of numerosity discrimination in arrays of random dots , 1983, Vision Research.

[25]  A E Burgess,et al.  Visual signal detection. IV. Observer inconsistency. , 1988, Journal of the Optical Society of America. A, Optics and image science.

[26]  D. M. Green,et al.  Signal detection theory and psychophysics , 1966 .

[27]  P. Z. Marmarelis,et al.  Analysis of Physiological Systems: The White-Noise Approach , 2011 .

[28]  J. Cuzick A Wilcoxon-type test for trend. , 1985, Statistics in medicine.

[29]  Peter Neri,et al.  How inherently noisy is human sensory processing? , 2010, Psychonomic bulletin & review.

[30]  Joshua A Solomon,et al.  Noise reveals visual mechanisms of detection and discrimination. , 2002, Journal of vision.

[31]  W. P. Tanner PHYSIOLOGICAL IMPLICATIONS OF PSYCHOPHYSICAL DATA * , 1961, Annals of the New York Academy of Sciences.

[32]  R. W. Bowen Isolation and interaction of ON and OFF pathways in human vision: Contrast discrimination at pattern offset , 1997, Vision Research.

[33]  J. Victor Analyzing receptive fields, classification images and functional images: challenges with opportunities for synergy , 2005, Nature Neuroscience.

[34]  F. Rieke,et al.  Nonlinear Signal Transfer from Mouse Rods to Bipolar Cells and Implications for Visual Sensitivity , 2002, Neuron.

[35]  Marti A. Hearst Trends & Controversies: Support Vector Machines , 1998, IEEE Intell. Syst..

[36]  Sheng Chen,et al.  Model selection approaches for non-linear system identification: a review , 2008, Int. J. Syst. Sci..

[37]  Nils Lid Hjort,et al.  Model Selection and Model Averaging , 2001 .

[38]  W. W. Peterson,et al.  The theory of signal detectability , 1954, Trans. IRE Prof. Group Inf. Theory.

[39]  Christopher W. Tyler,et al.  A single-channel model for spatio-temporal contrast sensitivity at low-to-medium spatial frequencies , 2002 .

[40]  D G Pelli,et al.  Uncertainty explains many aspects of visual contrast detection and discrimination. , 1985, Journal of the Optical Society of America. A, Optics and image science.

[41]  Bernhard Schölkopf,et al.  A Unifying View of Wiener and Volterra Theory and Polynomial Kernel Regression , 2006, Neural Computation.

[42]  Richard F Murray,et al.  Optimal methods for calculating classification images: weighted sums. , 2002, Journal of vision.

[43]  H. Barlow The absolute efficiency of perceptual decisions. , 1980, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[44]  S. Dakin,et al.  Psychophysical evidence for a non-linear representation of facial identity , 2009, Vision Research.

[45]  Anirvan S. Nandy,et al.  Classification images with uncertainty. , 2006, Journal of vision.

[46]  Bruce G Cumming,et al.  A simple model accounts for the response of disparity-tuned V1 neurons to anticorrelated images , 2002, Visual Neuroscience.

[47]  J. L. Brown Visual Sensitivity , 1974 .

[48]  J. B. Levitt,et al.  Comparison of Spatial Summation Properties of Neurons in Macaque V1 and V2 , 2009, Journal of neurophysiology.

[49]  Vasilis Z. Marmarelis,et al.  Nonlinear Dynamic Modeling of Physiological Systems , 2004 .

[50]  Kenneth Knoblauch,et al.  Frequency and phase contributions to the detection of temporal luminance modulation. , 2005, Journal of the Optical Society of America. A, Optics, image science, and vision.

[51]  Alexander J. Smola,et al.  Learning with kernels , 1998 .

[52]  P. Neri Stochastic characterization of small-scale algorithms for human sensory processing. , 2010, Chaos.

[53]  M. J. Korenberg,et al.  The identification of nonlinear biological systems: LNL cascade models , 1986, Biological Cybernetics.

[54]  F. Rieke,et al.  Retinal processing near absolute threshold: from behavior to mechanism. , 2005, Annual review of physiology.

[55]  S. Klein,et al.  Facilitation of contrast detection by cross-oriented surround stimuli and its psychophysical mechanisms. , 2002, Journal of vision.

[56]  Henk Spekreijse,et al.  Linearizing: A method for analysing and synthesizing nonlinear systems , 1970, Kybernetik.

[57]  David T. Westwick,et al.  Identification of nonlinear physiological systems , 2003 .

[58]  P. Neri Estimation of nonlinear psychophysical kernels. , 2004, Journal of vision.

[59]  H. Barlow,et al.  The statistical efficiency for detecting sinusoidal modulation of average dot density in random figures , 1981, Vision Research.

[60]  R. F. Wagner,et al.  Efficiency of human visual signal discrimination. , 1981, Science.

[61]  A Burgess,et al.  Visual signal detection. III. On Bayesian use of prior knowledge and cross correlation. , 1985, Journal of the Optical Society of America. A, Optics and image science.

[62]  R. de Figueiredo The Volterra and Wiener theories of nonlinear systems , 1982, Proceedings of the IEEE.

[63]  Peter Neri,et al.  Nonlinear characterization of a simple process in human vision. , 2009, Journal of vision.

[64]  D L Wilson,et al.  Hyperefficient detection of targets in noisy images. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.

[65]  David J. Heeger,et al.  Spatiotemporal mechanisms for detecting and identifying image features in human vision , 2002, Nature Neuroscience.

[66]  H. Barrett,et al.  Effect of noise correlation on detectability of disk signals in medical imaging. , 1985, Journal of the Optical Society of America. A, Optics and image science.

[67]  R. W. Bowen Isolation and interaction of ON and OFF pathways in human vision: Pattern-polarity effects on contrast discrimination , 1995, Vision Research.

[68]  J. Movshon,et al.  Receptive field organization of complex cells in the cat's striate cortex. , 1978, The Journal of physiology.

[69]  Andreas Christmann,et al.  Support vector machines , 2008, Data Mining and Knowledge Discovery Handbook.

[70]  H. Barlow The efficiency of detecting changes of density in random dot patterns , 1978, Vision Research.

[71]  Nicholas J. Priebe,et al.  Inhibition, Spike Threshold, and Stimulus Selectivity in Primary Visual Cortex , 2008, Neuron.

[72]  Denis G. Pelli,et al.  Noise in the Visual System May Be Early , 1991 .

[73]  A E Burgess,et al.  Visual signal detection. II. Signal-location identification. , 1984, Journal of the Optical Society of America. A, Optics and image science.

[74]  J. Nachmias,et al.  Visual detection and discrimination of luminance increments. , 1970, Journal of the Optical Society of America.

[75]  Richard F Murray,et al.  Classification images predict absolute efficiency. , 2005, Journal of vision.

[76]  R Marken,et al.  Time and frequency analyses of auditory signal detection. , 1975, The Journal of the Acoustical Society of America.

[77]  Miguel P Eckstein,et al.  Classification images for detection, contrast discrimination, and identification tasks with a common ideal observer. , 2006, Journal of vision.

[78]  Peter Neri,et al.  Evidence for joint encoding of motion and disparity in human visual perception. , 2008, Journal of neurophysiology.