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Image Processing Laboratory (IPL). http://ipl.uv.es
Universitat de Valčncia, Spain

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Non-Gaussian Nature of Images and
Signal Representation in the Visual Brain
Jesús Malo et al. 
Descriptive Image Statistics,
Psychophysical Models and Illustrations,
and associated Data and Code
2015

Here we illustrate the relation between (low-level) image statistics and human vision, which is also the basis for meaningful priors in statistical image models and meaningful image distortion metrics.
Here we provide all the data and code for the complete illustration of the considered complementary issues: low-level human vision and the statistics of small patches of natural scenes.

This page is still under construction!: we are still putting together data from here and here, statistical techniques from here and here, and psychophysical models from here, in a single piece of code reproducing the illustrations below. This will take a while. Stay tuned!

  • Non-Gaussian nature of natural scenes
(A)-Calibrated natural images
(B)-Manifold of luminance values of 4d patches of pixels as a function of their spatial proximity
(C)-Correlation of tristimulus values: LMS spectral sensitivities and manifold of natural colors in LMS. PCA decorrelation and associated spectral sensitivities
(D)-Covariance and autocorrelation of luminance values in natural images
(E)-Eigenvalues and eigenvectors of color images. Achromatic, red-green and yellow-blue extended frequency analyzers and distinctive bandwidths from PCA of natural images
(F)-Marginals of PCA and ICA signals are not Gaussian. The global manifold is not Gaussian.
(G)-ICA features of natural images. Achromatic, red-green and yellow-blue local frequency analyzers and distinctive bandwidths from PCA of natural images.
(H)-Wavelet and ICA coefficients display distinctive statistical relations. Conditional probabilities of neighbors in the spatio-spectral wavelet domain.
(I)-Redundancy reduction using linear and nonlinear information maximization approaches (linear ICA and nonlinear SPCA)
(J)-Responses of nonlinear sensors optimizing information transmission.


  • Non-linear response of visual sensors
(A)-Opponent spectral sensitivities of psychophysical color models
(B)-Spatial bandwidth of achromatic and opponent channels in humans (Contrast Sensitivity Functions)
(C)-Receptive fields of V1 spatial frequency analyzers in the standard pshychophysical/physiological model
(D)-Illustration of nonlinearities and masking in the spatial texture sensors
(E)-Nonlinear responses in the divisive normalization model.

  • Parallelism and Non-Euclidean nature of the image space
(A) Redundancy reduction in linear and nonlinear color vision models
(B) Redundancy reduction in linear and nonlinear spatial vision models

Reproduction of subjective opinion using different distortion metrics (inverse of Mahalanobis is not there yet!)


Reproduction of subjective opinion using different distortion metrics (inverse of Mahalanobis is not there yet!)