Natural Images



Natural images exhibit a quite particular behavior. According to the Barlow hypothesis the sensors of a visual system should capture and isolate the features shared by natural images. In this page we review some of these statistical features and the optimal image and color representations obtained from them.
Our contributions in this issue include:
  • Local-to-global non-linear ICA techniques to describe non-Gaussian signals [Malo04b].
  • Statistical benefits (component independence) of perceptual non-linear image representations [Malo04,Malo&Laparra10].
  • Non-Euclidean geometry of the image space associated to the non-linear image representations for component independence [Epifanio03,Malo04a].
  • The natural images are just a small subset of all possible images:
    • The joint PDF of the luminance samples is highly non-uniform.
    • The covariance matrix is highly non-diagonal: there is a lot of correlation between neighboring luminances.
    • The autocorrelation functions are broad.
    • Natural images have 1/f band-limited spectrum.
  • The colors of natural objects are just a small subset of all possible colors:
    • The correlation between the tristimulus values of the natural colors is big.
  • Smoothness (predictability, correlation) leads to simple (Gaussian-like) image models.
  • Optimal image and color representation from Gaussian models: PCA
    • The Principal Components of natural images are DCT-like basis functions.
    • The Principal Components of natural colors (principal directions in the color space) are one achromatic channel, and two opponent chromatic channels.
    • While the three tristimulus images are equally smooth in generic RGB representations, opponent PCA-like representations imply an uneven distibution of bandwidth between channels.
  • Marginal PDFs of PCA coefficients are not Gaussian.
  • Gaussian smoothness is not enough for image synthesis.
  • The linear Independent Components of natural images are wavelet-like functions.
  • PCA / ICA techniques do not remove all the statistical dependence between the coefficients of natural images.
  • Statistical models in wavelet-like domains.
  • Factorization of the joint PDF using non-linear representations.
  • Local-to-global non-linear ICA for non-Gaussian signal representation

J. Malo & V. Laparra
Psychophysically Tuned Divisive Normalization factorizes the PDF of Natural Images
Neural Computation (2010)


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  V. Laparra and J. Malo
Masking-like Non-Linearities from Non-linear PCA
GRC: Sensory Coding and The Natural Environment (submitted 2008)
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V. Laparra and J. Malo
Color and Luminance Discrimination by Non-Linear PCA
Computational Vision and Neuroscience symposium (2008)
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J. Malo and J. Gutiérrez
V1 non-linear properties emerge from local-to-global non-linear ICA 
Network: Computation in Neural Systems Vol. 17, 1, pp 85-102  (2006)
Abstract Full Text

J. Malo, J. Gutiérrez, J. Rovira
Perturbation Analysis of the Changes in V1 Receptive Fields due to Context
Presented at the Gordon Research Conference: Sensory Coding and the Natural Environment. Oxford, UK. (2004)

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J.Malo, I.Epifanio, R.Navarro and E. Simoncelli,
Non-linear Image Representation for Efficient Perceptual Coding.
IEEE Trans. Im. Proc. Vol. 15, 1, pp 68-80 (2006) 
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J.Malo, R.Navarro, I.Epifanio, F.Ferri, J.M.Artigas
Non-linear Invertible Representation for Joint Statistical and Perceptual Feature Decorrelation.
Lecture Notes on Computer Science, Vol. 1876, pp. 658-667 (2000) 
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