|
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].
NATURAL IMAGES ARE SMOOTH...
- 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.
HOWEVER,
NATURAL IMAGES ARE MORE THAN GAUSSIAN
- 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.
NON-LINEAR REPRESENTATIONS
ARE NEEDED
- 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
PUBLICATIONS
|
J. Malo & V. Laparra
Psychophysically Tuned Divisive
Normalization factorizes the PDF of Natural Images
Neural Computation (2010)
|
|
V. Laparra and J. Malo
Masking-like Non-Linearities from
Non-linear PCA
GRC: Sensory Coding and The
Natural Environment (submitted 2008)
|
|
V. Laparra and J. Malo
Color and Luminance Discrimination
by Non-Linear PCA
Computational Vision and
Neuroscience symposium (2008)
|
|
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)
|
|
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)
|
|
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)
|
|
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)
|
|
|