Transcript Independent Component Analysis features of Color & Stereo

Independent Component Analysis
features of Color & Stereo images
Authors:
Patrik O. Hoyer
Aapo Hyvarinen
CIS 526: Neural Computation
Presented by: Ajay Kumar Yadav
Overview
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Introduction
Background Study
Data Preprocessing
Color Image Experiment
Stereo Image Experiment
Conclusion
Introduction
 Visual Cortex: part of the cerebral cortex
responsible for processing visual stimuli.
(Static, Moving & Pattern Recognition)
 Receptive fields are divided as:
 Sub-regions that exert an excitatory influence.
(light grey)
 Sub-regions that exert an inhibitory influence.
(dark grey)
 Stimulus Influence also depends on size,
orientation and position
(Hubel & Wiesel’s -1962, DeValois-1982, DeAngelis-1993)
Contd..
 Cones consist of three cell each responsible for each RGB
component. (tuned at wavelength of 430, 535, 590
nanometer)
 The degree to which the images are non-corresponding
is defined as binocular disparity. It is used to determine
the distance of an object from oneself, and its relation to
the fixation plane, is called stereopsis.
Background Study
 The sparseness-maximization network and
ICA are closely related. (Olshausen and
Field 1997)
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x   ai si
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 Hateren and Vander Schaaf qualitatively
compared the filter learned by ICA to
measurements of neural receptive fields.
 Van Hateren and Ruderman proved ICA
also fit the receptive field properties for
video images.
Data Preprocessing
 ICA preprocess the data in two steps:
 The mean of the data is subtracted to center the
data on the origin.
x  x  E{x}
 Whiten the data
T
z = Vx, so that E{zz }  I
 Goal: ICA transform W to minimize the statistical
dependencies between the estimated sources.
sˆ  Wz  WVPCA x  WDn1/ 2 EnT x
 After convergence
A  En Dn1/ 2W T
Color Image Experiment
 Standard RGB values are considered as input
data assuming the transformation to cone
outputs to be roughly linear.
 A total of 50,000 12 by 12 pixel image patches
were sampled randomly with dimensionality of
432.
 Data is preprocessed and correlation matrix
and eigen vectors are calculated.
 Constant RGB value is used in the display.
Correlation matrix
 Data is projected in 160
principle component
before whitening. Two
reasons are:
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To emulate the real
neuron functionality
Dimension is dropped to
lower computational
cost.
Results
**ICA basis of color images**
**Color content of three ICA filters**
**Percentage of achromatic**
Stereo Image Experiment
 Stereo image data:
 5 focus points at random from each image are
selected and estimated the disparities.
 Randomly sampled 16*16 pixel corresponding
image in patch area of 300*300 pixels centered
on each focus point.
 Due to the fluctuation patches are often similar
but horizontally shifted.
 During the preprocessing local mean was
removed from each component and correlation
matrix and eigenvalue decomposition are
calculated.
Stereo Images
**PCA Basis of Stereo Image**
Equal Response
Varying Response
**ICA Basis of Stereo Image**
Ocular Dominance
 The shift from one eye to the other takes place over a
distance of less than 50 microns, therefore column
dominated by one eye.
 If the sampling areas is smaller, correlation between the
patches would be higher.
 If the area gets larger, the dependencies between the
left and right patches get weaker
Disparity Tuning Analysis
 To analyze the
disparity tuning
several ICA basis were
estimated using
different number
random seeds.
 Only relatively high
frequency well
localized binocular
vectors are selected
Disparity Tuning Curves
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Each patch is shown to both
the eyes to get the tuning
curve and the mean is
considered as final curve.
These curves are defined in
two parts:
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Tuned excitatory
Tuned inhibitory
Tuned excitatory shows a
strong peak at zero.
Tuned inhibitory shows
opposite polarity.
Near unit’s right receptive
slightly shifted giving positive
preferred disparity.
Far unit has opposite
positional offset with negative
disparities.
Conclusion
 ICA could be applied in denoising,
compression or pattern recognition of color
or stereo data.
 ICA can be used to model computational
properties of visual cortex (V1) cell.
 Limitation:
 Since ICA emulate the behavior of cones it may
fail in dark or un-illuminated images.
 To get better correlation basis patch needed to
be small which may vary.
 Nonlinearities inherent in the conversion from
RGB to cones response will affect the ICA result.