Independent Component Analysis features of Color & Stereo images

Authors:Patrik O. HoyerAapo Hyvarinen

CIS 526: Neural Computation

Presented by: Ajay Kumar Yadav

Overview

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)

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.

1

n

i ii

x a s

Data Preprocessing

ICA preprocess the data in two steps: The mean of the data is subtracted to center the

data on the origin.

Whiten the dataz = Vx, so that

Goal: ICA transform W to minimize the statistical dependencies between the estimated sources.

After convergence

{ }x x E x

{ }TE zz I

1/ 2ˆ TPCA n ns Wz WV x WD E x

1/ 2 Tn nA E D W

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: 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** **ICA Basis of Stereo Image**

Equal Response

Varying Response

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 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: 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.