Blind Inverse Gamma CorrectionBlind Inverse Gamma Correction(Hany Farid , IEEE Trans. Signal Processing, vol. 10 no. 10, October 2001)(Hany Farid , IEEE Trans. Signal Processing, vol. 10 no. 10, October 2001)

An article reviewAn article review

Merav Kass

January 2003

• Imaging device non linearity character.

( )out in

00

1

1

=1

=0.5

=0.2

=2

=4

out

in

• Gamma correction:

• Inverse gamma correction – an advantageous to SP applications.

0.8 1.6

Inverse Gamma Correction - Inverse Gamma Correction - MotivationMotivation

• If is known:1( )corrected out out

The need in blind inverse gamma correctionblind inverse gamma correction arise!

• Typically, is determined experimentally.

The imaging device

calibration information

Blind Inverse Gamma Correction - Blind Inverse Gamma Correction - MotivationMotivation

WhatWhat is a blind inverse Gamma correction ? is a blind inverse Gamma correction ?

• It is an estimation process.

• No prior knowledge is assumed.

HowHow does it work ? does it work ?

• Minimize higher-order correlation in the frequency domain.

What? & How?What? & How?

Original SignalOriginal Signal

1w

2w

1a

2a12w

22w

1 2w w

1 2w w1w

2w

Modified SignalModified Signal

Gamma Correction

Higher Order CorrelationHigher Order Correlation

Higher order correlations in the frequency domain

Deviation of Gamma from unity

Gamma

Higher order

correlations

1

How higher order correlations can be measured ?

By estimating the bicoherence function:

1 2ˆ( , )b w w

It reveals the sort of higher order correlations introduced by nonlinearity.

AssumptionsAssumptions

• Only one parameter has to be estimated : gamma.

• The only thing we have to work with is the a gamma corrected image.

The AlgorithmThe Algorithm

Course of actionCourse of action

1invI

2invI

ninvI

Apply inverseOperation

k

kinvI I

Measure Correlations

1 2ˆ ( , )k kC b w w

n

C 1

C

C n

argm in ̂

The AlgorithmThe Algorithm

Experimental ResultsExperimental ResultsBefore After

= 0.42

= 0.80

= 1.10

= 1.63

= 2.11

On Average, the correct gamma is estimated within

7.5%

of the actual value.

• C() is a well behaved function.

• Calculation efficiency.

• The algorithm performance in presence of additive noise.

• The algorithm performance in presence of linear transformations.

• Colored images.

Additional NotesAdditional Notes

• One parameter model is assumed.

• The procedure assume to be uniform.

Restrictions and LimitationsRestrictions and Limitations