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