Blind Removal of Luminance Non-Linearities

We have developed a technique for blindly removing luminance non-linearities in the absence of any calibration information or explicit knowledge of the imaging device. The basic approach exploits the fact that non-linearities introduce specific higher-order correlations in the frequency domain (beyond second-order). These correlations can be detected using tools from polyspectral analysis.


Shown in the left column (from top to bottom) is:
   (1) a fractal signal f(x)
   (2) the power spectrum P(w)=F(w)F*(w)
   (3) the bispectrum B(w1,w2)=F(w1) F(w2) F*(w1+w2)
with F(w) the Fourier transform and F*(w) its complex conjugate.

Shown in the right column is:
   (1) a gamma corrected version of the signal f2.5(x)
   (2) the corresponding power spectrum
   (3) the corresponding bispectrum
Notice that the power spectrum is virtually unchanged, while there is a substantial increase in the bispectrum. This increased activity is proportional to the amount of gamma correction. The luminance non-linearity can be blindly estimated and removed by simply minimizing the correlations in the bispectrum.

Matlab routines

Related
material:
  1. Estimating Planar Surface Orientation Using Bispectral Analysis (ip07)
  2. Blind Inverse Gamma Correction (ip01)
  3. Blind Removal of Lens Distortions (josa01)
  4. Blind Removal of Image Non-Linearities (iccv01)
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