nitin@ur-laser.uucp (Nitin Sampat) (07/20/85)
Homomorphic(nonlinear) vs. linear filtering of real world photographic images.
I recently worked on this topic for my Master's thesis and I thought I
would share it with you guys.
What I did : Process real - world images ( amateur photographs ) with
different types of transfer functions in the frequency domain trying
to effect image enhancement. The images were processed both linearly and
nonlinearly(homomorphically) and "quality improvement" was effected.
The "improvement" was determined by subjective testing on a group of human
observers. The justification for this research comes from an interest by
Eastman Kodak to process amateur pictures in real time.
Since the human eye has a
logarithmic response (nonlinear) one would assume that
nonlinear operations would have better subjective improvement than
linear filtering. Stockham ( proc IEEE,august 1968 ) first proposed
homo. filtering wherein one takes the log of the image before taking its
FFT, multiplying the image and the transfer function in the frequency domain,
inverse transforming and then exponentiating to get the original signal.
In linear processing, the exact same procedure is repeated except
you don't take the log before Fourier transforming.
What I found : Homomorphic filtering although theoretically an
obvious choice, has some practical problems. (I worked with 512 X 512,
8 bit images ona Vax-11/785 ) The final image has very few gray levels
and appears very dark. Hence, it requires substantial post processing
(contrast stretching, histogram equalization etc.) before an acceptable
image could be displayed. I found histogram specificatioa(Frei) and
histogram equalization both did a "good job"). Linear filtering
does not require any significant post processing. After subjecting
the same image to linear and nonlinear filtering and the same post
processing(to be consistent), subjective analysis revealed that
to the amateur photographer, there is very little difference in the
2 techniques. In general, however, linear filtering was preferred.
Conclusion : Use linear filtering to process amateur type images.
P.S. Please note that this a brief summary and a lot of factors,
conditions, variables are not mentioned. As such, these statements
should not be regarded as absolute. If someone is interested in knowing
about details or has some specific question, send me mail and I'll
be glad to reply. Also, I wrote programs in Fortran - 77 to do
things like read and write images, compute power spectrum of image,
and ofcourse to effect linear and nonlinear filtering. If you
are interested, let me know.
Nitin
{seismo,allegra}!rochester!ur-laser!nitin