Re: [APML] Synthetic Luminance Channel for Film Images

[Roland Roberts <roland@astrofoto.org>]

>>>>> "Thor" == Thor Olson <Thor.Olson@EFI.COM> writes:


    Thor> If you look at the statistics of your three channels they
    Thor> have:

    Thor>        mean    std
    Thor> red    19.88  4.77
    Thor> green  30.87  5.67
    Thor> blue   42.53 11.24

    Thor> I don't think it's quite proper to divide the mean by the
    Thor> standard deviation for an object that is supposedly "black",
    Thor> but that's a different topic.  Just looking at the std
    Thor> numbers, blue is obviously the noisiest channel, so any
    Thor> luminance formula that places more weight on blue will tend
    Thor> to give a noisier result.

    Thor> In this case equal weights gives std=5.05, [...]

I'm sorry to nit pick (but only a little or I wouldn't post at all...)

Equal weighting gives mean = 31.09, std 4.49.  You add variances, so
the equal weighting case gives

    variance(average) = (1/9) * (4.77^2 + 5.67^2 + 11.24^2)

The factor of 1/9 comes from a propagation of errors type calculation:

    variance [f(x)] = (df/dx)^2 * variance(x)

The somewhat non-intuitive result that the stdev has dropped is due to
taking the average instead of the sum.  the stdev of the sum is, of
course, higher than any particular channel; stdev = 13.46.  The S/N of
the sum (or average) has increased to 6.9 vs the original best-case
(green) of 5.4.

    Thor> I don't happen to believe that "luminance layering" improves
    Thor> the signal to noise of the result without distorting the
    Thor> orginal color information.  It essentially moves the noise
    Thor> around, taking advantage of the human visual systems
    Thor> relative blindness to high frequencies in the chroma
    Thor> channels.

This is probably true.  But, depending on your filter arrangement, for
CCD work, the synthetic luminance layer you create by simply adding
the three channels may be equivalent to a shot with no filters; about
what you would have done to create an independent luminance layer.  Of
course, this synthetic luminance layer is *not* independent.

    Thor> But since truly calibrated colorimetric images are so
    Thor> difficult, we've already crossed the "correct color"
    Thor> boundary and should be looking for ways to make attractive
    Thor> (but uncalibrated) pictures.  And this seems like another
    Thor> tool to apply to the cause.

I agree completely; if you are doing photometry color calibration is
important but for most of the pictures we do I think "reasonable
color" and "attractive" are the things to keep in mind.

roland
-- 
		       PGP Key ID: 66 BC 3B CD
Roland B. Roberts, PhD                             RL Enterprises
roland@rlenter.com                     76-15 113th Street, Apt 3B
roland@astrofoto.org                       Forest Hills, NY 11375

--  APML Archives at <http://astro.umsystem.edu/apml/>  ---
             Unsubscribe at <majordomo@seds.org>