65 lines
3.2 KiB
HTML
Executable File
65 lines
3.2 KiB
HTML
Executable File
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
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<html>
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<head>
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<title>About Gamma</title>
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<meta http-equiv="content-type"
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content="text/html; charset=ISO-8859-1">
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</head>
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<body>
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<h2 style="text-decoration: underline; font-weight: bold;">About Gamma</h2>
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When calibrating display devices, the notion of "gamma value" quickly
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becomes a topic for discussion. Various numbers are often bandied about
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as if they have a well known and accepted meaning, but it turns out
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that gamma values are not a very precise way of specifying real world
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device behavior at all.<br>
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<br>
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A "gamma" curve is typically thought of as an ideal power curve, but no
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real world device has the necessary zero output at zero input to be
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able to match such a curve, and in general a display may not exactly
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reproduce an idealized power curve shape at all. The consequence of
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this is that there are countless ways of matching a real world curve
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with the ideal gamma power one, and each different method of matching
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will result in a different notional gamma value.<br>
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<br>
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Argyll's approximate specification and reading is simply the gamma of
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the ideal curve that matches the real 50% stimulus relative-to-white
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output level. I think this is a reasonable (robust and simple)
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approximation,
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because it matches the overall impression of brightness for an image. A
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more sophisticated approximation that could be adopted would be to
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locate the idea power curve that minimizes the total delta E of some
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collection of test values, but there are still many details that the
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final result will depend on, such as what distribution of test values
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should be used, what delta E measure should be used, and how can a
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delta E be computed if the colorimetric behavior of the device is not
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known ? Some approaches do things such as minimize the sum of the
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squares of the output value discrepancy for linearly sampled input
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values, and while this is mathematically elegant, it is hard to justify
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the choice of device space as the metric.<br>
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<br>
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There are many other ways in which it could be done, and any such
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approximation may have a quite different numerical value, even though
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the visual result is very similar. This is because the numerical power
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value is very sensitive to what's happening near zero, the very point
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that is non-ideal. Consider the sRGB curve for instance. It's
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technically composed of a power curve segment with a power of 2.4, but
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when combined with its linear segment near zero, has an overall curve
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best approximated by a power curve of gamma 2.2. Matching the 50%
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stimulus would result in yet another slightly different approximation
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value of about 2.224. All these different gamma values represent curves
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that are very visually similar.<br>
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<br>
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<img style="width: 400px; height: 400px;"
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alt="Plot of sRGB curve vs. power of 2.224" src="srgbplot.gif"
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align="left"><br>
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<br>
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The result of this ambiguity about what gamma values mean when applied
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to real world curves, is that it shouldn't be expected that there are
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going to be good matches between various gamma numbers, even for curves
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that are very visually similar, unless the precise method of matching
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the ideal gamma curve to the real world curve is known.<br>
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<br>
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<br>
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</body>
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</html>
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