Theory of The Transformation
It is often casually stated that the decoding gamma for sRGB data is 2.2, yet the above transform shows an exponent of 2.4. This is because the net effect of the piecewise decomposition is necessarily a changing instantaneous gamma at each point in the range: it goes from gamma = 1 at zero to a gamma of 2.4 at maximum intensity with a median value being close to 2.2. The transformation was designed to approximate a gamma of about 2.2, but with a linear portion near zero to avoid having an infinite slope at K = 0, which can cause numerical problems. The continuity condition for the curve which is defined above as a piecewise function of, is
Solving with and the standard value yields two solutions, ≈ or ≈ . The IEC 61966-2-1 standard uses the rounded value . However, if we impose the condition that the slopes match as well then we must have
We now have two equations. If we take the two unknowns to be and then we can solve to give
Substituting and gives ≈ and ≈, with the corresponding linear-domain threshold at ≈ . These values, rounded to, and, are sometimes used to describe sRGB conversion. Publications by sRGB's creators rounded to and, resulting in a small discontinuity in the curve. Some authors adopted these values in spite of the discontinuity. For the standard, the rounded value was kept and the value was recomputed to make the resulting curve continuous, as described above, resulting in a slope discontinuity from 12.92 below the intersection to 12.70 above.
Read more about this topic: SRGB
Famous quotes containing the words theory of the, theory of and/or theory:
“The theory of the Communists may be summed up in the single sentence: Abolition of private property.”
—Karl Marx (1818–1883)
“In the theory of gender I began from zero. There is no masculine power or privilege I did not covet. But slowly, step by step, decade by decade, I was forced to acknowledge that even a woman of abnormal will cannot escape her hormonal identity.”
—Camille Paglia (b. 1947)
“By the “mud-sill” theory it is assumed that labor and education are incompatible; and any practical combination of them impossible. According to that theory, a blind horse upon a tread-mill, is a perfect illustration of what a laborer should be—all the better for being blind, that he could not tread out of place, or kick understandingly.... Free labor insists on universal education.”
—Abraham Lincoln (1809–1865)