Since a few questions have popped up on IRC and it really is a weird concept to grasp I thought I'd expand a bit on the color math that is being discussed here. Sorry it is so long, I hope it is somewhat entertaining though :) Simon Budig (simon@xxxxxxxx) wrote: > I think you are missing that "unbounded" also allows *negative* R, G or B > coordinates. That makes the colors imaginary in the sRGB color space, > but it still is possible to convert them to all other RGB color spaces. > > Unbounded sRGB can express all the colors XYZ can express. > Transformations from userRGB to sRGB to userRGB are lossless. The normal sighted human eye contains three types of cones which respond differently to a given light spectra. In 1931 researchers have tried to map the response of these cone types by having people stare at projection screens and match colors. The results of these experiments were combined and resulted in the definition of a "CIE standard observer", with the most important aspect being functions describing the "standard" response of the three cone types to light wavelengths: http://en.wikipedia.org/wiki/File:CIE_1931_XYZ_Color_Matching_Functions.svg The "Tristimulus values" X, Y, Z refer to the three cone types. They can be determined by weighting the spectral power distribution with the resp. response curve and then computing the integral over the wavelength range from 380 to 780nm. Related to XYZ is "xy", which simply is the color information normalized to a given intensity: x = X/(X+Y+Z) and y=Y/(X+Y+Z). The horseshoe-diagram you see frequently when colors are discussed (http://en.wikipedia.org/wiki/File:CIE1931xy_blank.svg ) lives in the "xy" plane. Note that these are absolute colors we're talking about here. For a given spectral power distribution we end up with certain XYZ values. This totally ignores other aspects of the human vision system. In particular knowing the XYZ coordinate of a color does not help at all in determining if something is perceived as "white". This is where the "whitepoint" becomes relevant. For example if you look at a piece of letter paper lighted by candle light you perceive it as white, since your eye is trained to take the color of the environment light source into account. Also experiences are relevant as well. You just assume that this piece of paper is white, since this is what you are used to and then your vision system takes this as a reference point. If you'd see the same XYZ color in a daylight context, you'd probably be surprised how reddish yellow it actually is. Taking a photo of a candlelight scene with a digital camera set to a "daylight" whitepoint will give you an idea. No, the yellow color is not the camera lying to you, it is the eye not being allowed to lie to you. Another important aspect of the XYZ system is, that it contains "imaginary colors": Color coordinates where it is impossible to create light spectra for. If you look at the color matching functions referenced above you see why: they do have huge overlaps, most wavelengths trigger two or even all three of the cone types simultaneously. Looked at it from the math point of view that means for example that "if Y is nonzero, then X or Z will be nonzero as well". The XYZ coordinate (0, 1, 0) is an imaginary color. It is impossible to construct a real world light spectrum that results in this XYZ coordinate. Pure light with about 520nm wavelengh might get you close, but you still have X and Z components > 0. The rounded boundary in the horseshoe diagram represents the pure wavelengths and the weird shape is determined by the overlaps in the color matching functions. XYZ is very useful in that it is a good tool to describe absolute colors and it is a superset of all the color impressions the "CIE standard observer" can perceive. It is the "safe bet" of color spaces. However, since "pure X", "pure Y" and "pure Z" are basically a physical impossibility they cannot be used to build real world computer monitors. It has turned out that variants of Red/Green/Blue are a useful compromise to compose color impressions. The Phosphors used in CRTs and the filters used in LCDs have a specific spectral distribution and can be varied in their intensity, resulting in an absolute XYZ coordinate. In the real world we have a maximum brightness for each of the components and reducing the intensity moves the XYZ coordinate on a straight line towards (0,0,0), i.e. black. Since the integral math behaves additively the three independent components construct a skewed cube in the XYZ color space. This is the "gamut": the range of color impressions that can be shown with this particular monitor. If you now normalize the intensities of the coordinates within this skewed cube you end up with a triangle in the xy-space, which is useful to describe the range of colors available to you with a given set of base colors: http://en.wikipedia.org/wiki/File:CIE1931xy_gamut_comparison.svg The corners of the triangle are the xy-coordinates of the phosphors/filters used. These are the "primaries" or "chromaticities" of the given RGB space. (Note that ProPhotoRGB uses primaries which are imaginary colors. There never will be a computer monitor using ProPhotoRGB primaries.) The triangle shape is no random accident: It is the convex hull of the three primaries: the points within are a weighted sum of the three corners, where the sum of the weights = 1. Since physics does not allow for "subtracting" color spectra from each other we cannot escape from this triangle to display more colors. This is where the sRGB color space has severe problems representing color impressions with intense and pure colors which are perfectly within the realm of the real world. Using sRGB primaries to additively construct your color will impose harsh limits on you. ...that is if you are concerned about the real world implementation in a computer monitor. When we talk about "unbounded" sRGB in the Gegl/Babl context we do away with this restrictions: We allow absurdly high intensities way beyond the physical capabilities of a specific light source. And we allow for negative intensities. Yes, negative intensities are 100% absurd and wrong when you think about them in terms of implementing computer monitors. However, we don't need to model a real computer monitor. We are not bound to the laws of physics when dealing with pixels in memory. Allowing negative coefficients for the RGB values makes it possible to escape the dreaded gamut triangle. In fact this makes the unbounded sRGB color space as expressive as AdobeRGB, ProPhotoRGB and XYZ. To reiterate: Every XYZ coordinate can be represented in the terms of sRGB primaries. For example: The Green Primary of the AdobeRGB 1998 colorspace is - specified with its own primaries - at the coordinates (0, 1, 0) (which is somewhat obvious). Using e.g. the slightly convoluted color calculator at http://www.brucelindbloom.com/ we can convert this to XYZ = ( 0.185554, 0.627349, 0.070687 ). (Note that there is a normalization involved here: AdobeRGB (1, 1, 1) is converted to an XYZ value scaled to Y = 1.0. We also get the xy coordinate of the green point here: xy = (0.21, 0.71) ) This in turn translated into unbounded linear sRGB yields: sRGB = (-0.398283, 1.0, -0.042939) And thats it. The color represented by (0,1,0) in AdobeRGB is equivalent to the color represented by (-0.40, 1.0, -0.04) in unbounded linear sRGB ("bablRGB"). Yes, there are negative coefficients, no, we don't need to worry about them. And we can use the same math in reverse to reconstruct the AdobeRGB value to use it as userRGB for our multiplication operation. We end up at RGB=(0,1,0) where we started. Note that there is nothing special about the sRGB that makes this possible. The same math would work with any other primaries, as long as they don't form a line in the xy diagram (i.e. they need to be linearily independant in XYZ). However, for this to work we absolutely must not clamp negative values to zero. As soon as we do that huge errors will be introduced. Gegl/Babl don't - at least not for the float types. We're sane there. If anybody wants to dive deeper into that topic: Browse Bruce Lindblooms site. It has tons of valuable ressources, gives you formulae for various conversions and gives a lot of great insights. I hope this helps, Simon -- simon@xxxxxxxx http://simon.budig.de/ _______________________________________________ gimp-developer-list mailing list List address: gimp-developer-list@xxxxxxxxx List membership: https://mail.gnome.org/mailman/listinfo/gimp-developer-list List archives: https://mail.gnome.org/archives/gimp-developer-list
