HDR and UCS : do HDR techniques require a new UCS space?

As David Wright said, Colorimetry ends in the retinal cone outer segments [1]. Color Appearance is at the other end of the human visual system. Appearance incorporates all the spatial processing of all the color responsive neurons. Thus color vision can be analyzed from two ways: from the color matching response of retinal receptors or from the color appearance, result of the whole vision system. If we start from cone response, we go through color matching tests as Wright and Guild did [2-4]. If we start from appearance, we ask observers to describe the apparent distance between hues, chromas and lightnesses as Munsell, and then as Nickerson, Newhall and Judd did [5]. In a recent work Indow, Romney and D'Andrade [6] have worked backward from geometry of the Munsell Book to cone responses. They solved for the 3-D color space transform that placed LMS cone responses in the color-space positions measured for the Munsell Book of Color. In other words, they knew the LMS Cone color space at the cone inner segments, and they knew the equally-spaced color appearance space at the end. They solved for the best process to map all the cone responses to all the Munsell locations. Their fit of all data is a two step process: • First, correct for veiling glare. All retinal receptors have a response proportional to log quanta catch. Munsell space reports that lightness is the cube root of quanta catch at the display. • Second, their mathematical solution found a very strong color-opponent processes. Recalling the cone sensitivity functions, they have considerable overlap. To overcome this crosstalk one needs strong opponent processing. Stiehl et al. [7] showed that veiling glare converts cube-root scene luminance to logarithmic retinal luminance (see Fig. 1). Appearance follows the retinal stimulus, after glare, not the scene stimulus. D'Andrade used the cube-root of LMS cone responses thus approximating the retinal image of the Munsell chips. The cube root is the key feature that fits LMS cones to Munsell space locations. The cube root is due to intraocular scatter. Depending on the scene, all retinal image areas have variable glare affecting lightness values below 5/ Munsell designations. Glare limits the dynamic range of the retinal image [8]. Figure 1. Stiehl et al. results CIEL*a*b* has the same cube root and opponent channel mechanism. The way that L*a*b* handles the lightness component of High Dynamic Range (HDR) scenes with two components. The first uses a cube-root function in both lightness and chroma for high light levels. The second uses a linear function to force the calculation to zero asymptote. The same is true of sRGB. In all cases, it normalizes the long-, middle- and short-wave integrals to the maxima in each channel: (X/Xn), (Y/Yn), (Z/Zn). Human vision normalizes appearances to maxima in L, M and S channels [9]. This operation converts quanta catches to relative integrated radiances. The next step in all calculations raises these normalized integrals to the power of 1/3, or cube root. In HDR terminology, this step scales the large range of possible radiances into a limited range of appearances. Figure 2 shows calculated CIE Lightness L* vs. log luminance for a range covering 6 log units. The vertical yellow line identifies the luminance levels of the two equations. On the right side the cube root equation applies; on the left side the linear one applies. L* describes white as 100. On this graph L* = 100 plots at 0 relative optical density, or 100 % (Y/Yn). In order to get L* = 50, we have to reduce luminance to 18%. The yellow line delimits the ranges of L* equations and falls at 9 % in apparent lightness and 0.9 % in luminance. There is no cube root function on the left side. Here equation controls the shape of the asymptote to 0 lightness. L* = 1 falls at OD = 3.0, or 0.1% luminance. In other words, L* suggests that 99% of possible apparent lightneses fall in 3 log units of scene dynamic range. Since a* and b* use the same compressive cube root function on (Y/Yn), (X/Xn), (Z/Zn), then L* a* b* evaluates the very large range of X, Y and Z in the scene, over a 3 log unit cube. Uniform color spacing is achieved by the cube-root function, plus a linear segment below 0.9 % relative luminance. The orange line delimits the equation split in the sRGB space conversion and green squares plot the sRGB gamma that is very similar to L* cube root function. Following the above considerations, we see no need to modify common color spaces in response to HDR imaging. Appearance is the response to the retinal image. It follows the spatial distribution of light in the scene from which intraocular glare sets the range of light on the retina. Figure 2. Lightness vs relative OD