HLS/HSL/HIS Model

In 1979, the Graphics Standards Planning Committee’s core committee adopted the perceptual HIS model which consists of two cylindrical cones joined on their flat surfaces.

The HLS model, which literature sometimes refers to as HSL and HIS (hue, intensity, and saturation), borrows some ideas from the HSV model but uses a double hexacone versus a double cylindrical cone model. In the acronym, HLS stands for hue, lightness, and saturation. It is essentially an HSV space distortion consisting of a double hexacone space created by pulling the white point up off the V = = 1 surface. Unlike the HSV model, fully saturated hues are located along the cross section’s perimeter containing L = 0.5.

The HLS model is useful because, like the HSV model, it decomposes RGB triad values into values more closely related to human perception. However, its simplistic approach similarly provides differing luminosities for given L values. Like HSV, this model is useful in midpoint gamma corrections which separate chromaticity from luminosity, allowing luminosity recalculations with subsequent recombination of chromaticity and luminosity that preserve color content.

Figure 13-4  The HLS model

When reading about these models, it is useful to note there are no standards governing HLS, HSL, HIS, etc. acronym use. So, expect to find confusing if not conflicting literature. Finally, the HlsToRgb2 function implements Ken Fishkin’s accelerated HLS to RGB transformation found in Graphics Gems Volume 1.

HSI Model

The HSI model is yet another perceptual model, but its mathematical computations are extremely computationally intensive and beyond this book’s scope. Like the HSV model, the RGB cube is deformed into another shape using stacked cross sections determined by projective geometry. Unlike the HSV model which has a hexagon cross section, the HSI cross section is an equilateral triangle which provides hue and saturation information, leaving cross section altitude to determine the intensity component which is determined by the equation:

I = (R + G + B)/3

However, accurate color reproduction is impossible using this equation because it is at variance with visual perception processes.

Figure 13-5  The HSI model and solid

CIE XYZ

Recalling Thomas Young’s color matching experiments, adjusting the intensity and combining three suitable primary lights matches many selected colors. The three radiance values collectively required to achieve a match are referred to as the sample’s tristimulus values and are provided graphically in Figure 13-6.

Adding the three radiances together and dividing each of a sample’s tristimulus value by the sum provides the sample’s chromaticity coordinates. Thus, the tristimulus values indicate how much of each light’s maximum radiance was required to produce the sample match, and the trichromatic coefficients indicate how much fractional radiance each primary light contributed to produce the match. So, if R, G, and B are a sample’s tristimulus values, r, g, and b are its normalized trichromatic coefficients, where:

r = R/(R + G + B)

g = G/(R + G + B)

b = B/(R + G + B)

Figure 13-6  Tristimulus value graph

Clearly, the sum of r, g, and b is always 1.0. So, subtracting the sum of r and g from 1.0 produces b’s value. Like the proportional coordinate discussion, matches with the same chromaticity coordinates represent the same tints, shades, and tones and only vary in intensity, information the normalization process loses.

However, recall that in certain spectral regions it is impossible to stimulate adjacent red or green cones without stimulating both, sometimes considerably. This stimulation “cross talk” introduced the “negative light” concept required to produce color matches. So, if we tried to create a three-dimensional color solid as coordinates, it would contain some negative values. Suppose we require g’s value to always be non-negative. This requires r’s values to assume negative values. Figure 13-7 displays the trichromatic coefficients corresponding to the Figure 13-6 tristimulus values.

Figure 13-7  Chromaticity coordinates for the spectral colors using the NPL primaries