1.2 THE DIMENSIONS INTRODUCED

Hue

The hue of any given colour is its closest match within the range of "pure" or "saturated" colours. In terms of physical colour stimulus, this is the range of hues seen in the spectrum (red, orange, yellow, green, cyan, blue, violet), plus the nonspectral (purple) hues seen when the two ends of the spectrum are mixed. In terms of colour itself, that is, the mental experience generated by our visual system, it is the range of the four fundamental opponent hues, red, yellow, green and blue, and their respective intermediates. The Commission Internationale de L’Eclairage (CIE) acknowledges the opponent model in defining hue as "the attribute of a visual sensation according to which an area appears to be similar to one of the perceived colours, red, yellow, green and blue, or a combination of two of them".

For an isolated light, hue depends primarily by the physical property of dominant wavelength, although the hue of light of most wavelengths varies somewhat with brightness (Bezold-Brucke effect) and saturation (Abney effect).

For an object in a natural scene, the capacity of our visual system for colour constancy means that its perceived hue is determined to a large extent by the dominant wavelength of its reflectance under white light, as long as the illumination of the scene is not too strongly coloured. Nevertheless, an object can vary considerably in perceived hue depending on surrounding, interspersed and previously viewed colours, and even on the attitude of the viewer. In viewing an image, our capacity to extract object colour information from a visual scene can cause us to perceive hues very different from the actual image hues.

Figure 1.2.1. Classification of hue systems based on criterion used as basis for hue opposition.

Hues form a continuous loop, and are generally represented graphically by a 360 degree range in a system that may take the form of a circle, hexagon, triangle, or other closed geometrical figure (Fig. 1.2.1). Hue systems additionally differ among themselves by the criterion used for placing hues opposite each other (which affects the spacing of the hues), by the hues that are treated as principal or "primary", and by the sequential direction of the hues (i.e. clockwise or counterclockwise spectral sequence). Many hue systems also have a particular orientation (i.e. a specific hue placed at the top of the figure), or a particular hue treated as the first in the sequence.

Hue systems are classified on this site according to the criterion used to place hues opposite each other:

  • Hue systems based on the historical primaries are organized around the conventional complementary pairs red-green, orange-blue and either yellow-purple or yellow-violet. They include numerous 18th-21st century examples of the so-called "artists' color wheel", which are still taught today in simplistic colour theory courses. These hue systems reflect historical confusion of colourant-mixing and opponent relationships.
  • Hue systems based on opponent hue relationships are organized around the opponent hue pairs red-green and yellow-blue, and include various historical examples and the modern NCS system..Contrary to what one might expect, hues are not equally spaced perceptually in these systems.
  • Hue systems based on additive complements oppose hues of lights that make white light when mixed. They include systems by Newton, Helmholtz, Rood and Ostwald, and the CIE L*u*v* system. The opposite hue pairs are familar to many from the main hue axes in the HSB hue system used in graphics programs: digital magenta-green, red-digital cyan, and yellow-blue.
  • Hue systems based on colourant-mixing complements oppose hues of paints or dyes that make a neutral grey or black when mixed. They are generally organized around the optimal colourant-mixing primaries and their complementaries, magenta/crimson-green, cyan-red and yellow-violet.
  • Hue systems based on perceptually uniform spacing oppose hues that are separated by an equal number of perceptual steps in either direction around the hue circle. They include the Munsell system and CIE L*a*b* system.

Additive, colourant-mixing, and opponent hue systems can be structured around sets of hues regarded as primary, these primaries being different in each type of system (Fig. 1.2.1C-E). In digital programs HSB hue angle (H) is calculated from the ratios of the (nonlinear) RGB additive primaries by a simple formula (Fig. 1.2.1D). The Munsell hue circle (Fig. 1.2.1F) is not based on primary hues, but has five principal hues, red, yellow, green, blue and purple (R, Y, G, B and P) and five intermediate hues (YR, GY, BG, PB and RP). Each of these ten hues in theory has ten numbered divisions, with the fifth division, for example 5R, being regarded as the typical version of the hue. The Munsell Book of Color however has only four hue pages for each principal and intermediate hue, for example 2.5R, 5R, 7.5R and 10R, making a total of 40 hues.

Value (= greyscale value, lightness, tone)

Value is the scale between black and white. The terms value, lightness, greyscale value and tone all refer to the same scale, although sometimes "tone" can specifically connote the degree of darkness as opposed to lightness. Value is defined scientifically as the perceived brightness of an object compared to that of a perfect white object under the same illumination.

Value can be quantified in various ways, such as on a scale of ten, as in the Munsell system, or of 100, as in CIE lightness (L*) and the "L" in Lab colour space, used in Photoshop. Black and white glossy paints attain Munsell values of about 0.5 and 9.5 respectively, leaving basically nine numbered values for coloured paints. Other painters use an informal value scale of nine perceptually equal steps between black and white paint inclusive.

For physical, light reflecting objects, value depends on the physical property of reflectance, the proportion of the incident light energy that is reflected by the object, but the mathematical relationship is indirect. In the first place, light energy must be converted to luminance (Y) by being weighted wavelength by wavelength according to its effect on the human visual system (highest for yellowish green light; lowest at the ends of the spectrum). Secondly, value has a nonlinear relationship to luminance - a surface that looks visually halfway between black and white reflects only about 18% of the light energy reflected by a white surface.

For image colours on a light-emitting screen, value (= L in Lab space) depends in a similar, nonlinear way on luminance relative to an area of the screen perceived to be white.

Chroma

Figure 1.2.2. Diagrams showing four pairs of opposite hue pages from the 1915 Atlas by Albert Munsell. A. 5BG and 5R pages. B. 5B and 5YR pages. C. 5PB and 5Y pages. D. 5G and 5RP pages.

Chroma is the strength of an object colour, the degree of visual difference from neutral grey. For an object to have high chroma, its reflectance must be such that it reflects a large amount of light from part of the spectrum, and little light from the remainder. The potential range of chroma therefore varies strongly for different values and hues: at maximum value (white) and minimum value (black), chroma can only be zero. As we move away from these extremes the range of possible chroma increases up to a maximum at some intermediate value. The value at which this maxiumum chroma occurs depends on the hue, and for example is very high for yellow and low for violet and blue. The dimension of chroma (Greek for "colour") was introduced by Albert Munsell (1905), who also quantified the concept, and in doing so established that for different hues, the maximum chroma obtainable with paints not only occurs at different values, but also varies in absolute magnitude (Fig. 1.2.2).

Chroma can be represented graphically by distances outward from the centre of a hue circle, either in perceptually equal steps, and hence to varying distances from the centre (as in the Munsell Book of Color), or normalized to produce the regular circular arrangement seen in simpler geometrical conceptions like the historical "artists' colour wheel".

Figure 1.2.3.Orthogonal colour spaces, A, CIE L*a*b* and B, YCbCr, each showing gamut of sRGB colours. plotted using the program ColorSpace by Philippe Colantoni (www.couleur.org).

In several important mathematical colour spaces, colours are arranged consistently with the dimensions of hue, value and chroma, but in specifying the colours hue and chroma are replaced by two chroma dimensions at right angles to each other, in directions loosely related to the opponent hues. Thus instead of being described as having an orange hue at a certain chroma, a colour is specified as having so much reddish chroma and so much yellowish chroma. In CIE L*a*b* colour space (Fig. 1.2.3A), widely used in colourimetry and colour management, and in the similar "Lab" colour space used in graphics programs such as Photoshop, the +a/-a and +b/-b chroma dimensions correspond roughly with the Munsell 10RP/10G and 5Y/5PB hue axes respectively. The colour spaces known as YCbCr (Fig. 1.2.3B), YUV and YIQ, used in television, video and jpg compression are also of this kind. These orthogonal spaces permit a colour to be specified from spectrscopic measurements without requiring direct human judgement of hue and chroma, and their arrangement is much better suited to calculating colour differences. When a more intuitive representation is required, CIE L*a*b* coordinates can be very simply converted to metric hue, value and chroma (LCH = L*H*C* or HLC), which correlate closely though not perfectly with the corresponding Munsell dimensions. The RAL Design Atlas, a physical colour atlas that embodies this system, has hue pages of coloured chips arranged like those of the Munsell Book of Color.

Brightness and "brilliance"

We speak of light itself as being brighter or dimmer, rather than having lighter or darker greyscale value, and this scale of perceived intensity of light is called brightness. Brightness is a psychological experience that is difficult to quantify, and is strongly influenced by the state of adaptation of the observer. For example, your laptop screen is probably comfortably bright when viewed indoors, but very dim outdoors, even though it emits exactly the same amount of light energy. When we speak of brightness in the context of graphics programs we are generally concerned with relative brightness measured in relation to a finite scale set by the maximum brightness on a given device, as for example the nonlinear R, G and B brightnesses of an RGB colour. Relative brightness is correlated with the physical quantity of relative light energy, but via the same nonlinear relationship as explained for value and luminance.

Figure 1.2.4. HSB Brightness in relationship to Lab Lightness (= value).

Although colours on a computer screen can be described in terms of hue, value and chroma, they are very frequently specified in graphics programs in terms of the hue, saturation and brightness of the light coming from the screen, using a colour space known as HSB (=HSV)(Fig. 1.2.4). Brightness (B) and saturation (S) in HSB are both defined relative to the range of RGB (screen) colours. HSB Brightness is brightness relative to the maximum available for RGB colours of a given hue (H) and saturation (S).

We've seen that the greyscale value of an object is defined scientifically as the brightness of the light it reflects compared to that reflected by a perfectly white object under the same lighting. Coloured objects necessarily absorb certain chunks of the spectrum, and therefore necessarily reach their maximum possible brightness at lower greyscale values than neutral objects. Colours at this maximum possible brightness for their hue and saturation include full or "pure" colours, tints (mixtures of white and "pure" colours) and white. We recognize this in common speech when we describe all such colours as being bright, even though not all are light. Less "bright" colours appear "greyed", meaning having a content of black, while colours that are brighter than "bright" present an appearance of luminosity that ranges from fluorent (fluorescent-looking) to self-luminous. This scale of brightness relative to the natural limit for a given hue and saturation has been called brilliance (Evans, 1972). Bright colours, which exhibit neither positive brilliance (luminosity) nor negative brilliance (blackness) are said to have zero greyness (G0).

Saturation and "Colorfulness"

In contrast to value, where we have several words for essentially the same concept, the single word saturation is employed for a number of different but rarely properly distinguished concepts.

In common speech the term "saturation" is often used with the meaning of relative chroma of an object colour, implying comparison with some "fully saturated" state. However a "fully saturated" object colour is a problematic concept. For example, a quinacridone magenta oil paint is "fully saturated" if one considers only currently available artists’ paints, yet is desaturated to varying degrees if one brings into consideration fugitive or fluorescent paints, digital colours, or theoretical optimal colours. The dimension of chroma (absolute strength) of colour makes no assumptions about a maximal state, and so is greatly preferable for object colours. (Another term for the concept of chroma relative to an assumed maximum is chromaticness from the Swedish NCS system, discussed below).

Saturation is widely and much more appropriately employed for the quite different matter of purity of colour of lights, where there is a fully saturated state (monochromatic light) in existence to be compared. Saturation as a quality of light depends on the physical property of spectral purity, or freedom from admixed white light. It can be quantified in various ways, but all divide up the range from zero for white light to a maximum either for monochromatic light, or the for most saturated light possible for a given device. All monochromatic light might be treated as having a saturation of 100%, but in some scientific formulations red, green and violet spectral hues are said to attain higher levels of saturation than others.

Figure 1.2.5. RGB colours of HSB Hue = 0 projected onto* the Munsell 7.5R hue page, showing lines of uniform saturation and brightness. ( *Although the colours all have the same digital hue angle (H=0), they actually drift somewhat in Munsell hue).

Saturation (S) in HSB is a physical measure of spectral purity relative to the maximum possible for that hue (H) in RGB colours, and is based on a simple formula dividing the RGB colour into a white and a coloured component. Lines of uniform HSB hue and saturation (Fig 1.2.5) are of great importance in digital painting, because along such lines brightness varies while the ratio of RGB brightnesses, and therefore the effective balance of wavelengths or chromaticity, does not change. Such lines form what I have called shading series, which our visual system "reads" as changing levels of illumination (as in Fig. 1.2.6 below).

Current literature on colour appearance models quantifies saturation as the "colorfulness" (absolute colour intensity) of a light stimulus relative to its brightness (Fairchild, 2004). Thus if two lights have the same saturation, but one is brighter, the latter will exhibit more "colorfulness". (I will retain the quotation marks and American spelling wherever I am using the word in this specific technical sense). In the same sense, two objects may reflect light of the same saturation, but if one reflects more light, that light will be of greater "colorfulness", and the objecty will be perceived to have higher chroma. Thus "colorfulness", not saturation, is the corresponding term for light to the chroma of objects. For example, in Fig. 1.2.6, strip AB has higher chroma than CD, but both reflect light of the same saturation. Surfaces with high chroma tend to reflect light of high "colorfulness", the latter varying however in proportion to the the level of illumination.

Figure 1.2.6. Is A the same colour as B or D? It all depends on how you look at it, which is why we need to be so careful about terminology. Viewed as objects in a scene, we see two strips, AB and CD, each of uniform value and chroma, AB lighter and higher in chroma than CD. Seen as image colours, however, A and B are surfaces of different value and chroma, and emit light of different brightness and "colorfulness". They have been painted this way in order to represent the brighter and more "colorful" light that a surface of uniform chroma reflects where it is more strongly lit. Seen as light, all four areas emit light of the same (100% pure) saturation - in each area, only the red phosphors are glowing (right). Areas A and D happen to emit light of the same hue, saturation and brightness - that is, they are identical image colours, even though they are perceived as very different object colours in the scene. Indeed, because these "inferred" object colours are so insistent, it may be very difficult to see these image colours as identical. Image: David Briggs, 2007, Photoshop CS2.

 Other dimensional systems

In schemes such as the modern Swedish NCS system and the historically important Ostwald system, object colours are considered to be resolvable into white, black and coloured components. Dimensions known as whiteness, blackness and chromaticness (= relative chroma) respectively are represented on an equilateral triangle with white, black and the supposed "pure" colour at the upper, lower and outer corners respectively (Fig. 1.2.7C). The "pure"colour is always shown at a level halfway between black and white, regardless of its Munsell value, which is not represented in these systems. One fundamental difficulty for all such systems is the selection of a representative of each hue to be regarded as the "pure" colour, which as we have seen is a problematic concept for object colours.

Figure 1.2.7. Four approaches to dividing up a hue page. In different places and modes within Photoshop, the expression "saturation" can refer to HSV saturation, HLS "saturation", chromaticness or chroma!

Many digital programs use a colour space known as HLS (=HSL), which is based on easily calculated but arbitrary dimensions confusingly called "lightness" (L) and "saturation" (S) (Fig. 1.2.7D). Colours assigned a so-called "lightness" of 0.5 include all digital hues at their maximum strength, as well as a middle grey, and so include colours varying widely in Munsell value. Like the NCS and Ostwald systems, this gives the colour space the form of a symmetrical double cone, much simpler than the irregular "tree-shape" of Munsell and CIE L*a*b*. So-called "saturation" in HLS is essentially chroma relative to the maximum possible for that hue and "lightness".

We will consider all of these dimensions in more detail in Parts 7-9, and then go on to outline their practical importance for painters in Part 10. But first we need to review some of the basic facts of light and colour.

Modified April 19, 2012. Original text here.

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