Hue in the HSB/HSL encodings of RGB

An image with the hues cyclically shifted in HSL space

The hues in the image of this Painted Bunting are cyclically rotated with time.

Hue is one of the main properties of a color, defined technically (in the CIECAM02 model), as "the degree to which a stimulus can be described as similar to or different from stimuli that are described as red, green, blue, and yellow,"^[1] (the unique hues). The other main correlatives of color appearance are colorfulness, chroma, saturation, lightness, and brightness.

Usually, colors with the same hue are distinguished with adjectives referring to their lightness and/or chroma, such as with "light blue", "pastel blue", "vivid blue". Exceptions include brown, which is a dark orange,^[2] and pink, a light red with reduced chroma.

In painting color theory, a hue refers to a pure color—one without tint or shade (added white or black pigment, respectively).^[3] A hue is an element of the color wheel. Hues are first processed in the brain in areas in the extended V4 called globs.^[4][5]

Computing hue [link]

In opponent color spaces in which two of the axes are perceptually orthogonal to lightness, such as the CIE 1976 (L*, a*, b*) (CIELAB) and 1976 (L*, u*, v*) (CIELUV) color spaces, hue may be computed together with chroma by converting these coordinates from rectangular form to polar form. Hue is the angular component of the polar representation, while chroma is the radial component.

Specifically, in CIELAB:^[6]

Failed to parse (Missing texvc executable; please see math/README to configure.): h_{ab} = \mathrm{atan2}(b^*, a^*)\;

while, analogously, in CIELUV:^[6]

Failed to parse (Missing texvc executable; please see math/README to configure.): h_{uv} = \mathrm{atan2}(v^*, u^*) = \mathrm{atan2}(v', u')\;

Where, atan2 is a two-argument inverse tangent.

Computing hue from RGB [link]

Preucil^[7] describes a color hexagon, similar to a trilinear plot described by Evans, Hanson, and Brewer,^[8] which may be used to compute hue from RGB. To place red at 0°, green at 120°, and blue at 240°.

Failed to parse (Missing texvc executable; please see math/README to configure.): h_{rgb} = \mathrm{atan2}\left( 2 \cdot R - G - B, \sqrt{3} \cdot (G - B) \right)

Note: This is equation assumes the form atan2(x,y), many programs and spreadsheets use atan2(y,x).

Equivalently, one may solve:

Failed to parse (Missing texvc executable; please see math/README to configure.): \tan( h_{rgb}) = \frac{\sqrt{3}\cdot (G - B)}{2\cdot R - G - B}

Preucil used a polar plot, which he termed a color circle.^[7] Using R, G, and B, one may compute hue angle using the following scheme: determine which of the six possible orderings of R, G, and B prevail, then apply the formula given in the table below.

HSV color space as a conical object

An illustration of the relationship between the "hue" of colors with maximal saturation in HSV and HSL with their corresponding RGB coordinates.

Note that in each case the formula contains the fraction Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{M - L}{H - L} , where H is the highest of R, G, and B; L is the lowest, and M is the mid one between the other two. This is referred to as the Preucil Hue Error, and was used in the computation of mask strength in photomechanical color reproduction.^[9]

Hue angles computed for the Preucil circle agree with the hue angle computed for the Preucil Hexagon at integer multiples of 30 degrees (red, yellow, green, cyan, blue, magenta, and the colors mid-way between contiguous pairs) and differ by approximately 1.2 degrees at odd integer multiples of 15 degrees (based on the circle formula), the maximum divergence between the two.

The process of converting an RGB color into an HSL color space or HSV color space is usually based on a 6-piece piecewise mapping, treating the HSV cone as a hexacone, or the HSL double cone as a double hexacone.^[10] The formulae used are those in the table above.

Specialized hues [link]

The hues exhibited by caramel colorings and beers are fairly limited in range. The Linner hue index is used to quantify the hue of such products.

Hue as a qualification in the names of artist's colors [link]

Manufacturers of pigments use the word hue e.g. 'Cadmium Yellow (hue)' to indicate that the original pigmentation ingredient, often toxic, has been replaced by safer (or cheaper) alternatives whilst retaining the hue of the original. Replacements are often used for chromium, cadmium and alizarin.

Hue vs. dominant wavelength [link]

Dominant wavelength (or sometimes equivalent wavelength) is a physical analog to the perceptual attribute hue. On a chromaticity diagram, a line is drawn from a white point through the coordinates of the color in question, until it intersects the spectral locus. The wavelength at which the line intersects the spectrum locus is identified as the color's dominant wavelength if the point is on the same side of the white point as the spectral locus, and as the color's complementary wavelength if the point is on the opposite side.^[11]

Hue difference: Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta h or Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta H^* ? Hue difference: Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta h or Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta H^* ?

There are two main ways in which hue difference is quantified. The first is the simple difference between the two hue angles. The symbol for this expression of hue difference is Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta h_{ab}

in CIELAB and Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta h_{uv}
in CIELUV. The other is computed as the residual total color difference after Lightness and Chroma differences have been accounted for; its symbol is Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta H^*_{ab}
in CIELAB and Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta H^*_{uv}
in CIELUV.

See also [link]

• Lightness (color)
• Colorfulness
• Chromaticity
• Munsell color system
• Bezold-Brücke shift

References [link]

External links [link]

• Editing of hue in photography