CIECAM02

CIECAM02 is a color appearance model (Engl. Color Appearance Model) by the International Commission on Illumination CIE (commission internationale de l'éclairage) and the successor of CIECAM97.

It is based on the CIECAM97 model and contains some revisions and simplifications. These include a linear chromatic adaptation transformation, a post-adaptation using a hyperbolic compression response function and changes in the perception parameters.

The two essential components of the color appearance model are the chromatic adaptation transform CIECAT02 and equations for the calculation of the mathematical correlation between perception attributes such as luminance (brightness), brightness (lightness), chroma (chroma), saturation (saturation), color (colorfulness) and hue (hue) . These are the six technically defined dimensions of a color appearance.

CIECAM02 takes into account the Stevens effect , the Hunt effect , the Bartleson-Breneman phenomena, the simultaneous contrast , discounting the illuminant and the incomplete adaptation . Compared to the full Hunt color appearance model , the transition from day to night vision is not taken into account. The model is therefore only suitable for a limited brightness range and is not to be regarded as complete, but in return it also offers a relatively low mathematical complexity and is therefore particularly suitable for practical applications. It is also relatively easy to invert.

The model can be used to predict the attributes of the color appearance or to calculate corresponding color values ​​in a changed environment. CIECAM02 is used in the Windows Color System (WCS) of Windows Vista .

Parameters for the observation circumstances

The observation field

Model of the human observation field (adaptive field)

CIECAM02 uses a slightly reduced model of the observation field as used in the Hunt color appearance model . In the model, the inner circle represents the stimulus which, based on the functions of the CIE 2 ° standard observer, delivers the tristimulus values . The outer circle is the background encompassing 10 °, in which the relative brightness of the background is measured. Outside of the circular field of vision lies the environment (peripheral area), which represents the rest of the room. The totality of background and environment is called the adaptive field . ${\displaystyle (XYZ)^{T}}$ ${\displaystyle Y_{b}}$

For practical applications, however, this model cannot be regarded as decisive, but only as a basis and must be adapted accordingly to the circumstances. In image processing z. B. the stimulus is usually defined by a single pixel and the brightness of the background is defined with that of a neutral gray tone (20%), because the background does not vary greatly due to the spatial brightness distribution within an image, which is independent of the ambient situation. With the fixed definition of its dimensions of 10 °, the background would also be dependent on the scaling of the image and the viewing distance, possibly of several observers. The same is true for a stimulus of 2 ° dimensions.

White point and absolute brightness

Two further elementary parameters for CIECAM02 are the white point and the absolute brightness of the adaptive field . The tristimulus value of the white point is also based on the CIE 2 ° standard observer and is generally defined by the existing light source. In the case of self-luminous media such as monitors or projections, however, this lies between the white point of the light source and that of the medium itself, again without any fixed definitions. With the determined white point, the XYZ space in which both the white point and the stimulus are located is normalized. ${\displaystyle (X_{w}Y_{w}Z_{w})^{T}}$ ${\displaystyle L_{A}}$ ${\displaystyle Y_{w}=100}$

On the one hand, the absolute brightness of the adaptive field can be measured with a photometer. If none is available, it can generally be assumed that the adaptive field is a gray (20%) area (gray-world assumption), and accordingly assumes the value of 20% of the existing ambient brightness. Does the viewed medium have a higher absolute brightness than the surroundings, e.g. B. When projecting in a dark room, the brightness of the medium is considered to be decisive. ${\displaystyle L_{A}}$ ${\displaystyle L_{A}}$

Environmental parameters

The environmental parameters can be determined via the ratio of the absolute brightness of the environment and that of the stimulus and are recorded in the following table:

Surrounding field	F.	c	${\displaystyle N_{c}}$
average	1.0	0.69	1.0
twilight	0.9	0.59	0.95
dark	0.8	0.525	0.8

F: degree of adaptation

c: environmental impact

${\displaystyle N_{c}}$ : Factor for chromatic induction

In most cases, average environmental parameters are available. A dim environment is given when the absolute brightness of the environment is 20% of the brightness of a self-luminous medium. A dark environment is when there is almost no ambient light, e.g. B. when projecting in a dark room. For media that are not self-luminous, “average” environmental parameters are generally assumed.

These values ​​can be interpolated linearly for intermediate levels.

Practical use

As already indicated, the specifications of the input parameters are kept very vague and require an interpretation that corresponds to the circumstances.

The following table contains some suggestions for four possible applications, whereby in the fourth case the determination of in view of the increased ambient brightness remains questionable: ${\displaystyle L_{A}}$

Example parameters for CIECAM02

Environmental situation	Ambient light in lux ( ) ${\displaystyle \mathrm {cd/m^{2}} }$	Brightness of the scene white point in ${\displaystyle \mathrm {cd/m^{2}} }$	${\displaystyle L_{A}}$ in ${\displaystyle \mathrm {cd/m^{2}} }$	White point	Environmental parameters
Colored surface in a light chamber	1000 (318.3)	318.3	63.66	WP of the light chamber	average
TV evening	38 (12)	80	16	Between WP of the environment and the TV	twilight
Projection in a darkened room	0 (0)	150	30th	Between WP of the projector and E (equal energy ill.)	dark
Computer monitor in the office	500 (159.2)	80	16	Between the WP of the monitor and the office lighting	average

Another point is the determination of the tristimulus values. If the stimulus is in the form of a self-luminous medium, the values ​​can be determined using the photometric data of the medium. In the case of non-self-luminous media, the stimulus is determined by the spectrum of the light source and the filtering properties of the medium, which makes it much more difficult to determine the parameters. You have to proceed in a similar way with regard to the white point.

Chromatic adaptation transformation

Suppository responses for CAT02 and HPE

The chromatic adaptation transformation of CIECAM02 is primarily characterized by the fact that it takes place in two different color spaces. First, a modified von Kries adaptation transformation is presented in a modified Li et al. RGB space, which is characterized by an increased spectral sharpness of the R and B components compared to the natural spectral responses of the cones. The chromatic adaptation transformation is a modified CMCCAT2000 and is referred to as CIECAT02 . During the development of CIECAM02 the main focus was on a linearization of the Bradford transformation from CIECAM97s , which had an exponential non-linearity in the blue channel and thus made an analytical inversion impossible. The results of CIECAT02 were compared with psychophysical measurement data and proved to be downwardly compatible, if not better, compared to the transformation from CIECAM97s. The adapted color values ​​are then transferred via the XYZ color space into the Hunt-Pointer-Estevez space and subjected to a post-adaptation in the form of a compression response function. The HPE room is suitable for the further steps, since its spectral response functions are more like those naturally occurring in the cones. The perception parameters are later determined from the Hunt-Pointer-Estevez space or the determined color values ​​are transferred to the 5-dimensional JChQM color space.

CIECAT02

Degree of adaptation ${\displaystyle D(L_{A},F)}$

Degree of adaptation

To get the tristimulus values ​​in the Li et al. To transmit RGB color space, the following matrix is ​​used:

${\displaystyle M_{CAT02}={\begin{bmatrix}0{,}7328&0{,}4296&-0{,}1624\\-0{,}7036&1{,}6975&0{,}0061\\0{,}0030&0{,}0136&0{,}9834\end{bmatrix}}}$

The inverse matrix, which is required for the back transformation into the XYZ color space, has the following form:

${\displaystyle M_{CAT02}^{-1}={\begin{bmatrix}1{,}096124&-0{,}278869&0{,}182745\\0{,}454369&0{,}473533&0{,}072098\\-0{,}009628&-0{,}005698&1{,}015326\\\end{bmatrix}}}$

For the chromatic adaptation, the degree of adaptation dependent on and is required: ${\displaystyle L_{A}}$ ${\displaystyle F}$ ${\displaystyle D}$

${\displaystyle D=F\left(1-{\frac {1}{3{,}6}}e^{\frac {-L_{A}-42}{92}}\right)}$

If the stimulus originates from a non-self-illuminating medium, it is assumed that a complete adaptation of the visual system to the illuminant can be assumed (discounting the illuminant). The complete CIECAT02 transformation can then be expressed as follows: ${\displaystyle D=1}$

${\displaystyle {\begin{bmatrix}X'\\Y'\\Z'\end{bmatrix}}=M_{CAT02}^{-1}{\begin{bmatrix}{\frac {Y_{w}D}{R_{w}}}+(1-D)&0&0\\0&{\frac {Y_{w}D}{G_{w}}}+(1-D)&0\\0&0&{\frac {Y_{w}D}{B_{w}}}+(1-D)\end{bmatrix}}M_{CAT02}{\begin{bmatrix}X\\Y\\Z\end{bmatrix}}}$

For RGB values ​​of the white point, its tristimulus values ​​must also be transferred to the CAT02 space. Based on the normalization of the tristimulus values ​​on , CIECAT02 changes to: ${\displaystyle Y_{w}=100}$

${\displaystyle {\begin{bmatrix}X'\\Y'\\Z'\end{bmatrix}}=M_{CAT02}^{-1}{\begin{bmatrix}{\frac {100D}{R_{w}}}+(1-D)&0&0\\0&{\frac {100D}{G_{w}}}+(1-D)&0\\0&0&{\frac {100D}{B_{w}}}+(1-D)\end{bmatrix}}M_{CAT02}{\begin{bmatrix}X\\Y\\Z\end{bmatrix}}}$

Readjustment

luminance level adaption factor ${\displaystyle F_{L}(L_{A})}$

Compression response function ${\displaystyle R'_{A}(L_{A},R')}$

Compression response function ${\displaystyle (F_{L}=1)}$

The post-adaptation ensures that the Hunt and Stevens effects are taken into account. On the one hand, the transformation matrix is ​​required in the HPE color space:

${\displaystyle M_{HPE}={\begin{bmatrix}0{,}38971&0{,}68898&-0{,}07868\\-0{,}22981&1{,}18340&0{,}04641\\0{,}00000&0{,}00000&1{,}00000\end{bmatrix}}}$

It is used to map the pre-adapted tristimulus values ​​into the HPE space:

${\displaystyle {\begin{bmatrix}R'\\G'\\B'\end{bmatrix}}=M_{HPE}{\begin{bmatrix}R'\\G'\\B'\end{bmatrix}}}$

In order to calculate the compression response function, the “luminance-level adaption factor” is required, which can be calculated directly from . ${\displaystyle F_{L}}$ ${\displaystyle L_{A}}$

${\displaystyle F_{L}=0{,}2k^{4}(5L_{A})+0{,}1(1-k^{4})^{2}(5L_{A})^{1/3}}$

With

${\displaystyle k=\left({\frac {1}{5L_{A}+1}}\right)}$

The compression response function for the red value is as follows:

${\displaystyle R'_{a}=\left({\frac {400\left({\frac {F_{L}R'}{100}}\right)^{0{,}42}}{\left[27{,}13+\left({\frac {F_{L}R'}{100}}\right)^{0{,}42}\right]}}\right)+0{,}1}$

The relationship can be applied in the same way to the green and blue values. It should be noted that the amounts from , and must be used here and a possible negative sign must be transferred to the result. ${\displaystyle R'}$ ${\displaystyle G'}$ ${\displaystyle R'}$

Perceptual parameters

The perception parameters are calculated directly from the compressed RGB values ​​in the HPE space and span a 5-dimensional perception color space. The perception parameters are the color or hue (hue) , relative brightness (lightness) , the absolute magnitude (brightness) , color or relative chroma (chroma) , absolute chroma (colorfulness) and saturation (Saturation) , which in itself is a redundant parameter is and accordingly does not create an independent dimension. ${\displaystyle h}$ ${\displaystyle J}$ ${\displaystyle Q}$ ${\displaystyle C}$ ${\displaystyle M}$ ${\displaystyle s}$

Precalculations

While only the absolute brightness of the adaptive field and the ambient parameters were of importance for the chromatic adaptation, the relative brightness of the background is now of major importance when calculating the psychophysical values, since it has an influence on the subjective color perception through any simultaneous contrasts that may be present . The following parameters can be determined from: ${\displaystyle Y_{b}}$ ${\displaystyle Y_{b}}$

${\displaystyle n={\frac {Y_{b}}{Y_{w}}}}$

${\displaystyle N_{bb}=N_{cb}=0{,}725\left({\frac {1}{n}}\right)^{0{,}2}}$

${\displaystyle z=1{,}48+{\sqrt {n}}}$

${\displaystyle N_{bb}}$and stand for the achromatic and the chromatic induction factor of the background and are therefore a measure of the extent to which this affects the perception of the stimulus and are therefore sufficient for the simultaneous contrast. Under the assumption introduced above that the background is gray (20%), and to 1. express the same relationship, but will appear in the following as an exponent and not as a factor. From the color values ​​in the HPE space, preliminary Cartesian coordinates can first be calculated in a red-green (a) and yellow-blue (b) metric. ${\displaystyle N_{cb}}$ ${\displaystyle N_{b}b}$ ${\displaystyle N_{c}b}$ ${\displaystyle z}$

${\displaystyle a=R'a-{\frac {12G'_{a}}{11}}+{\frac {B'_{a}}{11}}}$

${\displaystyle b=\left({\frac {1}{9}}\right)(R'_{a}+G'_{a}-2B'_{a})}$

Hue H

As in other color spaces, the hue in others is defined by the angle of . ${\displaystyle H}$ ${\displaystyle (a,b)^{T}}$

${\displaystyle h=\tan ^{-1}\left({\frac {b}{a}}\right)}$

Depending on this, the eccentricity factor can be calculated, which later has an influence on the calculation of chroma or colourfulness by stretching or compressing the plane spanned by depending on the angle. This satisfies the fact that the level of chroma or colourfulness is defined as a function of the hue. ${\displaystyle (a,b)^{T}}$

${\displaystyle e={\frac {1}{4}}\left[\cos \left(h{\frac {\pi }{180}}+2\right)+3{,}8\right]}$

The hue quadrature , a completely redundant value in itself, which, however, assigns a multiple of 100 to the four colors defining the metric and thus has a right to exist, is obtained through linear interpolation using the values ​​in the following table. ${\displaystyle H}$

	red	yellow	green	blue	red
i	1	2	3	4th	5
${\displaystyle h_{i}}$	20.14	90.00	164.25	237.53	380.14
${\displaystyle e_{i}}$	0.8	0.7	1	1.2	0.8
${\displaystyle H_{i}}$	0	100	200	300	400

${\displaystyle H=H_{i}+{\frac {100{\frac {(h-h_{i})}{e_{i}}}}{{\frac {(h-h_{i})}{e_{i}}}+{\frac {(h_{i+1}-h)}{e_{i+1}}}}}}$

Relative brightness (lightness) J

In order to calculate the relative brightness, an achromatic response is calculated in advance by means of a weighted summation of the color values, which additionally contains a noise term defining the black point. The sum is also weighted with the achromatic induction factor of the background.

${\displaystyle A=\left[2R'_{a}+G'_{a}+\left({\frac {1}{20}}\right)B'_{a}-0{,}305\right]N_{bb}}$

The relative brightness itself then results from the ratio of the achromatic response of the stimulus and that of the white point. Up to this point, the white point must undergo the same transformations as the stimulus itself in order to obtain its achromatic response. The predetermined from the background and the environment exponent provides the functional relationship for a convex or concave curvature and thus provides for a consideration of the simultaneous contrast over and Bartleson-Breneman equations above . ${\displaystyle z}$ ${\displaystyle c}$

${\displaystyle J=100\left({\frac {A}{A_{w}}}\right)^{cz}}$

Absolute brightness Q

The determination of the absolute from the relative brightness of the stimulus is basically a reversal of the psychophysical adjustments made so far. The absolute brightness of the adaptive field does not affect the perceived relative brightness of the stimulus, but the absolute brightness is definitely influenced by it. Correspondingly, the "luminance level adaption factor", which was already consulted in the compression response function, reappears here . Also and are used here in a reciprocal sense to the previous applications. ${\displaystyle F_{L}}$ ${\displaystyle A_{w}}$ ${\displaystyle c}$

${\displaystyle Q=\left({\frac {4}{c}}\right){\sqrt {\left({\frac {J}{100}}\right)}}(A_{w}+4)F_{L}^{0{,}25}}$

Chroma C

The computation of the chroma requires the computation of a preliminary quantity , which contains an amount of . This also includes the eccentricity factor and the chromatic inductions of the environment and the background and . ${\displaystyle t}$ ${\displaystyle (a,b)^{T}}$ ${\displaystyle e}$ ${\displaystyle N_{c}}$ ${\displaystyle N_{c}b}$

${\displaystyle t={\frac {(50000/13)N_{c}N_{cb}e(a^{2}+b^{2})^{1/2}}{R'_{a}+G'_{a}+\left({\frac {21}{20}}\right)B'_{a}}}}$

About the chroma is then under addition of calculated. The brightness of the background also affects the perceived color intensity. ${\displaystyle t}$ ${\displaystyle C}$ ${\displaystyle n}$

${\displaystyle C=t^{0{,}9}{\sqrt {\frac {J}{100}}}(1{,}64-0{,}29^{n})^{0{,}73}}$

Colorfulness M

Exactly as with the calculation of the absolute brightness, in contrast to the relative chroma, an increase in the brightness of the adaptive field has an effect on the chroma or the absolute chroma. The “luminance level adaptation factor” appears again here.

${\displaystyle M=CF_{L}^{0{,}25}}$

Saturation p

As already mentioned, saturation is a redundant variable in the sense of CIECAM02 and can be calculated directly from the color and absolute brightness . ${\displaystyle M}$ ${\displaystyle Q}$

${\displaystyle s=100{\sqrt {\frac {M}{Q}}}}$

Cartesian coordinates

In some cases it can be advantageous to display individual stimuli in Cartesian coordinates. The trigonometric relationships are listed here for the relative psychophysically relevant JCh space. Together with span and open the three-dimensional space. and must not be confused with the provisional Cartesian coordinates and . The space presented here experiences an eccentric curvature relative to the originally spanned space as well as various scalings above the color plane caused by and . ${\displaystyle J}$ ${\displaystyle a_{c}}$ ${\displaystyle b_{c}}$ ${\displaystyle a_{c}}$ ${\displaystyle b_{c}}$ ${\displaystyle a}$ ${\displaystyle b}$ ${\displaystyle e}$ ${\displaystyle Y_{b}}$ ${\displaystyle L_{a}}$

${\displaystyle a_{c}=C\cos(h)}$

${\displaystyle b_{c}=C\sin(h)}$

Corresponding relationships can be established for the QMh room or QMs room.

Web links

Commons : CIECAM02  - Collection of Images, Videos and Audio Files

• Color Appearance Models: CIECAM02 and Beyond
• CIECAM02 , University of Koblenz-Landau