Hunt Model Calculations

Amongst the large number of CAMs, one of the most complex ones is the Hunt model.⁶² According to the best knowledge of the author it is uniquely extended to unrelated colours, too. Hunt treats any colours as unrelated if isolated from other colours (e.g. bright light sources, uniform areas against unilluminated backgrounds) and recommends that for typical monitor colours in dark room this is the situation (these are exactly the conditions for the experiments presented). Since the numeric attributes of Hunt model also apply to an approximately 2° stimulus, it was neither assumed to predict the size effect discussed in this chapter better than either CIELAB or CIECAM02. Nevertheless, as it offers some predictions on the appearance of unrelated colours, it might be interesting to see how the typical Hunt-defined perceptual attributes of the immersive scene, assumed now as unrelated colour, correlate with either perceptual attribute of its equivalent colour, if any, for which every attribute is able to be calculated without any “related/unrelated arguments”.

First, without going into any detailed description of the steps and calculations Hunt model uses (its final procedure is published in Ref.62), some basic ideas are discussed, how the model generally works. Similar to the CIE colour appearance model, it uses several input parameters that include the tristimulus values of the sample, those of its background, surround, the reference white, some chromatic and brightness induction factors to determine and quantify the correlates of perceptual attributes of related colours:

brightness (Q), colourfulness (M94), saturation (s), hue (hs), lightness (J), chroma (C94), etc.

The equivalent colours displayed on the CRT were considered as related ones due to the viewing situation they appeared in. For the background input values, the trichromatic values of the three backgrounds were used, the white surroundings served as reference white, adapting field luminance was set to one fifth of the luminance of the reference white (LA=Yw/5, which is a widely accepted rule of thumb for displayed images even in CIECAM02), and induction factors were Nb=25 and Nc=0.95. The illuminant parameter was discounted and set to 0.

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immersive brightness (Q)

equivalent brightness (Q)

Figure I/19. Comparison (black markers) of the Hunt-model-predicted brightness values of the immersive colours (using unrelated calculation) and that of their equivalent colours (using related colour model). Data were determined from the mean tristimulus values of the 21 test colours and from those of their equivalent colours. Open dots represent the modified brightness of the immersive colours using Eq. (I/21).

If the model is used for unrelated colours (detailed description is in Ref.3), according to Hunt, it is not realistic to take the adapting field luminance (LA) as zero. The sample and the scattered light will provide an effective adapting luminance well above zero.

Furthermore Hunt introduces the concept of a so called conditioning field that he defines as the field unrelated colours are seen immediately after (e.g. a pilot may first look at the displays of the flight deck, and then out of the cockpit at the signal lights). In our case the conditioning field is exactly the repeatedly appearing grey background that is used to prevent observers from being exposed to the immersive colours for unlimited duration. In the calculations, therefore, the luminance and chromaticities of the three different levels of

greys were used as conditioning field and luminance of the adapting field was also set to equal that of the conditioning field (LA=LC). The rest of the input parameters (e.g. scotopic luminances) were calculated by using the approximations recommended by Hunt, chromatic surround induction factor, Nc, was set to 0.5. The output of the model for unrelated colours offers quantitative values for brightness (Q), colourfulness (M) and saturation (s).

First, the brightness values of the immersive colour (unrelated calculation) and that of its equivalent colour (related colour model) are compared (Figure I/19). The clouds of the data corresponding to the different luminance conditions (Y=5.32, 15.78 or 34.9 cd/m²) are well-noticeably separated. Surprisingly enough, Hunt model in this context predicts the test colours to exhibit more brightness than their equivalent stimuli do. It is also interesting, that the brightness of the equivalent colours of the lighter test colours (e.g. Y=34.9) is predicted to be lower than that of the darker ones (e.g. Y=5.32), which is possibly due to the response of the built-in Helmholtz-Kohlrausch effect to the changing background of the test colours.

A possible modification of the brightness attribute of Hunt model for immersive colours is that they should be shifted to be as close as possible to the brightness values of the corresponding equivalent colours (i.e. to force the black points of Figure I/19 to be as close to the 45° line as it is possible keeping the vertical coordinates at a constant value). A simple linear distortion seems appropriate for this purpose, and performing the optimization in terms of minimizing a squared error, the following equation results:

imm Hunt

' 0.2576 48.9287

Q = − Q + , (I/21)

where QHunt is the brightness of the immersive stimulus calculated with simply as it is in the Hunt model for unrelated colours and Q’imm may be a next step, the modified brightness that approximates the brightness of the equivalently perceived related colour.

The basic difference between Eq. (I/21) and either Eq. (I/11) or Eq. (I/18) is that there the lightness/luminance of an equivalently perceived colour was specified, while here the brightness measure of Hunt model is redefined for the immersive situation to match the brightness value of a visually matching colour stimulus in a well-defined visual situation (i.e. mathematically it is an inverse procedure). Analogously, Eq. (I/11) or Eq. (I/18) can be rearranged, answering also the question: What lightness/luminance (measured) should

be set for the immersive stimulus that its lightness/luminance be perceived as a desired value?

As a matter of fact, Eq. (I/21) assigns almost uniformly a near Q’imm=33.7 value to all of the 21 test colours, and since the data points represent 3 different luminance levels this approach is – though logical – a little contradicting (even colours with higher luminance are assigned less brightness than for others). Brightness of the equivalent samples on the CRT may not be what observers assess and match, and it is not surprising if the presence of the white border and the continuous grey background is considered when they make their adjustments. Possibly, a relative quantity should be found observers match with the brightness perception of the immersive colour, hence, it is interesting to examine a brightness-lightness comparison. In Figure 20 the lightness of the equivalent colours are depicted as the function of the brightness of the immersive ones. Note that this brightness is the original brightness of Hunt model from the calculation for unrelated colours denoted as QHunt above. As can be seen from Figure 20, this approach correlates more with what would be expected as an outcome of the experiment. Observers seem to discard that the small CRT stimulus also has a brightness in itself and they rather order the lightness attribute of the equivalent colour (its brightness relative to its white surround) to represent the amount of light the immersive scene is perceived to emit.

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immersive brightness (Q)

eqivalent lightness (J)

Figure 20. Lightness of the equivalent colours depicted against the brightness of the 21 immersive stimuli.

From this and the previous sections of the Discussion it is clear that whichever model, colour space, or measure is considered, none of them is perfect in that sense whether they can be used as a starting point for colour size effect calculations or not. Most of them are hard to adjust to the criteria an extremely large surface determines. For the future, it is an essential question to settle down the system (colour space, colour appearance model, or simply chromaticity coordinates) the size effect is to be described in.