Individual Corresponding Colors Data and Chromatic Adaptation Transforms

It has been well established, through the study of observer metamerism, that color matching functions vary across individual observers. Chromatic adaptation transforms, however, have not been similarly studied to examine carefully for individual differences. Existing chromatic adaptation transformations, such as CAT02 that is embedded within CIECAM02, are fitted to population data on corresponding colors that tell us little about individual differences and have inherently large uncertainty. It is often stated that fitted von Kries type models fit within the population of observers (e.g. within the inter observer variability) rather than accurately fitting the mean of the data (e.g. within the standard error of the mean of a population or an individual) That suggests two questions examined in this work: Do such models actually predict the mean results? And can individual data on chromatic adaptation be described with 3x3 von Kries type models. These questions are approached by collecting corresponding colors data with very high accuracy and precision allowing the analysis and examination necessary to begin creating the next generation of accurate chromatic adaptation transforms.  Corresponding colors are color stimuli that match across changes in viewing conditions.[1] For example, if a stimulus under incandescent adaptation is matched with another stimulus that appears identical, but is viewed under daylight illumination, then those two stimuli are considered corresponding colors. Currently, chromatic adaptation models for practical applications are loosely based on the von Kries (1902) hypothesis that the separate cone types have independent gain controls with the level set by the stimulation of the cone types themselves and derived by fitting psychophysical data.[2] Prediction errors of these chromatic adaptation transforms, or CATs, are no less than about 4.0 CMC(1:1) or CIE DE2000 units, when evaluating models such as CMCCAT2000, CMCCAT97, CAT02 and CIECAT94.[3] The collected datasets of Luo and Rhodes (1999) that are commonly used in chromatic adaptation modeling are mostly from experiments incorporating only single observations per observer per color and a small number of observers due to the inherent difficulty in the experimental techniques.[4] Kuo et al. (1995) found that typical inter observer variation for studying chromatic adaptation was about 4 CMC(1:1) units (which are similar in magnitude to CIE DE2000 color difference units)[5] Hence, if a CAT has an error of prediction equal to, or less than, 4 units, it might be considered satisfactory. So the limitation of the number of observers and observations in the experiments is subject to significant improvement to get precise corresponding colors data. This research firstly aims to collect highly precise individual corresponding colors data. To begin to achieve this objective, a small number of observers and colors, but large number of trials are adopted. Experimental data are evaluated firstly and then utilized to evaluate existent chromatic adaptation models. Finally the necessity of building individual CATs is explored. Experimental To get highly precise corresponding colors data, a large number of repetitions of the psychophysical experiment is required. In this work, 30 repeat trials are adopted rather than the more typical single trial. Due to the large number of replicates, a small number of colors and observers are used for this stage of the research. Ultimately five colors were evaluated by six observers for 30 trials each across one change in illumination. The experimental stimuli were reflecting objects produced by printing ink on paper. A variety of color patches were provided on reference sheets for observers to choose as matches to the color appearance of a set of five test patches. Observers marked the spatial location of the matching patch on a response sheet with the same layout of color patches as seen on reference sheets. Additionally, to test color appearance memory ability after two minutes of adaptation break, two additional colors were evaluated under illumination identical with the test condition (no change in adaptation) Preparation of Test Sheets and Reference Sheets Red, blue, green, yellow and a light (tan) colors were selected for the experiment. It is known from previous research that highly chromatic colors have larger errors in CAT predictions than lower chroma colors. So high chroma red, blue, green and yellow were adopted as test colors referring to the Helson data. Historically, superior datasets are most often reflectance media such as the Lam data,[6] the Helson data, and the Kuo Luo data. So reflecting media was adopted in this experiment. All the test patches and reference patches were printed on a Canon iPF6400 printer using Onyx Rip Queue 11 printing software with Gold Fibre Silk paper (310g/m2) and Canon Lucian ink. The side size of each square color patch was 2.2cm calculated in terms of the viewing distance of about 65cm to produce a 2 degree viewing field. Two test color patches are juxtaposed on each test sheet with 4.5 cm distance between them to avoid direct simultaneous contrast influence on each other. Each test patch had its corresponding reference sheet which has enough patches with enough color range for observers to choose a satisfactory corresponding color. Observation for each test patch was repeated 30 times, the positions of reference patches on reference sheets was varied from trial to trial to avoid being remembered by observers. Thus four sets of 4X4 patch reference sheets were prepared. The four sets of reference sheets had different color patches. To make the four sets of 4X4 patch reference sheets, a set of 5X5 reference sheets was made and then randomly decomposed into four 4X4 sets. Firstly, the center patch of 5X5 color patches was calculated by CAT02. Then preliminary experiment was implemented to adjust the colors of 5X5 patches to ensure sufficient color range and appropriate increment between adjacent horizontal and vertical patches. At the same time, the colors of all these patches should be within the gamut of the printer. After iterative printing, observation and adjustment, 5X5 patch reference sheets are determined. Fig. 1 is 5X5 color patches on a*b* plane for the red color center.  An example of the CIELAB sampling used to prepare reference sheets for corresponding colors elections. In this case the red color center is illustrated. To test the color memory ability of observers, two color patches, blue and yellow, were put on one test sheet. Four sets of corresponding 4X4 patch reference sheets were also made that included colorimetric matches to the test colors. Observers then made memory matches to these two patches following the same experimental protocol but with no change in adaptation. In one session, five test colors were repeated for two trials. With two color patches on each test sheet, there were five test sheets for the chromatic adaptation experiment. Adding the one memory color test sheets, there are altogether six sheets in an experimental session. The six sheets were printed and spiral bound. The four sets of 12 reference sheets were also printed and spiral bound into four collections denoted with A, B, C and D. In each experimental session each observer was assigned one of the four collections of reference sheets. The spiral binding was minimally obtrusive and a neutral black color. Preparation of Test Sheets and Reference Sheets The two adaptation light sources adopted for the experiment were illuminant A and illuminant D65 simulators, which are the most commonly used illumination in previous research. They were provided by incandescent and daylight of GTI Colormatcher CMB3064 light booth. The mean tristimulus values, in cd/m from a white reference standard, and normalized tristimulus values of the booth's incandescent and daylight illumination are shown in Table 1. The viewing area of the light booth was 76cm height, 163cm width, and 76cm depth. It was big enough to execute the experiment with room for a wide adapting field of view. When the experiment began, an observer sat in front of the light booth. A sample holder was put in the center of the light booth. The test sheets collection and one reference sheet collection were put respectively on the two sides of the sample holder. Each of six test sheets are required for a round of the experiment. Each round included the four steps outlined below. Table 1. Absolute (cd/m from a diffuse white reference) and relative tristimulus values of the incandescent (A) and daylight (D65) illumination used in the experiments. Incandescent (A) Daylight (D65) Xrw Yrw Zrw Xw Yw Zw Mean Measurement 473.40 437.60 160.50 325.0 341.20 397.10 Normalized Results 108.18 100.00 36.67 95.25 100.00 116.38 1. The observer takes two minutes to adapt to the incandescent illumination at first.[7] 2. Then the observer would put the test sheet on the sample holder and have 60 seconds to remember the appearance of the two test colors. Observers were allowed to use whatever method they felt would allow most accurate memory of the colors for a short period of time. 3. Then they put the test sheet aside and covered it with a piece of white paper. The light source automatically switched to daylight and the observer again adapted to it for two minutes. 4. After the second adaptation, the observer put the corresponding reference sheet on the sample holder and had 60 seconds to choose the best matches from a 4X4 collection of patches on the reference sheet sets by marking on the answer sheet as shown in Fig. 2. They could mark directly on the location of the matching patch (shaded areas) or select a location between 2 or 4 patches (or even outside all patches) on the grids to indicate the matching color fell between, or outside, the appearance of the patches provided.