Appendix A A. General Statistics A.1 Morrisey s Incomplete Matrix Solution for Case V Because there was unanimous agreement for some pairs, a zero-one proportion matrix resulted. All values that were not one-zero were converted to standard normal deviates and the scale values were solved using Morrisey s incomplete matrix solution. The text below is based on the description given by Engeldrum in, Psychometric Scaling: A Toolkit for Imaging Systems Development (2, pg 117). The column vector, z, contains all the z-score values excluding the incomplete proportions. Matrix X is formed such that the columns correspond to the samples and the rows represent the judged pair. Note that for an incomplete matrix there are (k+1)n rows, where k is less than n(n-1)/2. The entries of X consisted of +1 and -1 in the columns of the pair that were compared (pairs that did not produce zero-one proportions). An n by 1 column forms the S vector, which represents the unknown scale values. The rank of the X matrix is increased by adding the constraint that the sum of the scale values equals zero. Thus, an extra row of 1 sis added as the final row in the X matrix, and a added as the last element of vector Z. The final matrix formulation is illustrated in equation (A.1). The least squares solution, equation (A.2), is used to solve for S. (A.1) z z z M 12 13 24 1 1 = M 1 1 1 M 1 1 M 1 1 S S S S S k + 1 n n M 1 L L L M L M 1 n n n 1 2 3 4 (A.2) S = (X' X) 1 X' z 16
A.2 Average Absolute Deviation (AAD) and χ 2 Goodness-of-fit The goodness-of-fit of the paired comparison and rank order data was tested using both the average absolute deviation (AAD) and Mosteller s χ 2 Test. First, the difference of the scale value pairs, Si-Sj, was computed and the result transformed to predicted probabilities (p ) using the standard normal cumulative distribution function. Note, these proportions are what is expected if the Case V model is correct. The proportions obtained experimentally (p) can be compared to the predicted proportions (p ) by computing the average absolute deviation as shown in equation (A.3). The results from this equation indicate the percent difference between the observed and predicted data. (A.3) p' p 2 = n(n 1) i> j p' p, where p' = predicted proportion p = observed proportions n = number of stimuli. from results, from the data, and The chi-square test is computed on the arcsine transformation of the matrix of predicted proportions (p ) and observed proportions (p) as suggested by Mosteller (1951) and given in equations (A.4) and (A.5). 1 (A.4) θ' = sin 1 ( 2 p' 1) in rad θ = sin ( 2 p 1) in rad (A.5) χ 2 = J i> j ( θ' θ ), where J = number of observers with (n -1)(n - 2)/2 degrees of freedom 2 161
A.3 Supplement to Table 5.3 Table A.1 Goodness-of-fit measured for Paired Comparison Case V solution wakeboarder vegetables firefighters kids bug Pioneer Plasma χ 2 AAD χ 2 AAD χ 2 AAD χ 2 AAD χ 2 AAD Rank Order 8.15.58 12.74.4 17.326.83 1.667.48 16.28.819 Paired Comparison 18.93.63 21.957.53 6.1562.51 19.452.72 89.82.1396 wakeboarder vegetables firefighters kids bug Apple Cinema χ 2 AAD χ 2 AAD χ 2 AAD χ 2 AAD χ 2 AAD Rank Order 7.84.53 3.957.45 1.125.7 15.425.69 19.73.863 Paired Comparison 19.69.95 2.891.93 9.2618.61 36.858.74 5.18.1116 Critical value χ 2 (α =.95; df = 1) = 18.31 where P{ χ 2 (v) 18.31). Poor fits are indicated by bold type in the table. 162
Appendix B B. Supplementary u v Chromaticity Plots (Chapter 6) B.1 Achromatic Patch Adjustment.49 D65 vs. D93.48.47.46.45.44.43.42 D65 D93 Mean D65 Mean D93.41.16.17.18.19.2.21.22 Figure B6.6 Plots subject s final patch adjustments for D65 and D93 white point images. The black marker represents the mean D65 u v coordinates and the green marker represents the mean D93 u v. 163
Normal Image D65 White Point Normal Image D93 White Point.48.47.46.45.44.43.42.41.16.18.2.22 Mosaic Image D65 White Point.48.47.46.45.44.43.42.41.16.18.2.22 Mosaic Image D93 White Point data D93 wtpt D65 wtpt Mean.48.47.46.45.44.43.42.41.16.18.2.22 Gray Image D65 White Point.48.47.46.45.44.43.42.41.16.18.2.22 Gray Image D93 White Point.48.47.46.45.44.43.42.41.16.18.2.22.48.47.46.45.44.43.42.41.16.18.2.22 Figure B6.7 Plots subject s final patch adjustments for N, M, and G images groups. The black marker represents the D65 u v white point and the cyan marker represents D93 white point. The green marker represents the mean u v for the data in each plot. 164
.5 3faces.5 auto.48.48.46.44.46.44 data mean image (D65) mean image (D93) D65 wtpt D93 wtpt.42.16.18.2.22.24.42.16.18.2.22.24.5 botonists.5 business.48.48.46.46.44.44.42.16.18.2.22.24.42.16.18.2.22.24.5 chemist.5 graymushrooms.48.48.46.46.44.44.42.16.18.2.22.24.42.16.18.2.22.24 165
.5 livestock.5 lunch.48.48.46.44.42.16.18.2.22.24.46.44.42.16.18.2.22.24 data mean image (D65) mean image (D93) D65 wtpt D93 wtpt.5 scooter.5 smoke.48.48.46.46.44.44.42.16.18.2.22.24.42.16.18.2.22.24.5 watermellon.5 worker.48.48.46.46.44.44.42.16.18.2.22.24.42.16.18.2.22.24 Figure B6.8 & B6.9 Patch adjustments separated across individual images. Red markers represent mean a* b* of the image with a D65 white point, and green markers represents the mean a* b* of the image with the D65 white point. The black and blue markers indicate the D65 and D93 true white points as a reference. 166
.5 botonists N.tif.5 botonists N D93.tif.48 left face right face.48 left face.46.46 right face.44.44.42.16.18.2.22.24.42.16.18.2.22.24 business N.tif.5 left face right face.48.46.5.48.46 business N D93.tif left face right face.44.42 wall&text.44.42.4.16.18.2.22.24.4 wall&text.16.18.2.22.24.5 smoke N.tif.5 smoke N D93.tif.48 right face left face.48.46.46 right face left face.44.44.42.16.18.2.22.24.42.16.18.2.22.24 Figure B6.13 Mean u v data extracted from areas that received the most is indicated by the cyan, magenta, and yellow (for the business image) makers. Red makers indicate the mean u v of the image, and black and blue markers plot the white points of the image as references. 167
B.2 Selecting the Most Achromatic Region.49.48 D65 vs. D93 D65 D93 Mean D65 Mean D93.47.46.45.44.43.42.41.16.17.18.19.2.21.22 Figure B6.16 Plots subjects achromatic selections for D65 and D93 white point images. The black marker represents the mean D65 u v coordinates and the green marker represents the mean D93 u v. 168
25 2 frequency 15 1 5 5 1 15 2 25 3 35 4 45 Y (cd/m2) Figure B6.17 Histogram of luminance values from the achromatic selection task across all images. 169
.5 3faces.5 auto.48.48.46.44.42.16.18.2.22.24.5 botanists.46.44.42.16.18.2.22.24.5 business data mean image (D65) mean image (D93) D65 wtpt D93 wtpt.48.48.46.46.44.44.42.16.18.2.22.24.42.16.18.2.22.24.5 chemist.5 graymushrooms.48.48.46.46.44.44.42.16.18.2.22.24.42.16.18.2.22.24 17
.5 livestock.5 lunch.48.46.48.46 data mean image (D65) mean image (D93) D65 wtpt D93 wtpt.44.44.42.16.18.2.22.24.5 scooter.42.16.18.2.22.24.5 smoke.48.48.46.46.44.44.42.16.18.2.22.24.5 watermelon.42.16.18.2.22.24.5 worker.48.48.46.46.44.44.42.16.18.2.22.24.42.16.18.2.22.24 Figure B6.18 Achromatic selection data separated across individual images. Red markers represent mean a* b* of the image with a D65 white point, and green markers represent the mean a* b* of the images with the D65 white point. The black and blue markers indicate the D65 and D93 true white points as a reference. 171
Appendix C C. Supplementary Manipulation Plots (Chapter 5) 25.. 2. apple median L* plasma median L* manipulated - orignal (L*) 15. 1. 5.. -5. -1. wake1 wake3 wake5 wake4 wake6 veggies1 veggies3 veggies5 veggies6 veggies4 fire2 fire3 fire4 fire5 fire6 kids1 kids2 kids4 kids5 kids6 bug1 bug2 bug4 bug5 bug6 25. 2. apple median h plasma median h manipulated - orignal (hue) 15. 1. 5.. -5. -1. wake1 wake3 wake5 wake4 wake6 veggies1 veggies3 veggies5 veggies6 veggies4 fire2 fire3 fire4 fire5 fire6 kids1 kids2 kids4 kids5 kids6 bug1 bug2 bug4 bug5 bug6 172
25. 2. apple median C* plasma median C* 15. 1. 5.. -5. -1. 35. 3. apple median E94 plasma median E94 manipulated - orignal (DE94) 25. 2. 15. 1. 5.. wake1 wake3 wake5 wake4 wake6 veggies1 veggies3 veggies5 veggies6 veggies4 fire2 fire3 fire4 fire5 fire6 kids1 kids2 kids4 kids5 kids6 bug1 bug2 bug4 bug5 bug6 wake1 wake3 wake5 wake4 wake6 veggies1 veggies3 veggies5 veggies6 veggies4 manipulated - orignal (C*) fire2 fire3 fire4 fire5 fire6 kids1 kids2 kids4 kids5 kids6 bug1 bug2 bug4 bug5 bug6 Figure C Graphs show the median pixel differences from the original image in CIE lightness (L* ab ), chroma (C* ab ), and hue (h ab ) coordinates using the forward models of the two displays. The median color differences (DE94) are also shown as a reference. 173