In this section the color image difference described in chapter 8 will be illustrated. First, the image series used by Gaddipati et al. [GaMY97] will be used to test the color image difference (CID), the metric introduced by Rushmeier et al., root mean squared error, and Gaddipati's metric. We have implemented Rushmeier's metric, although it is not 100% clear which viewing distance should be taken into account. We have chosen, in this example, the viewing distance so that the maximum displayable frequency is 60 cycles per visual degree for our metric, and the number of rectangles was 5000. The distance chosen by Gaddipati et al. is also not clear from their paper. Results are given in table 9.8, and images are shown in color plate 18a. Table 9.8 shows the differences between images rendered using various number of slices. This are rendering from a volume visualization done using various numbers of slices. Root mean squared error method (RMSE) is given for each component and for luminance image. The results for Gaddipati's metric are given only graphically in [GaMY97], and therefore they are not so precise.
green
blue
Y
method 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 RMSE
red 4.162 2.320 1.688 1.276 1.051 0.869 0.770 0.710 0.648
1.492 0.938 0.551 0.429 0.327 0.289 0.236 0.218 0.194
4.815 2.655 1.191 1.564 1.282 1.095 0.883 1.027 0.809
0.665 0.386 0.262 0.202 0.163 0.137 0.114 0.111 0.092 Rushm. 16.763 1.108 0.534 0.399 0.206 0.104 0.093 0.060 0.070 Gaddi. 20.0 21.0 4.5 7.1 3.0 3.0 0.8 2.1 1.0 CID 1.490 0.636 0.428 0.346 0.279 0.243 0.211 0.290 0.225
Note the increasing difference at the end of the series which occurs by CID, Gaddipati's and Rushmeier's metric. This differences are not visible, but it is interesting that they occur in all three metrics.
Image series 2 in color plate 18b, shows images rendered using progressive radiosity. Numbers of rays shot is given under each image. We measured the CID, in order to estimate the sufficient number of rays. Results are given in table 9.9. Up to now we were always assuming the maximum displayable frequency is 60 cycles per degree. We have measured the differences in the third image series for increased viewing distances as well. The distance between the 500K rays and the 1M rays images was measured. Results are given in table 9.10. The results are valid for a 17 inch monitor, with 1280 pixels resolution. If it is known that the image will be displayed on such a monitor, and it will be observed from a distance of 3 meters, it is sufficient to render the image using only 500K rays. This information can save us a lot of rendering time.
| viewing distance [cm] | CID |
| 50 | 1.345 |
| 100 | 1.268 |
| 150 | 1.184 |
| 200 | 1.129 |
| 300 | 1.020 |
| 400 | 0.935 |
| 500 | 0.861 |
| 1000 | 0.630 |
We have measured the distance between the 50K and the 100K image using 950000 rectangles. Results are shown in table 9.11. It is clear that the difference converge, and 5000 or 10000 rectangles are sufficient in almost all cases.
| number of rectangles | CID |
| 500 | 3.375642 |
| 1000 | 3.421180 |
| 2000 | 3.440896 |
| 5000 | 3.412503 |
| 10000 | 3.409281 |
| 20000 | 3.422541 |
| 40000 | 3.419777 |
| 80000 | 3.415657 |
| 160000 | 3.417164 |
| 320000 | 3.417722 |
| 640000 | 3.417656 |
| 900000 | 3.417328 |
| 910000 | 3.417486 |
| 920000 | 3.417535 |
| 930000 | 3.417455 |
| 940000 | 3.417468 |
| 950000 | 3.417440 |
The next example is shown in color plate 19a. This color plate shows an image series rendered using ray tracing and various numbers of samples per pixel. We have measured the difference between the 40, 80 and 160 samples per pixel images. Results are given in table 9.12. These results show us that the 40 and the 160 samples per pixel images can not be distinguished from a distance of 200 cm. Note that the rendering time was 4 times longer for 160 samples per pixel image.
| viewing dist. | 40-160 | 80-160 |
| 50cm | 1.878 | 1.476 |
| 100cm | 1.409 | 1.112 |
| 200cm | 0.789 | 0.597 |
| 400cm | 0.380 | 0.276 |
The final example is illustrated in color plate 20. Color plate 20a
shows original flower image, and color plate 20b original crow
image. We have applied 
blurring filter on the flower image
(20c), and we have added some color patches to the original flower
image (20d). There is also an image which has the same luminance, but
colors are quite different (20e). Note that Rushmeier's metric would
report no difference for this two images. There is also a combination
of the blurred flower image and the crow image shown in color plate
20f. Resulting differences are given in table
9.13. All CID differences are computed assuming the maximum
displayable frequency is 60 cycles/degree, and using 5000
rectangles. Note that the often used root mean square error method
reports a lower difference between the flower image with some color
patches added (20d) and the original flower image (20a), than between
the blurred (20c) and the original image (20a). A human observer would
always report a different result.
b c d e f
crow blur 3x3 corrupted constant Y combination b+c CID CID CID CID CID
a 52.547 3.771 5.098 25.732 30.582
RMSE RMSE RMSE RMSE RMSE
38.948 9.549 5.285 0 28.562 CID CID CID CID CID
b 0 51.595 54.732 50.143 23.489
RMSE RMSE RMSE RMSE RMSE
0 36.930 38.986 38.949 25.770 CID CID CID CID CID
c 0 7.759 27.275 28.110
RMSE RMSE RMSE RMSE RMSE
0 10.584 9.549 26.452 CID CID CID CID CID
d 0 28.406 29.599
RMSE RMSE RMSE RMSE RMSE
0 13.097 26.284 CID CID CID CID CID
e 0 30.579
RMSE RMSE RMSE RMSE RMSE
0 28.725
Color Plate 18
Color Plate 19
Color Plate 20
