Tone Mapping Techniques

We will start with fictitious unit methods, as most rendering packages are still not able to render raw images in absolute units. Test image 1 was rendered using the RADIANCE package [Ward94a], without taking its advantage of absolute units rendering.

Test scene 1 is a simple, back lit scene consisting of few objects. Strong back light (window in our case) causes problems for most tone mapping techniques. Color plate 1a shows the image obtained by the mean value mapping technique. Since the average value is high, the whole image is too dark. The exponential mapping technique (Color plate 1b) produces a little bit brighter image, since the average is mapped to 0.632, and not to 0.5 as by the mean value mapping method. Schlick's mapping technique tries to display the exterior and the interior part of the scene simultaneously. Although, this is the only mapping that displays exterior automatically, we find the final result still a little bit too dark. The factor M in the computation of parameter p (see eq. 5.1, 5.2) was set to 2, in Color plate 1c. Note that this is the best case, and increasing M (which is often needed for various media) would cause an increase of parameter p.

The minimum information loss methods were tested using the same raw image. Color plate 1d illustrates the minimum information loss technique. We have added an error function of type c (see Error Function section). Color plate 1e shows that there is no visible difference. Applying the minimum area loss method does not show a significant difference, either (Color plate 1f). Actually, the differences between these three methods will rarely be significant. The interior of the scene is displayed with a lot of details. The results of interreflections can clearly be seen (color leak on the walls), and the overall impression corresponds, in a way, to a photo of the scene.

Test scene 1 has the mean value tex2html_wrap_inline5839

, and Schlick's parameter p=54.428318, assuming M=2 (see section Schlick's mapping). Note that the mean value mapping method will actually display all pixels in the range tex2html_wrap_inline5845

. Table 9.1 shows the data for the minimum loss methods. Starting and ending points of the intervals are shown in the table. Error function was of type c, with tex2html_wrap_inline5847

and d=1/3 of the clipping interval.

method a b contrast loss

min. info loss 0.017948 0.897421 50 17.604%

with error fun. 0,020447 1.022327 50 18.867%

min. area loss 0.017998 0.899913 50 18.839%

Table 9.1: Scene 1 minimum loss data

**Table 9.1:** Scene 1 minimum loss data
method	a	b	contrast	loss
min. info loss	0.017948	0.897421	50	17.604%
with error fun.	0,020447	1.022327	50	18.867%
min. area loss	0.017998	0.899913	50	18.839%

Color plate 2 illustrates the interactive calibration. All images have contrast c=50, and aperture values are -3, -1.5, 0, and 3. This mapping technique gives us the possibility to examine particular parts of the image. For example, the reflection of the red sphere in the window can be seen when the aperture is set to 3. On the other hand, interesting interreflection details can be examined if the aperture is shifted to -3 or to even more negative values.

The next scene is mapped using only the interactive calibration. The logarithmic histogram of this scene is shown in the interactive calibration section (fig. 4.1). Color plate 4 shows this scene mapped using contrast 5 and 105, and aperture 0. This is a very low overall contrast image, so mapping using contrast 5 did not cause significant information loss. Note that the image mapped using a small contrast window has much higher contrast, than the image generated with a large clipping contrast.

Scene 3 is a more complex scene rendered using the RADIANCE software. Color plates 5a, 5b and 6a show the third scene mapped using the mean value, exponential and Schlick's mapping technique. Note that the mean value and the exponential mapping methods do not display any details under the table. On the other hand Schlick's method shows details under the table, but the overall impression is very poor. The reason lies in the very high overall contrast of the raw image. This raw image has the mean value tex2html_wrap_inline5853

and Schlick's parameter p=9719.833, assuming M=2, which is the best case. The lost information by the minimum information loss methods here is very large for a contrast of 50. Table 9.2 shows the data for this scene. The error function was chosen the same as earlier. As the loss for contrast 50 was too large, we increased the contrast, so long as the loss was under 10%, and the new contrast was c=2300. Of course, it would be incorrect to linearly map such a large clipping interval, and Schlick's mapping was applied on this clipping interval. Results of the minimum loss techniques are shown in Color plates 6b, 7a, 7b, 8c, and 8d. Due to very similar mapping intervals of the minimum information loss and the mean value mapping, these images will look almost the same in this case.

method a b contrast loss

min. info loss 0.040442 2.022103 50 28.329%

with error fun. 0,041810 2.090512 50 30.134

+Schlick's mapp. 0.002300 5.290552 2300 9.065%

min. area loss 0.045311 2.265544 50 38.811%

Table 9.2: Scene 3 minimum loss data

**Table 9.2:** Scene 3 minimum loss data
method	a	b	contrast	loss
min. info loss	0.040442	2.022103	50	28.329%
with error fun.	0,041810	2.090512	50	30.134
+Schlick's mapp.	0.002300	5.290552	2300	9.065%
min. area loss	0.045311	2.265544	50	38.811%

All so far shown images illustrate how various final images can be generated from the same raw image. Note that this type of image manipulation is not possible without the raw image. Once the mapping is done, pixel values are discretised in the range tex2html_wrap_inline5861

, and every brightening or darkening of the image will cause a large information loss.

Up to now we have not mentioned incident light metering. As stated before, incident light metering was designed in order to reproduce original objects' colors. It will be illustrated using 3 scenes. Comparisons with mean value, Schlick's, Ward's and Tumblin and Rushmeier's (TR) mapping techniques will be made. In order to apply Ward's and TR mapping methods, we have used default values suggested by the RADIANCE rendering package. Note that TR images are a little bit darker, but the settings were the same as for Ward's mapping technique. Increasing the light sources' strength drastically, would brighten TR images, but we wanted to examine the difference between dark and bright scenes here, and the relative difference would remain the same even for extremely strong light sources.

The idea of color reproduction is illustrated in color plates 9 and 10. Two simple scenes were rendered using no interreflection. The only difference between the two scenes is the color of the room. In the first case (left) the walls are almost white and in the second (right) the walls are dark gray. The cubes' colors are the same and the light settings are equal as well. The color bar under each image shows the originally selected cubes' and walls' colors. Color plates 10c, 10d and 10e show results of the new incident light mapping. It can be seen that all colors are reproduced faithfully.

Due to the different average, mean mapping produces different colors for the two scenes (although the cubes have the same colors and the light settings are the same). Ward's mapping fails to reproduce the colors as well as the TR-mapping. Note that all these three alternative mapping techniques are based on the average scene luminance, and therefore the colors can not be reproduced faithfully for both cases as the average values are different for these two scenes. The mapping method proposed by Schlick [Schl94] produces acceptable images for the first two cases. Schlick's mapping depends on a parameter p, which depends on the total raw image contrast. As the contrasts of the two scenes are similar, the parameter p does not differ much. But if the orange box in the bright scene is substituted by a black box the overall contrast is drastically increased and Schlick's method fails. The new, incident light metering method reproduces original colors correctly in all cases. Note that it would be possible to manually calibrate Schlick's parameter p, but then the method would not be automatic any more. There is the possibility to manually adjust the exposure in the RADIANCE package as well, but again this is no automatic method. Table 9.3 gives data for this scene. The mean values differ a lot. The parameter p required for Schlick's mapping is almost the same for the first two settings, but increases for the third. Data for the median value of radiances are also given in the table. Note that these values do not differ much from the mean values. We have used mean mapping for comparison throughout this paper since this is the most widely used method. Using the median value of radiances would not affect the final results significantly.

dark bright black

room room cube

mean radiance 0.002511 0.01341 0.01339

median radiance 0.001796 0.01432 0.01429

median irradiance 0.009160 0.009160 0.009160

parameter p 1.415 1.267 17.652

Table 9.3: Data for the cubes scene.

**Table 9.3:** Data for the cubes scene.
	dark	bright	black
	room	room	cube
mean radiance	0.002511	0.01341	0.01339
median radiance	0.001796	0.01432	0.01429
median irradiance	0.009160	0.009160	0.009160
parameter p	1.415	1.267	17.652

The next scene (color plates 11, 12 and 13) is also rendered without interreflections. Again, two different object color settings were used, one with bright colors, the other with dark colors. Almost all objects are differently defined in the two settings, only the Christmas balls are equal. On the other hand the light definition is the same for both settings. The color bar displays a selection of three of these colors: box lid, chair and wall.

The results of the new mapping are shown in color plates 12a (scene with bright surfaces) and 12b (scene with dark surfaces). Color plate 11a shows the dark scene using the mean value mapping. The bright scene mapped with the mean value approach looks almost the same, so it is not displayed. Color plate 11b shows the irradiance image of scene 2 (all objects are diffuse, medium gray).

Color plate 13 shows the same images generated using Ward's and the TR-mapping. It is obvious that these mappings cancel out the differences which should be visible. Data for this scene is given in tables 9.4 and 9.5.

settings bright dark

images 12a, 13a, 13c 11a, 12b, 13b, 13d

mean value 0.9842 0.2533

tex2html_wrap_inline5865 0.7401 0.7401

Table 9.4: Data for the fifth scene (without interreflection)

**Table 9.4:** Data for the fifth scene (without interreflection)
settings	bright	dark
images	12a, 13a, 13c	11a, 12b, 13b, 13d
mean value	0.9842	0.2533
	0.7401	0.7401

box lid chair wall

bright 0.9 0.2 0.2 0.5 0.1 0.1 0.8 0.8 0.8

dark 0.18 0.04 0.04 0.1 0.02 0.02 0.08 0.08 0.08

Table 9.5: RGB values for color bar 5

**Table 9.5:** RGB values for color bar 5
	box lid	chair	wall
bright	0.9 0.2 0.2	0.5 0.1 0.1	0.8 0.8 0.8
dark	0.18 0.04 0.04	0.1 0.02 0.02	0.08 0.08 0.08

Finally, the sixth scene (color plates 14, 15, 16, and 17) is rendered with interreflections. Tables 9.6 and 9.7 show the data for this scene. Color plates 15a and 15b are irradiance images that display the irradiance distribution in the scene. The intensity was extracted from the r,g,b irradiances using the max(r,g,b) principle (see Incident Light Metering chapter). Note the differences in the irradiance distribution for dark (color plate 15b) and bright (color plate 15a) scenes due to interreflections (shadows are much brighter in the bright irradiance image). The reference color bar in plate 16 shows selected colors for the sofa and the wall in the bright and dark scene. All other objects change too, except for the tree which remains unchanged. The results of the new mapping technique are displayed in color plates 16a and 16b.

Mean value mapping was used to map images in color plates 14a and 14b. Again, the mean value method fails to reproduce the originally set colors. Color plate 17 show the same scene mapped using Ward's and TR-mapping. Note how the tree becomes significantly brighter with almost all methods, only the newly proposed algorithm leaves the tree unchanged (that it looks a little bit lighter is a perceptual sensation caused by the darker background).

settings bright dark

images 14a, 15a, 16a, 17a, 17c 14b, 15b, 16b, 17b, 17d

mean value 0.01816 0.04813

tex2html_wrap_inline5865 0.04282 0.03183

Table 9.6: Data for the sixth scene (with interreflections).

**Table 9.6:** Data for the sixth scene (with interreflections).
settings	bright	dark
images	14a, 15a, 16a, 17a, 17c	14b, 15b, 16b, 17b, 17d
mean value	0.01816	0.04813
	0.04282	0.03183

wall sofa

bright 0.3 0.8 0.8 0.87 0.5 0.25

dark 0.1 0.3 0.3 0.18 0.1 0.05

Table 9.7: RGB values for color bar 6

**Table 9.7:** RGB values for color bar 6
	wall	sofa
bright	0.3 0.8 0.8	0.87 0.5 0.25
dark	0.1 0.3 0.3	0.18 0.1 0.05

Note that the TR-mapping is intended to be used for a different purpose. Scenes with various light settings would be displayed different. Images look a little bit too dark as the method functions in a huge range of luminances (the method works fine up to a luminance level of tex2html_wrap_inline5869

and just for comparison a snow covered ground in full sunlight emits tex2html_wrap_inline5871

according to [Glas95]). Note that light settings are not extremely low in our settings, and Ward's images were mapped using the same light levels and the same software. When using stronger light sources the TR-mapping will produce brighter images for both scenes, but again corresponding objects will appear similar although their color definition is very different.

The tone mapping techniques results end here. It can easily be seen from the above examples that there is no mapping technique that can be recommended for general use, but usually there is at least one technique that gives satisfactory results for each purpose.