# Adaptive Logarithmic Mapping For Displaying High Contrast Scenes

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4 Figure 4: The Stanford MEMORIAL Church processed with different bias parameters: b =.65, b =.75, b =.85, and b =.95 (from left to right). The scene dynamic range is 343,:. Radiance map courtesy of Paul Debevec b =. b =.95 b =.85 b =.75 b =.5 b =.25 b =. Figure 3: The bias power function for different value of the parameter b (refer to Equation (3)). In our application, useful value for b falls into the range.5.. by b (refer to Equation (3)). L d = L dmax. log (L wmax + ) log(l w + ) ( ( ) ) ( ) log(b) log 2 + Lw log(.5) L wmax 8 (4) L dmax is used as a scalefactor to adapt the output to its intended display. In the denominator decimal logarithm is used since the maximum luminance value in the scene is always re-sampled to decimal logarithm by the bias function. We use a value for L dmax = cd/m 2, a common reference value for CRT displays. The bias parameter b is essential to adjust compression of high values and visibility of details in dark areas. The result of different values for parameter b are visible in Figures 4 and 6. The graph in Figure 5 shows the curves of the mapping function for a scene with maximum luminance of 23 cd/m 2. scene illuminant characteristic is not accurately known in most cases, we assume a D 65 white point, to further convert tristimulus values between Rec.79 RGB and CIE XYZ. The XYZ luminance component Y of each pixel (L w for world luminance) and the maximum luminance of the scene L wmax are divided by the world adaptation luminance L wa and eventually multiplied by an exposure factor set by the user. The tone mapping function presented in Equation (4) is used to compute a displaying value L d for each pixel. This function is derived by inserting Equation (3) into the denominator of Equation (2). Equation (4) requires luminance values L w and L wmax (scaled by L wa and the optional exposure factor) which characterize the scene as well as L dmax which is the maximum luminance capability of the displaying medium. The parameter of the bias function is denoted Display Luminance logmap(bias(.)) logmap(bias(.9)) logmap(bias(.8)) logmap(bias(.7)) logmap(bias(.6)) logmap(bias(.5)) World Luminance Figure 5: Example plots of the tone mapping function (refer to Equation (4)) for L wmax = 23 cd/m 2. The maximum displayable value (white) is. For bias parameters smaller than b =.7 clamping to L dmax will occur.

5 Values for b between.7 and.9 are most useful to generate perceptually good images, but ideally a unique fixed parameter working for most situations is needed. In an informal evaluation, we asked five persons to interactively choose from six different scenes, among four images tone mapped with different bias parameters (Figure 4 was a part of the survey) the ones they felt looked the most realistic and the most pleasing. In terms of preference a bias parameter around.85 was consistently proposed. Results for realism were scattered for different images but consistent for each subject. Averaging preferences and realism from this simple evaluation, we propose a default bias parameter b =.85. This indeed produces consistent, well balanced images with any kind of scenes. A side effect of changing the bias parame- gamma function. At the origin s vicinity, the gamma function exhibits a very steep slope. Even though we use floating point precision, after correction and quantization to 24 bit, originally dark pixels will all be transformed to medium values. This results in significant contrast and detail loss in shadowed areas. Ward s Histogram Adjustment method 7 ensures that all displayable values are represented in the final image. However, other tone mapping methods potentially suffer from this phenomenon and the contrast of their resulting images might be improved by considering this problem. Gamma functions with better perceptual accuracy have been Figure 6: Closeup of a light source of the ATRIUM scene at Aizu University (refer to Figure 8 for the full view of this scene in daylight conditions). This figure illustrates how high luminance values are clamped to the maximum displayable value. The images were computed using the following bias parameter values: b =.5, b =.7, and b =.9 (from left to right). The scene dynamic range is,75,37:. ter is some brightness fluctuation of the output image. The image brightness is approximately doubled for b =.85 and tripled for b =.7 in respect to images for b =.. This affects the realism of images even though the increase of contrast due to the bias value reduction naturally leads to brighter images. We introduce here a scalefactor to world adaptation luminance, aiming at keeping a constant brightness impression. Again the adaptation is based on a default bias parameter equal to.85: L wa = L wa /( + b.85) 5 Figures 4 and 6 benefited from this scalefactor, the global brightness impression is almost constant, even though the contrast among images is very different. 4. Gamma Correction Gamma correction must be applied to the tone mapped data to compensate for the non-linearity of displaying devices. It is common to use a gamma coefficient γ = 2.2 for noncorrected displays, the gamma correction function is L d = Lw /γ. In our pipeline, this correction is applied to linear RGB tristimulus values after tone mapping and conversion from CIE XYZ. We would like to address a potential problem of the gamma = 2 ITU linear Figure 7: Comparison of the gamma power function usually used in computer graphics with the ITU-R BT.79 transfer function. The essential difference is the less drastic mapping of dark pixels in the ITU-R BT.79 function. proposed, for example the srgb color space includes a specific transformation. The international standard recommendation is the ITU-R BT.79 transfer function ; it describes the transformation done by a video camera to produce the best possible images on a calibrated display. This function is close to γ = 2, but assumes a γ =.25 correction of the display to compensate for the viewing environment. The principal differences between the gamma power function and the ITU-R BT.79 transfer function (refer to Figure 7) are smaller output values for dark pixels in the latter case. This results in better contrast and details in dark areas and potential attenuation of the noise often found in dark parts of photographs. In its original form, the ITU-R BT.79 gamma correction is: { E 4.5L L.8 =.99L L >.8 where L is the linear value of each RGB tristimulus and E the nonlinear pixel value to be displayed. The ITU-R BT.79 transfer function has fixed parameters. This lacks convenience for computer graphics applications, where different transfer values might be needed depending on the lighting conditions surrounding the display, custom user settings, and operating system. We adapted the function to use familiar γ values and we use a simple fit of the linear segment at the origin. Our transfer function based on the

7 Resolution Software Hardware fps TM fps TM Table 2: Statistics for software and hardware implementations of our tone mapping operator. Values denote the average number of frames per second and the overhead in milliseconds introduced by tone mapping. bases depending on scene content. The log 2 function is used in darkest areas to ensure good contrast and visibility, while the log function is used for the highest luminance values to reinforce the contrast compression. In-between, luminance is remapped using logarithmic values based on the shape of a chosen bias function. This scheme enables fast nonlinear tone mapping without objectionable image artifacts. Although our technique is fully automatic, the user can interactively choose varying image details versus contrast by effectively changing the shape of the bias curve using an intuitive parameter. Because of the computation performance our tone mapping can be used for playing HDR video sequences while providing the user unprecedented control over the video brightness, contrast compression, and detail reproduction. As future work we intend to perform perceptual experiments to determine an automatic bias value as a function of the scene content and its dynamic range of luminance. Our approach might be further extended by using different functions to interpolate between logarithmic bases. Also, the HVS models of temporal adaptation could be incorporated to our tone mapping algorithm to make the displaying of video sequences more realistic. Acknowledgements We would like to thank Paul Bourke for permitting us to use his OpenGL based stereo animation viewing software as a framework for our HDR movie player. Also, we would like to thank Paul Debevec, Greg Ward, Raanan Fattal, Jack Tumblin, and Gregory Downing for making their HDR images and animations available. We thank Grzegorz Krawczyk for help in measuring timings for the GPU version of our HDR video player. This work was supported partly by Telecommunications Advancement Organization of Japan within the framework of A Support System for Region-specific R&D Activities and by the European Community within the scope of the RealReflect project IST Realtime visualization of complex reflectance behavior in virtual prototyping. References. J. Blinn. Dirty Pixels. IEEE Computer Graphics & Applications, 9(4): 5, P.E. Debevec and J. Malik. Recovering High Dynamic Range Radiance Maps from Photographs. Proceedings of ACM SIGGRAPH 97, ACM, , P.E. Debevec. Rendering Synthetic Objects Into Real Scenes: Bridging Traditional and Image-Based Graphics With Global Illumination and High Dynamic Range Photography. Proceedings of ACM SIGGRAPH 98, ACM, 89 98, K. Devlin, A. Chalmers, A. Wilkie, and W. Purgathofer. Tone Reproduction and Physically Based Spectral Rendering. Eurographics 22: State of the Art Reports, Eurographics, 23, Industrial Light & Magic, OpenEXR, High Dynamic Range Image File Format. Lucas Digital Ltd, G.W. Larson. LogLuv Encoding for Full-Gamut, High- Dynamic Range Images. Journal of Graphics Tools. A K Peters Ltd., 3():85 83, G.W. Larson, H.E. Rushmeier, and C. Piatko. A Visibility Matching Tone Reproduction Operator for High Dynamic Range Scenes. IEEE Transactions on Visualization and Computer Graphics, 3(4):29 36, , 5 8. N.J. Miller, P.Y. Ngai, and D.D. Miller. The Application of Computer Graphics in Lighting Design. Journal of the Illuminating Engineering Society, 4():6 26, K. Perlin and E.M. Hoffert. Hypertexture. Computer Graphics (Proceedings of ACM SIGGRAPH 89), ACM, 23, , C.A. Poynton. A Technical Introduction to Digital Video. John Wiley & Sons, 996. Recommendation ITU-R BT.79-4, Parameter Values for the HDTV Standards for Production and International Programme Exchange, ITU, E. Reinhard, M. Stark, P. Shirley, and J. Ferwerda. Photographic Tone Reproduction for Digital Images, ACM Transactions on Graphics, 2(3): , A. Scheel, M. Stamminger, and H-P. Seidel. Tone Reproduction for Interactive Walkthroughs. Computer Graphics Forum, 9(3):3 32, C. Schlick. Quantization Techniques for the Visualization of High Dynamic Range Pictures. Photorealistic Rendering Techniques, Springer-Verlag, 7 2, T.G. Stockham. Image Processing in the Context of a Visual Model, Proceedings of the IEEE, 6: J. Tumblin and H.E. Rushmeier. Tone Reproduction for Realistic Images. IEEE Computer Graphics and Applications, 3(6):42 48, 993., 2, 3

8 7. J. Tumblin, J.K. Hodgins, and B.K. Guenter. Two Methods for Display of High Contrast Images. ACM Transactions on Graphics, 8():56 94, W.A. Wagenaar. Stevens vs. Fechner: a Plea for Dismisal the Case. Acta Psychologica, Amst, 39, , G. Ward. Real Pixels. Graphics Gems II. Academic Press, 8 83, 99., 6 2. G. Ward. A Contrast-Based Scalefactor for Luminance Display. Graphics Gems IV. Academic Press, 45 42, 994., 2

9 Figure 8: A selection of high dynamic range images processed with our tone mapping function. Table shows some statistics concerning the tone mapping computation for these images. On the right side, some frames captured from our HDR movie player showing Paul Debevec s Rendering with natural light animation.

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