Rendering Hair with Back-lighting 1

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1 Rendering Hair with Back-lighting 1 Tzong-Jer Yang, Ming Ouhyoung Communications & Multimedia Laboratory, Dept. of Computer Science and Information Engineering, National Taiwan University, Taiwan, ROC Abstract This paper presents a technique to reproduce human hair s luster with back-lighting, which is most noticeable for light-colored hair. This technique uses an auxiliary buffer, called a density map, to calculate the intensity of light passing through overlapped hairs. The density map for each light source is created by extracting the color values from the frame buffer after models are rendered from the light source s point of view with pixel blending. This technique can be applied to existing hair rendering pipelines with less than 20 percent computational overhead. 1. Introduction Traditionally hair rendering is one of the most challenging issues in computer graphics. The challenge comes mainly from large number of individual hairs. To render human hair realistically, several researchers have published different approaches, and have obtained acceptable results. However, human hair s shining under back-lighting conditions did not receive much attention. In fact, a back-lighting effect adds a crucial bit of realism to hair rendering, because it is quite common in natural scenes and makes a strong impression to people. Without a technique to simulate the back-lighting effect, animators will need to avoid putting an actor against light sources, which severely limits their artistic set up. This paper presents a technique that can simulate the back-lighting effect through the use of an auxiliary buffer, called a density map. The density map utilizes pixel blending that is now widely available on graphics hardware or libraries. Rather than recording the degrees of shadowing for shadow buffers, we record the degrees of translucency of overlapped hairs for density maps. In conjunction with shadow buffers, the density maps can help to calculate the intensity of back light piercing through a strand of hair more realistically. We will use the density map to represent human hair s back-lighting effect, especially for the light-colored hair, and show how it can be integrated into an existing hair rendering pipeline efficiently. 2. Previous researches In 1989, Kajiya and Kay proposed a rendering primitive, a texel, to deal with fine detailed scenes, and presented an impressive result for a teddy bear [1]. The texel works well on furry objects, but there is no clear method on how to apply it to long hairs. However, the anisotropic lighting model derived for hair is useful, and is continuously adopted by succeeding researchers and commercial products [2][3][4][7]. In Kajia s lighting model, the diffuse component is obtained by integrating a Lambert surface along a half cylinder, and the specular component is calculated from an ad hoc Phong specular model. A comprehensive hair rendering pipeline was proposed by LeBlanc and Daldegan et al. [3][4]. The hair rendering pipeline is based on pixel blending and shadow buffers, and provides a practical method to render anti-aliased hair with shadows for animation purposes. Anjyo et al. proposed another lighting model for fast rendering, however it is also rather restrictive [5]. The diffuse reflection component is neglected, and the specular reflection is obtained based on Blinn s specular model. Random numbers are introduced to distinguish hair strands. This model is relatively suitable for darkcolored hair that absorbs most of the diffuse component and shines with strong specular reflection [8]. During the same period, Watanabe and Suenaga tried to simulate hair s shining under back-lighting conditions 1 Web site:

2 [6]. They used a double Z-buffer mechanism to identify thin areas of hair, and assigned higher color intensities to pixels within these thin areas. The double Z-buffer mechanism makes use of two Z-buffers, and takes the difference between the two Z-buffers as the thickness. Figure 1 explains this double Z-buffer mechanism. Two Z-buffers are calculated first, where one is a front Z-buffer, and the other is a rear Z-buffer. Assume z i F and z i R are the depth values at position P on both the front and rear Z-buffers respectively, then the thickness of hair at position P equals z i F - z i R. This approach is straightforward, however it s not correct. z i F P thickness z i R a result, if we know that a pixel on the screen is overlapped with fewer hairs, we can assign it with a larger light intensity to reflect the back-lighting effect. To know hair thickness for each pixel, an intuitive idea is to record the number of hairs across a pixel during the rasterization stage of the rendering pipeline. We realize the idea using pixel blending. 3.1 Pixel blending In [10], Porter and Duff introduced an Alpha channel to composite images with anti-aliasing. A short description of this image composition methodology, or pixelblending, can refer to [3]. In summary, one can treat each pixel as a square box, and calculates the portions of objects inside the square box. The intensity of a pixel P n after blending in the nth objects is therefore determined by P = ( 1 A ) P 1 + A O, P0 = B (1) n n n n n Front Z-buffer Rear Z-buffer where A n is the fraction of pixel area covered by the nth object, O n is the color intensity of the nth object, and B is the color intensity of the background images. Figure 1. The double Z-buffer. The hair thickness at P is z i F - z i R. Consider the situations illustrated in Figure 2. The thickness of two distant hairs will be mistakenly larger than that of a cluster of hairs tied together. The result is not correct since the thickness of overlapped hairs is determined by the number of individual hairs, not by their distance. Consequently, the back-lighting effect will be visually inconsistent with human s perception. The pixel blending technique can be implemented by introducing an additional component for each pixel in the frame buffer. The additional component, or an alpha channel, is used to control how a new source pixel value is blended into an existing destination pixel. For a pixel, we can calculate the fraction of pixel area covered by an object, and assign the pixel s alpha channel with that fraction. The color of the pixel will be a blending of the object s color and the pixel s original color. Similarly, we may not need to calculate the fraction of covered pixel area actually, but assign it with a value explicitly. thicker thinner A good feature resulted from the pixel blending helps us to know hair thickness for each pixel. Examine equation (1) again. If one lets all A n equal A, and lets all O n equal O, one obtains Front Z-buffer (a) Rear Z-buffer Front Z-buffer (b) Rear Z-buffer Figure 2. Incorrect hair thickness calculated with the double Z-buffer mechanism. (a) Two hairs separated far away will be thicker than (b) a cluster of hairs tied together. 3. Back-lighting effects using density maps From daily observations, when human hair blocks a light source, the thinner parts of hair seem to shine. As P o = B P = ( 1 A ) P + AO = P + ( O P ) A P = ( 1 A ) P + AO = P + ( O P ) A n n 1 n 1 n 1 where 0 O, B, A 1, hence 0 P n 1 for all n. Furthermore, if one sets O to be 1, the largest value, then one will have P n P n-1 for all n since O P n for all n. The property of P n P n-1 for all n gives us a mechanism to know the thickness of hairs overlapped on a pixel. Figure 3 illustrates the condition of P n P n-1 for all n.

3 When more hairs intersect at a pixel, the intensity of the pixel gets larger. Consequently, we can use the intensity of a pixel as a ratio to compute the intensity of light passing through hairs. For example, if the intensity of a pixel is 0.8 and the intensity of light is 0.6, we can infer that the intensity of light reaching s is ( )*0.6 = If the intensity of the pixel changes to 0.2, the intensity of light reaching s will become ( )*0.6 = 0.48, which is exactly what we would expect when fewer hairs overlap, more light passes. more hairs intersect at this pixel more hairs intersect at this pixel be drawn with the largest intensity. While drawing the hair model, we enable pixel blending with a small alpha value, for example, 0.1. This can be done since the alpha value is set explicitly. The alpha value will cause the pixels occupied by the hair model to have intensities ranging from 0 to 1, which represents the degrees of translucency, and a higher intensity value corresponds to a lower translucency. A pixel s intensity may eventually reach 1.0 although there are still hairs to be overlapped on the pixel. This situation does not bother us since hair saturates after reaching a certain density, and overlapping more hairs on the pixel will completely obscure the background. The alpha value can also reflect hair s material. A higher alpha value will increase a pixel s intensity more rapidly, which means thicker hair or darker hair with a lower degree of translucency. The procedure of creating a density map for each light source is summarized in the following. a hair (a) a hair Figure 3. The intensity of a pixel becomes larger when more hairs intersect at the pixel. (a) A condition shows the distribution of hairs, while (b) shows the resulted intensities of pixels. The darker color means larger intensity. 3.2 Density map We now describe how we use pixel blending to create an auxiliary buffer, or a density map, for generating the back-lighting effect. We call it a density map because it contains density information for each pixel. The higher density for a pixel means more hairs intersecting at this pixel, and therefore attenuates more light. The density map for each light source is created by extracting the color values from the frame buffer after models are rendered from the light source s point of view. Assume that a color value ranges from 0 to 1, and the models are divided into two categories: a scene model and a hair model. First, we clear the frame buffer to be of the color value 0, which means that density values are all 0s for all pixels initially. Then both the scene model and the hair model are rendered with the color value 1, so we can have the property of P n P n-1 for all n if we control the alpha values to be the same for all pixels. (b) 1. Clear the frame buffer to be 0, the lowest intensity. This is usually done by setting color to be black for all pixels. 2. Disable lighting, and set the drawing color to be 1, the largest intensity. This is usually done by setting color to be white. 3. Take the scene model and project it using one light source. Render the scene model on the frame buffer with pixel blending disabled. 4. Take the hair model and project it using the same light source. Render the hair model on the same frame buffer with pixel blending enabled. The alpha value for pixel blending should be set to reflect hair s material attribute. 5. Extract the resulting frame buffer as the density map for the light source. 6. Extract the resulting depth buffer as the shadow buffer for the light source. 7. Repeat step 1 to step 6 for each light source. Therefore, we have one density map and one shadow buffer for each light source. 4. Integrate the density map into an existing hair rendering pipeline In [3], LeBlanc et al. proposed a comprehensive hair rendering pipeline that can render anti-aliased hair with shadows. The density map can be integrated into the hair rendering pipeline efficiently to render hair with back-lighting. While drawing the scene model, we should disable pixel blending because the scene model is opaque, and the disabling of pixel blending will cause the scene model to

4 4.1 A lighting model for back-lighting To add the back-lighting effect using the density map, we have to modify the following lighting model first. The lighting model adopted in [3] is n [ θ φ θ π ] H = LA K A+ S i Li K D sin( ) + K s cos ( + ) light overlapped hairs refracted reflected absorbed light overlapped hairs refracted light back-lighting viewing angle where H is the resulting hair intensity, L A is the ambient light intensity received, K A is the ambient reflectance coefficient, S i is the amount that ith light should be attenuated by shadowing, L i is the light intensity received, K D is the diffuse reflectance coefficient, K S is the specular reflectance coefficient. The angles φ and θ are defined as in Figure 4, where θ is the angle from the tangent vector of the hair strand to the light vector, and φ is the angle from the tangent vector of the hair strand to the vector. A detailed explanation can be found in [1][3]. ω e φ Figure 4. Hair lighting geometry, where l points to a light source, e points to s, r is the reflection of l, and t is the tangent vector of the hair strand. Our modified lighting model that adds the back-lighting effect is presented as t θ n [ sin( θ ) cos ( φ θ π )] H = L K + S L K + K + + A A i i D s ( 1 D ) L f ( ω ) i i o 1 if ω back-lighting viewing angle (160 in our case) f ( ω ) = 0 otherwise where (1-D i ) represents the fraction of the ith light intensity received by s. The value of D i is obtained from the density map. The ad hoc function f(ω) indicates that the back-lighting effect only happens when the s are against the light source, as shown in Figure 5. Where ω is the angle from the light vector to the vector, as shown in Figure 4. l r f(ω) = 1 the effective area of back-lighting Figure 5. A back-lighting effect takes place when the s are against the light source. The ad hoc function f(ω) is introduced to specify the effective area of back-lighting. In fact, the modified lighting model can be explained as H = the ambient light intensity + the intensity of reflected light + the intensity of refracted light. Although we simulate the refraction of light with an empirical model, the result is consistent with our visual perception. 4.2 Hair rendering pipeline with the back-lighting effect We now describe the modified hair rendering pipeline in the following. 1. Generate density maps and shadow buffers for all light sources. The procedure is described in Section Render the scene model with density maps and shadow buffers. 3. Take the hair model, and project all hair segments onto the viewing coordinate system. Sort all hair segments by their average depth. 4. Scan the hair segments in reverse depth order. For each segment, a. Determine the intensity H of each of the segment s endpoints, using the modified lighting model. b. Determine the fraction of pixel coverage for the line segment based on the width of hair and viewing projection. Set this as the line segment s alpha value. Note that the alpha value is unrelated to the one used in creating depth maps. c. Draw line segment as an alpha-blended line into the frame buffer, using linear color interpolation between the intensities of the endpoints.

5 (a) (b) (c) (d) (e) (f) Picture 1. (a) Rendered without back lighting. (b) Rendered with back lighting (alpha=0.1). (c) Rendered with back lighting (alpha=0.05). (d) The white line points to the light source; the black line points to the s. (e) The density map of (b). (f) The density map of (f). 5. Results We implemented the modified hair rendering pipeline on a Silicon Graphics Indigo 2 Extreme. This hardware model supports Z-buffer hidden surface removal, alpha blending and linear color interpolation. The hair models used are generated from a 3D hairstyle fitting system [9] and several in-house tools. Furthermore, the rendering resolution is 1024x768 with a 24-bit true color visual. 5.1 Effect of density map source is arranged against the s, which simulates a back-lighting environment, as shown in Picture 1(d). Picture 1(a) and 1(b) are resulted images without and with back-lighting calculation, respectively. Note that the shinning hairs in Picture 1(b) resulted from the back light. The alpha value used to create a density map represents hair s thickness. Picture 1(c) is an extreme case that sets the alpha value to 0.05, much thinner hair, while Picture 1(b) sets the alpha value to 0.1. The corresponding density maps for both Picture 1(b) and 1(c) are shown in Picture 1(e) and 1(f), respectively. Our first example, Picture 1, shows a simple hair model for illustrating the effect of density map only. One light

6 (a) (b) Picture 2. (a) The 3 white lines point to 3 light sources; the black line points to the s. (b) The density maps created from the 3 light sources. Without back-lighting With backlighting Computing buffers Light 1 Light 2 Light 3 Reading Computing Reading Computing buffers buffers buffers buffers Reading buffers Rasterization Total Table 1. The rendering time (in second) of a complex hair model shown in Picture 3 rendered with and without back-lighting. The total time includes some other computations that are not listed here. 5.2 Performance A hair model with a more complex hairstyle is rendered in Picture 3, and the configuration is shown in Picture 2(a). Again, we rendered the hair model without and with back-lighting effect, as presented in Picture 3 (left) and Picture 3 (right), respectively. Picture 2(b) shows the density maps created for Picture 3 (right). The hair model contains 18,700 hairs with a total of 490,700 line segments, and the rendering time is shown in Table 1. The computation of density maps takes an additional 18% of rendering time. 6. Conclusion be reproduced by introducing an auxiliary density map. The creation of the auxiliary density map takes a little more time since we can create it during the calculation of shadow buffers and the underlying technique, pixel blending, is widely supported by hardware. This solution is not necessary to be physically accurate, but coincide with human s visual perception. To simulate a natural realistic hair, modeling is a more important issue. During our experiments about the backlighting effect, we found that if a hair model appeared unnatural, the resulting luster of hair was also not satisfactory, even if we applied the back-lighting effect. Therefore, we spent a lot of time in improving hair models before rendering. We have demonstrated how the back lighting effect can

7 7. Acknowledgments We are grateful to Jasmine Yung-Huei Yan for her assistance in the modeling of hair. 8. References [1] James T. Kajiya, and Timothy L. Kay, Rendering Fur with Three Dimensional Textures, ACM Computer Graphics, 23(3), Boston, July 1989, pp [2] Robert E. Rosenblum, Wayne E. Carlson, and Edwin Tripp III, Simulating the Structure and Dynamics of Human hair: Modelling, Rendering and Animation, The Journal of Visualization and Computer Animation, 2, 1991, pp [3] Andre M. LeBlanc, Russell Turner, and Daniel Thalmann, Rendering Hair using Pixel Blending and Shadow Buffers, The Journal of Visualization and Computer Animation, 2, 1991, pp [4] Agnes Daldegan, Nedia Magnenat Thalmann, Tsuneya Kurihara, and Daniel Thalmann, An Integrated System for Modelling, Animating and Rendering Hair, EUROGRAPHICS, 12(3), 1993, pp. C-211-C-221. [5] Ken-ichi Anjyo, Yoshiaki Usami, and Tsuneya Kurihara, A Simple Method for Extracting the Natural Beauty of Hair, Computer Graphics, 26(2), Chicago, July 1992, pp [6] Yasuhiko Watanabe and Yasuhito Suenaga, A Trigonal Prism-Based Method for Hair Image Generation, IEEE Computer Graphics & Applications, January 1992, pp [7] Barbara Robertson, Hair-Raising Effects, Computer Graphics World, Oct [8] Clarence R. Robbins, Chemical and Physical Behavior of Human Hair, Van Nostrand Reinhold Co., [9] C. L. Liang, A 3D Hairstyle Fitting System for Hair Modeling, Rendering, and Facial Texture Mapping, Master thesis, Dept. of CSIE, National Taiwan University, Taiwan, [10] Thomas Porter, and Tom Duff, Compositing Digital Images, ACM Computer Graphics, 18(3), July 1984, pp