                ‡

Bunyo Okumura Takashi Machida †Naokazu Yokoya ‡Graduate School of Information Science, Nara Institute of Science and Technology† Cybermedia Center, Osaka University  

Various techniques are used for rendering virtual objects in a virtualized real scene under arbitrary illumination conditions. Especially, an environment mapping [Blinn and Newell 1976] has beendeveloped to render glossy objects in real time. However, this technique can only render an object consisting of smooth surfaces suchas a mirror. To overcome this problem, various improvements havebeen performed to an environment mapping [Cabral et al. 1999;
Kautz et al. 2000]. However, these methods can support only uniform surface reflectance properties. So, it is difficult to render surfaces with non-uniform reflectance properties in real time. In thispaper, we propose a real time rendering method for surfaces withnon-uniform reflectance properties. The proposed method is basedon computing a multi-scale environment map.

           In our method, a filtering of an omnidirectional real image is performed to create an environment map according to multiple roughness of surfaces in advance. This map is called a multi-scale environment map. We employ the Phong model to calculate reflections, and we apply an approximation to the Phong model. The
multi-scale environment map is created as a 3-dimensional voxel
data. The distance from the center of the voxel data corresponds
to the surface roughness parameter. The more far from the center
the distance is, the more smooth the object surface is. The direction
corresponds to the reflection vector.
Here, the geometry and the reflection image of a rough surface
should be low resolution than those of a smooth surface. Therefore, we employ a pyramidal image data structure and multi-scale
geodesic domes to reduce computation (See Figure 1). Moreover,the filter processing is performed only on pixels within omnidirectional images which significantly influence rendering results. Calculations are also accelerated by using a table which holds weightsof the filter.
Finally, reflections in surfaces are rendered in real time using
the multi-scale environment map as a texture. The texture coordinates t are determined as t  r  n, where r and n are a reflection
vector against a viewing vector and a surface roughness parameter, respectively. Additionally, the 3-dimensional texture mapping
function which is ordinarily supported by a graphics hardware canalso accelerates the texture mapping of a voxel data.

   In experiments, we first verify that the proposed method can wellapproximate the Phong model. Figure 2(c) illustrates the differences in rendering results between the Phong model (a) and theproposed method (b). The average of the differences of all pixels is
only less than 1 in regard to each RGB channel. With respect to rendering time, rendering of each frame takes about 2 hours with thePhong model. On the other hand, the proposed method can renderin real time.
In the next experiment, we show some rendering results for nonuniform glossy objects in a virtualized dynamic environment which
consists of an omnidirectional image sequence captured by an omnidirectional multi-camera system. Figure 3(a)-(d) show the rendering results from the 90th frame to the 105th frame. These results
are rendered at over 60 fps.

(a) Rendered by the(b) Rendered by the(c) Differences between
Phong model
proposed method
two methods
Figure 2: Comparison of the proposed method with the Phong model rendering.

(a) 90th frame.

(b) 95th frame.

(c) 100th frame.

(d) 105th frame.

Figure 3: Rendering of a glossy object in a dynamic environment.

   B LINN , J., AND N EWELL , M. 1976. Texture and reflection in computer generatedimages. In Communications of the ACM, 542–546.

Figure 1: A summary of generating a multi-scale environment map.
 e-mail: bunyou-o@is.aist-nara.ac.jp† e-mail: machida@ime.cmc.osaka-u.ac.jp‡ e-mail: yokoya@is.aist-nara.ac.jp

C ABRAL , B., O LANO , M., AND N EMEC , P. 1999. Reflection space image basedrendering. In Proceedings of SIGGRAPH 2001, 165–170.
K AUTZ , J., V ÁZQUEZ , P., H EIDRICH , W., AND S EIDEL , H. 2000. A unified approach to prefiltered environment maps. In Proceedings of Euro Graphics Rendering Workshop 2000, 185–196.