# Approximate Image-Space Multidirectional Occlusion Shading Model for Direct Volume Rendering
## 4 Results and Discussion  
We tested our approximate image-space multidirectional occlusion shading model on a Xeon CPU 2.66 GHz processor with NVidia GeForce GTX 295 graphics hardware, and for the volume rendering, we extended the ray-casting technique using the NVidia Cg shader. The color and depth from the volume rendering were stored in _floating point_ textures, and they were used in our shading model, as described in Section 3. For the rendering without transparency, we used only one component in the depth texture; however, for the transparent object occlusion or multiple layer rendering, we used four components in the depth texture. As described in Section 3.5, the approximated opacity was easily computed using a parameter (\(\beta\)), which was stored together in the color buffer. Therefore, an additional opacity buffer was not required. In the light model implementation presented in Section 3.2, the actual light samples were obtained by rotating samples on a disk with the radius \(r\), whose center was at \((R+0.5,0.5,0.0)\), to simplify the calculations. We rotated the samples by an angle \(\phi\) about the \(y\)-axis (\(R_{y}(\phi)\)) and then rotated them once more by an angle \(\theta\) about the \(z\)-axis (\(R_{z}(\theta)\)). The rotation matrix was obtained as follows. \[R_{z}(\theta)R_{y}(\phi)= \begin{pmatrix}\cos(\theta)\cos(\phi)&-\sin(\theta)& -\cos(\theta)\sin(\phi)\\ \sin(\theta)\cos(\phi)&\cos(\theta)&-\sin(\theta)\sin(\phi)\\ \sin(\phi)&0&\cos(\phi)\end{pmatrix} ,\]  
where \(0\leqq\theta\leqq 2\pi\) and \(0\leqq\phi\leqq\pi\). We used six different datasets to show the effects of our ISMOS model, as summarized in Table 1. The engine data are presented with different shading methods in Figure 6. Our ISMOS model was able to produce the different shading effects by simply adjusting the light parameters. The shadow (b,c) and ambient occlusion (d) provided more depth cues compared to simple local illumination (a). The ambient occlusion effect (d) from our ISMOS was similar to the effect (e) proposed by [PERSON] et al. [5]. Figure 8 presents the effect of the multiple directional light sources applied to the teddy bear dataset. The two directional lights in (f) provide more visual cues compared to the previous ambient occlusion method (c) and shading with a single light source (d,e). We show an occlusion caused by transparent layers on an opaque layer in Figure 9. The transparent skin occludes the light arriving on the bone, and the effect is shown in (b) and (c). The occlusion is also caused by the bone, and this is seen around the back side of the neck bone. As seen in the figure, less light on the bone is observed in (c) compared to (b) since the more opaque skin in (c) occludes the light arriving at the bone more than the more transparent skin in (b). The occlusions on multiple layers are computed and blended in (d). Figure 8: Multiple directional light effect applied to the teddy bear data. The dual light model is presented in (**a**), but our system supports more than two light sources. The local illumination is applied in (**b**), and the image-space horizon-based ambient occlusion [5] is used in (**c**). (**d,e**) were obtained with single light sources and (**f**) shows the effect of multiple light sources. The abdomen data are compared with different shading methods in Figure 10. The data were rendered with the opaque transfer function setting in (a-c) and transparent setting in (d-f). (c) shows the full occlusion of ISMOS and provides very good depth cues compared to (a) and (b). We also compare the multiple layer effect in (e) and (f), and a part of the scene is highlighted with a blue box. The shading is visible through the transparent object, and the multilayer occlusion shows more natural shading effect as seen in (f). The carp data were used to show how well our ISMOS worked on a complicated structure in Figure 11. We extracted a bone structure out of the data and applied ISMOS on it.