# Approximate Image-Space Multidirectional Occlusion Shading Model for Direct Volume Rendering
## 4 Results and Discussion
The opacity approximation is applied in (c,d), and we can see that the approximation is very reliable to represent the bone structure. Furthermore, the spotlight is used in (d), which enables us to focus on a certain area and to reduce the computation time since scenes outside the spotlight are simply occluded. Our ISMOS model in (c,d) provides proper visual cues of the object compared to (a,b). Similar effects are obtained with the beetle data as presented in Figure 12. We compare the accuracy of the opacity approximation in (c) and (d); and (f) and (g). Furthermore, we can see more natural shading effects with the multiple layer occlusion, and they are shown in (h) compared to (g). Moreover, the perceptual cue is improved with our ISMOS. For the performance measurement, we used ray casting with a \(580\times 580\) view port in the volume rendering. The performances are summarized in Table 1. As shown in the table, the performance overhead was similar for all datasets. An average 13.8 ms overhead was measured for full occlusion with one light source and an average 25.6 ms overhead with two light sources. The average performance difference between the full and partial occlusion was about 11.4 ms, and the opacity approximation required on average 15.9 ms. The number of light sources affected the performance, but the difference was fairly small. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Dataset** & **Size** & **Local** & **1 L**, & **1 L**, & **1 L**, & **1 L**, & **1 L**, & **2 Ls**, & **2 Ls**, & **2 Ls**, & **2 Ls**, & **2 Ls**, \\  & & **Illumi-** & **FO**, **1** & **PO**, **1** & **PO**, **m** & **PO**, **1**, & **PO**, **m**, & **FO** & **PO**, **1** & **PO**, **m**, & **PO**, **1** & **PO**, **m**, & **PO**, **1** & **PO**, **m**, \\  & & **nation** & & & & \(\alpha_{app}\) & \(\alpha_{app}\) & & & & & \(\alpha_{app}\) & & \(\alpha_{app}\) \\ \hline Engine & \(256\times 256\times 128\) & 23.3 & 19.7 & 15.8 & 13.4 & 12.1 & 11.2 & 16.1 & 13.6 & 12.5 & 10.1 & 9.2 \\ Teddy bear & \(512\times 512\times 63\) & 22.7 & 18.5 & 15.1 & 13.1 & 13.8 & 12.5 & 15.3 & 12.1 & 8.8 & 9.1 & 8.6 \\ Head & \(256\times 256\times 225\) & 22.2 & 19.6 & 16.1 & 10.2 & 11.0 & 8.3 & 18.1 & 15.3 & 8.1 & 8.9 & 6.9 \\ Abdomen & \(256\times 256\times 128\) & 20.0 & 13.5 & 11.2 & 10.8 & 8.9 & 7.5 & 11.4 & 9.7 & 8.6 & 7.9 & 7.0 \\ Carp & \(256\times 256\times 512\) & 20.8 & 14.1 & 13.3 & 12.7 & 12.1 & 11.8 & 12.1 & 11.9 & 11.1 & 9.5 & 8.8 \\ Stag beetle & \(832\times 832\times 494\) & 10.4 & 9.2 & 8.2 & 7.9 & 7.5 & 6.9 & 7.8 & 6.4 & 6.0 & 5.5 & 5.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance in fps. “1 L” means one light source, and “2 Ls” indicates two light sources. “FO” is full occlusion, and “PO” is partial occlusion. “PO, 1” indicates PO with one layer, and “PO, m” is PO with m layers. “\(\alpha_{app}\)” means that the opacity approximation is used in the column. Figure 9: Applying our ISMOS model for transparent scenes to the head dataset. (**a**) presents the direct volume rendering result with the local illumination. Our shading model is applied on the opaque bone layer in (**b,c**). More transparent skin is used for the partial occlusion in (**b**), whereas less transparent skin in (**c**). ISMOS is applied to all layers and the occlusions are blended in (**d**). Note that our focus was not the optimization of the ray casting volume rendering, but the overhead for our shading model. Therefore, our performance on the volume rendering might not be faster compared to other highly optimized volume renderings, but the overhead was the same all the time as long as the view port size was fixed. Although there was a performance overhead by applying our ISMOS model, we still obtained interactive performance for all datasets even with transfer function changes and light source changes.