# Approximate Image-Space Multidirectional Occlusion Shading Model for Direct Volume Rendering
## 2 Related Work  
Volume rendering has been widely used to explore volumetric datasets and provides useful insights into the volumetric datasets. For a better understanding of the data, illumination models have been intensively studied over the decades. Various optical approximation models, such as emission-absorption models [10], have been widely employed to build up the volume rendering system. [PERSON] [11] presented a local illumination model with gradients in the volume rendering, which enhanced the visual cues. Figure 1: Overview of the ISMOS model. (**a**) presents an illustration of the ISMOS model. (**b,c**) show different light sources that our model can simulate. The gray lines indicate the occluded paths from a pixel to the light samples, and the dark red lines are the paths without any occluded object. The light red lines are the paths passing through transparent objects. Figure 3: The rendering pipeline with the approximate ISMOS model. The conventional volume rendering is extended with frame buffers to simulate various shading models. Figure 2: The transmittance approximation for the transparent objects. (**a**) During the rendering, we stored an approximated functional representation of the transmittance characteristics per pixel. The transmittance is continuously decreasing along with the entire depth. Note that the transmittance approximation is executed in the first rendering pass on-the-fly. (**b**) The resulting image-space representation contains information on the distribution of the transmittance and the depth. However, the locally illuminated volume rendering might not give sufficient depth cues that enable unobstructed visualization of complicated features in the volumetric data. [PERSON] et al. [12] proposed a simple and effective interactive shading model that captured volumetric light attenuation effects, including volumetric shadows. They utilized a direct and indirect light contribution to render a translucent material. [PERSON] et al. [13] achieved an interactive global light propagation in the direct volume rendering. Their technique was nearly physically correct, unlike the model by [PERSON] et al. [12]. [PERSON] et al. [14] presented ambient occlusion and edge cueing for molecular visualizations. Their approach interactively enhanced the visual cues for the understanding of complex molecular surface renderings. Ambient occlusion has been applied in volume rendering to improve visual quality and understanding. [PERSON] et al. [15] used summed-area tables to compute the ambient occlusion and halos. They presented a vicinity occlusion map (VOM) and a density summed-area table (DSAT) to enhance depth perception for the volumetric data. However, the VOM works in limited circumstances, and the DSAT for the volume data requires extra 3D texture memory with a long preprocessing time. Local ambient occlusion in the volume rendering was proposed by [PERSON] et al. [16]. The approach is a gradient-free shading model and, therefore, less sensitive to noise. In their work, an extra 3D texture was generated to hold the emissive color and the ambient light of each voxel. However, the extra 3D texture was regenerated whenever the transfer function was changed. Recently, advanced illumination models [17; 18; 19; 20; 21; 22; 23; 24] for the volume rendering have been introduced. [PERSON] et al. [23] presented an interactive volume rendering with ambient occlusion and color bleeding. [PERSON] and [PERSON] [19] showed advanced light material interactions. Moving light sources [21; 22] have also been applied in the interactive volume rendering. In the work of [21; 22], the volumetric lighting was simulated for the scattering and shadowing. However, all of these studies utilized extra 3D texture memory to store the new volumetric lighting information, which required additional preprocessing operations. Since the rendering only needed to fetch the 3D lighting textures during the rendering, the rendering speed was comparatively faster than models with on-the-fly lighting computation. [PERSON] et al.