Level-Of-Detail Volume Rendering via 3D Textures Manfred Weiler, Rudiger¨ Westermann ¡ Chuck Hansen ¡ , Kurt Zimmerman , Thomas Ertl Visualization and Interactive Systems Group University of Stuttgart ¡ Scientific Computing and Imaging Institute University of Utah Figure 1: All images show 3D texture based volume rendering of the engine data set. On the left, the data set is displayed with full resolution. In the middle, two different levels of detail are used with lower resolution in the back. This reduces texture memory consumption to 57%. On the right, the adaptive representation using four levels of detail from front-to-back requires only 29% of the original texture memory. Here, the data set was rendered with only 32% of the originally needed number of texture lookups. 1 Introduction Abstract In this paper we present an adaptive approach to volume rendering Volume data sets most commonly occur in two fields: imaging and via 3D textures at arbitrary levels of detail. The algorithm has been computational science. 3D imaging devices continue to increase the resolution of their sampled volumes with the current generation designed to enable interactive exploration of large-scale data sets 3 while providing user-adjustable resolution levels. A texture map approaching data volumes of 1024 samples. Similarly, computa- hierarchy is constructed in a way that minimizes the amount of tex- tional science continues to increase the mesh resolutions for large ture memory with respect to the power-of-two restriction imposed scale simulation thereby increasing the size of the data to be visual- by OpenGL implementations. In addition, our hierarchical level- ized. The challenge is to provide interactive visualization of these of-detail representation guarantees consistent interpolation between large 3D scalar fields while avoiding rendering artifacts. different resolution levels. Special attention has been paid to the fix- Hardware assisted volume rendering can provide interactive vi- ing of rendering artifacts that are introduced by non-corrected opac- sualization of 3D scalar fields[2, 3, 8, 10]. The ability to interact ities at level transitions. By adapting the sample slice distance with with transfer functions and viewpoint orientation provides pow- regard to the desired level-of-detail, the number of texture lookups erful visual cues that would be difficult to reproduce in batch- is reduced significantly. mode volume rendering. 3D texture mapping hardware that is now also available on PC graphics adapters [6] is the most prevalent ¢ Universitat¨ Stuttgart, IfI, Abt. VIS, Breitwiesen- choice for hardware assisted volume rendering although dedicated str. 20-22, 70565 Stuttgart, Germany; E-mail: volume processors have recently been introduced[10]. While 3D [email protected] . texture mapping is a powerful tool that allows one to investigate volumes easily, either by direct volume rendering, or by visualiz- ing these functions on intermediate surfaces, the limited amount of texture memory is a serious constraint. Methods exist for per- forming volume rendering where the entire data volume resides in texture memory[2, 3]. If one exceeds the limits of physical texture memory, some graphics libraries allow for the paging of textures[14, 5]. However, such brute-force methods for dealing with volumes whose size exceeds physical texture memory severely hamper the interactivity of the rendering. Fortunately, most data sets have large regions that don’t contain this is not the common viewing frustum, this is not a severe limita- interesting£ data. This paves the way for the application of multires- tion. In the next section, we describe our multiresolution hierarchy olution representations of the volume data. Such representations followed by a description and solution to the artifact problem. allow regions of interest to be rendered at higher resolutions than other parts of the data set, allowing interactive rendering of data whose uniform grid is much larger than texture memory. A second 3 Level-of-detail texture representation benefit is the reduction of trilinear interpolations. Since coarser lev- els provide a filtered, more compact, representation of the original Since in practical applications the size of the volume data sets is data, resampling based upon the level-of-detail is desirable because likely to exceed the amount of available texture memory, the data it reduces the number of expensive trilinear interpolations. The is usually split into subvolumes or bricks that are small enough to problem with multiresolution methods is the introduction of ren- fit into texture memory. Each brick can be rendered separately in dering artifacts when adjoining regions differ in the level-of-detail. back-to-front or front-to-back order, but since for every frame all This paper describes a method for hierarchically subdividing the bricks have to be reloaded, the rendering performance decreases data. Care is taken to insure interpolation consistency between lev- considerably. els while maintaining a minimal amount of data replication. Even In order to overcome this limitation we propose a level-of-detail with the interpolation consistency, rendering artifacts can occur at texture representation that provides an alternative for interactive the boundaries between levels. We present a description of these rendering of large-scale data sets. The goal of this hierarchical errors and describe a solution which provides continuity at level representation is twofold: to convert the volume data into a mul- boundaries. In the next section, we briefly describe related work. tiresolution representation that entirely fits into the limited texture In section 3, we describe the level-of-detail representation. Section memory and to minimize texture lookups by adaptively resampling 4 provides insight into the rendering artifacts previously seen in the data with respect to the selected level-of-detail. multiresolution volume rendering. We conclude with some results Each brick locally stores approximations of the original data at and areas of future research. an ever coarser resolution. These copies are then used to adap- tively render arbitrary regions with reduced detail size. Even if the multiscale representation does not entirely fit into texture memory, 2 Related work texture loading will be reduced. In addition a considerable number of rasterization operations can be saved by choosing the sampling As described in the introduction, hardware assisted volume render- frequency according to the detail size present within each copy. In ing has been a reality for the past several years[1, 2, 10]. While summary, by taking advantage of a level-of-detail representation as dedicated hardware is now commercially available[10], 3D texture described, our goal is improved rendering performance. mapping approaches are the most prevalent due the vast numbers of In the remainder of this section let us assume that we initially machines, mainly SGIs, upon which this OpenGL extension runs. decompose the data set into a number of bricks. After constructing Fundamentally, these systems resample volume data, represented the texture hierarchy these bricks can be rendered at arbitrary reso- as a 3D texture, onto a sampling surface. The most common sur- lutions. As will be outlined below, some additional expense is re- face is a plane that can be aligned with the data, aligned orthogonal quired to guarantee continuous transitions between adjacent bricks to the viewing direction, or aligned in other configurations (such at different levels. Criteria that are applied to determine the number as spherical shells). The ability to leverage the embedded trilinear of initially selected bricks and the resolution level that is to be used interpolation hardware is at the core of this acceleration technique. for rendering will be discussed in subsection 3.4. This capability was first described by Cullip and Neumann[3]. They discussed the necessary sampling schemes as well as axis aligned and viewpoint aligned sampling planes. Further develop- 3.1 Texture decomposition ment of this idea, as well as the extension to more advanced medi- cal imaging, was described by Cabral et al.[2]. They demonstrated Prior to the rendering, the volume data set is subdivided into multi- that both interactive volume reconstruction and interactive volume ple bricks of smaller size, which get assigned the chunk of texture rendering was possible with hardware providing 3D texture acceler- that is necessary to render the brick at the original resolution. Each ation. Further improvements providing non-polygonal surface ren- brick builds its own local hierarchy by constructing copies of the dering and effective handling of arbitrary clipping geometries have original texture at ever coarser resolution. These different levels- been proposed in [12]. of-detail are stored in additional texture maps as shown in Figure 2. The work most similar to ours was reported by LaMar et al.[7]. ¦ ¦ They described a multiresolution approach to interactive volume ¥ Level Brick A Brick B rendering. The use of multiresolution for importance based volume ¤ 0 rendering is well motivated by LaMar et al. Their multiresolution 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 hierarchy filtered the volume to create levels-of-detail in an octree, 1 but they did not explicitly address the avoidance of interpolation er- 0 2 4 6 8 10 12 14 16 rors in their multiresolution model. They investigated several slic- § 2 ing methods and concluded that spherical shells were an approach ¨ to deal with rendering artifacts. Their solution did not guarantee 0 2 4 6 8 continuity between levels but attempted to reduce the visual arti- 3 facts through spherical sampling. 0 2 4 Our work differs from theirs in that we develop a multiresolution hierarchy that allows consistent interpolation between levels. We Figure 2: One-dimensional example of a data set with four levels also address the rendering artifacts that still persist when render- of detail. On every level the size of texture elements increases by ing two differing but adjacent levels. Our multiresolution hierarchy a factor of two.