Arie E. Kaufman

Volume graphics

Volume graphics, which employs a volume buffer of voxels for 3D scene representation, is discussed. Volume graphics offers advantages over surface graphics: it is viewpoint independent, insensitive to scene and object complexity, and suitable for the representation of sampled and simulated data sets. Moreover, geometric objects can be mixed with these data sets. Volume graphics supports the visualization of internal structures and lends itself to the realization of block operations, constructive solid geometry modeling, irregular voxel sizes, and hierarchical representation. The problems associated with the volume buffer representation (such as discreteness, memory size, processing time, and loss of geometric representation) are discussed.<<ETX>>

GPU Cluster for High Performance Computing

Inspired by the attractive Flops/dollar ratio and the incredible growth in the speed of modern graphics processing units (GPUs), we propose to use a cluster of GPUs for high performance scientific computing. As an example application, we have developed a parallel flow simulation using the lattice Boltzmann model (LBM) on a GPU cluster and have simulated the dispersion of airborne contaminants in the Times Square area of New York City. Using 30 GPU nodes, our simulation can compute a 480x400x80 LBM in 0.31 second/step, a speed which is 4.6 times faster than that of our CPU cluster implementation. Besides the LBM, we also discuss other potential applications of the GPU cluster, such as cellular automata, PDE solvers, and FEM.

Volume visualization

Volume visualization is a method of extracting information from volumetric datasets through interactive graphics and imaging, and is concerned with the representation, manipulation, and rendering of these datasets [Gallagher 1995; Kaufman 1991; Rosenblum 1994]. Volume data are 3D entities that may have information inside them, may not consist of surfaces and edges, or may be too voluminous to be represented geometrically. Volume visualization encompasses an array of techniques for peering inside the dataset and for interactively extracting meaningful information from it using transformations, cuts, segmentation, translucency, measurements, and the like. The primary sources of volume data are three: sampled data of real objects or phenomena, computed data produced by a computer simulation, and modeled data generated from a geometric model. Examples of applications generating sampled data are medical imaging (e.g., CT, MRI), biology (e.g., confocal microscopy), geoscience (e.g., seismic measurements), industry (e.g., nondestructive inspection), and chemistry (e.g., electron density maps) [Kaufman 1991]. Some examples of applications generating computed datasets, typically by running a simulation on a supercomputer, are meteorology (e.g., storm prediction), computational fluid dynamics (e.g., water flow), and materials science (e.g., new materials). Recently, many traditional computer graphics applications, such as computer-aided design and flight simulation [Cohen and Shaked 1993; Kaufman et al. 1993], have been exploiting the advantages of volumetric techniques for modeling, manipulation, and visualization, an approach called volume graphics [Kaufman et al. 1993]. Volumetric data is typically a set S of samples (x, y, z, v), representing the value v of some property of the data at a 3D location (x, y, z). If v is simply a 0 or a 1, with 0 indicating background and 1 indicating the object, the data is called binary data. The data may instead be multivalued, with v representing some measurable property of the data, such as density, color, heat, or pressure. The value v may even be a vector, representing, for example, velocity at each location. In general, the samples may be taken at random locations in space, but in many cases S is isotropic, containing samples taken at regularly spaced intervals along three orthogonal axes. Since S is defined on a regular grid, a 3D array (called volume buffer, cubic frame buffer, 3D raster) is typically used to store the values. S is therefore referred to as the array of values S(x, y, z), which is defined only at grid locations. A function may be defined to describe the value at any continuous location by approximating v at a location (x, y, z) using some interpolation function to S, such as zero-order (nearest-neighbor), piecewise function known as first-order (trilinear), or higher-order interpolation. The region of constant value that surrounds each sample in zero-order interpolation is known as a volume cell (voxel for short), with each voxel being a rectangular cuboid having six faces, twelve edges, and eight corners. The terms, voxel, grid location,

Virtual voyage: interactive navigation in the human colon

Virtual colonoscopy is a non-invasive computerized medical procedure for examining the entire colon to detect polyps. We present an interactive virtual colonoscopy method, which uses a physicallybased camera control model and a hardware-assisted visibility algorithm. By employing a potential field and rigid body dynamics, our camera control supplies a convenient and intuitive mechanism for examining the colonic surface while avoiding collisions. Our Zbuffer-assisted visibility algorithm culls invisible regions based on their visibility through a chain of portals, thus providing interactive rendering speed. We demonstrate our method with experimental results on a plastic pipe phantom, the Visible Human, and several patients. CR Categories: I.3.3 [Picture/Image Generation]: Display Algorithms; I.3.5 [Computational Geometry and Object Modeling]: Physically Based Modeling; I.3.6 [Methodologies and Techniques]: Interaction Techniques; I.3.7 [Three-Dimensional Graphics and Realism]: Hidden Line/Surface Removal; I.3.8 [Applications];

Penalized-distance volumetric skeleton algorithm

Introduces a refined general definition of a skeleton that is based on a penalized distance function and that cannot create any of the degenerate cases of the earlier CEASAR (Center-line Extraction Algorithm-Smooth, Accurate and Robust) and TEASAR (Tree-structure Extraction Algorithm for Skeletons-Accurate and Robust) algorithms. Additionally, we provide an algorithm that finds the skeleton accurately and rapidly. Our solution is fully automatic, which frees the user from having to engage in manual data pre-processing. We present the accurate skeletons computed on a number of test data sets. The algorithm is very efficient, as demonstrated by the running times, which were all below seven minutes.

Volume sculpting

We present a modeling technique based on the metaphor of interactively sculpting complex 3D objects from a solid material, such as a block of wood or marble. The 3D model is represented in a 3D raster of voxels where each voxel stores local material property information such as color and texture. Sculpting is done by moving 3D voxel-based tools within the model. The affected regions are indicated directly on the 2D projected image of the 3D model. By reducing the complex operations between the 3D tool volume and the 3D model down to primitive voxel-by-voxel operations, coupled with the utilization of a localized ray casting for image updating, our sculpting tool achieves real-time interaction. Furthermore, volume sampling techniques and volume manipulations are employed to ensure that the process of sculpting does not introduce aliasing into the models.

3D scan-conversion algorithms for voxel-based graphics

An assortment of algorithms, termed three-dimensional (3D) scan-conversion algorithms, is presented. These algorithms scan-convert 3D geometric objects into their discrete voxel-map representation within a Cubic Frame Buffer (CFB). The geometric objects that are studied here include three-dimensional lines, polygons (optionally filled), polyhedra (optionally filled), cubic parametric curves, bicubic parametric surface patches, circles (optionally filled), and quadratic objects (optionally filled) like those used in constructive solid geometry: cylinders, cones, and spheres. All algorithms presented here do scan-conversion with computational complexity which is linear in the number of voxels written to the CFB. All algorithms are incremental and use only additions, subtractions, tests and simpler operations inside the inner algorithm loops. Since the algorithms are basically sequential, the temporal complexity is also linear. However, the polyhedron-fill and sphere-fill algorithms have less than linear temporal complexity, as they use a mechanism for writing a voxel run into the CFB. The temporal complexity would then be linear with the number of pixels in the objects 2D projection. All algorithms have been implemented as part of the CUBE Architecture, which is a voxel-based system for 3D graphics. The CUBE architecture is also presented.

Efficient algorithms for 3D scan-conversion of parametric curves, surfaces, and volumes

Three-dimensional (3D) scan-conversion algorithms, that scan-convert 3D parametric objects into their discrete voxelmap representation within a Cubic Frame Buffer (CFB), are presented. The parametric objects that are studied include Bezier form of cubic parametric curves, bicubic parametric surface patches, and tricubic parametric volumes. The converted objects in discrete 3D space maintain pre-defined application-dependent connectivity and fidelity requirements.The algorithms introduced here emply third-order forward difference techniques. Efficient versions of the algorithms based on first-order decision mechanisms, which employ only integer arithmetic, are also discussed. All algorithms are incremental and use only simple operations inside the inner algorithm loops. They perform scan-conversion with computational complexity which is linear in the number of voxels written to the CFB. All the algorithms have been implemented as part of the CUBE Architecture, which is a voxel-based system for 3D graphics.

3D virtual colonoscopy

The authors present here a method called 3D virtual colonoscopy, which is an alternative method to existing procedures of imaging the mucosal surface of the colon. Using 3D reconstruction of helical CT data and volume visualization techniques, the authors generate images of the inner surface of the colon as if the viewers eyes were inside the colon. They also create interactive flythroughs and off-line automatically-produced animations through the inside of the colon. The visualization is accomplished with VolVis, which is a comprehensive system for interactive volume visualization. The authors are specifically interested in visualizing colonic polyps larger than one cm since these have a high probability of containing carcinoma. The authors present testing results of their method as applied to two plastic pipe simulations and to the Visible Human data set.

Cube-4—a scalable architecture for real-time volume rendering

We present Cube-4, a special-purpose volume rendering architecture that is capable of rendering high-resolution (e.g., 1024/sup 3/) datasets at 30 frames per second. The underlying algorithm, called slice-parallel ray-casting, uses tri-linear interpolation of samples between data slices for parallel and perspective projections. The architecture uses a distributed interleaved memory, several parallel processing pipelines, and an innovative parallel data flow scheme that requires no global communication, except at the pixel level. This leads to local, fixed bandwidth interconnections and has the benefits of high memory bandwidth, real-time data input, modularity, and scalability. We have simulated the architecture and have implemented a working prototype of the complete hardware on a configurable custom hardware machine. Our results indicate true real-time performance for high-resolution datasets and linear scalability of performance with the number of processing pipelines.