Intentional bogus ®rst page. This is required in order to make register changes take effect on the ®rst page of real text. A Survey of Algorithms for Volume Visualization T. Todd Elvins San Diego Supercomputer Center Advanced Scienti®c Visualization Laboratory P.O. Box 85608 San Diego, CA 92186-9784 USA Phone: (619) 534-5128 FAX: (619) 534-5113 E-mail: [email protected] "... in 10 years, all rendering will be volume rendering." Jim Kajiya at SIGGRAPH '91 Abstract complete agreement on a standard volume visualization Many computer graphics programmers are working in the vocabulary yet, a nomenclature is approaching con- area of scienti®c visualization. One of the most interest- sensus. Where multiple terms exist for the same concept, ing and fast-growing areas in scienti®c visualization is alternative terms are listed in parentheses. New pro- volume visualization. Volume visualization systems are cedures and heuristic approaches to short-cut volume used to create high-quality images from scalar and vector visualization's high CPU and large memory requirements datasets de®ned on multi-dimensional grids, usually for are a frequent occurrence. Some of the most popular pro- the purpose of gaining insight into a scienti®c problem. cedure and approaches will be discussed. Most volume visualization techniques are based on one Volume visualization is too large and is growing too fast of about ®ve foundation algorithms. These algorithms, for complete coverage in this paper. The reader is and the background necessary to understand them, are encouraged to consult the papers listed in the bibliogra- described here. Pointers to more detailed descriptions, phy for information on speci®c algorithms, scienti®c further reading, and advanced techniques are also given. applications, commercial projects, and advanced topics. Some of the topics not covered in this paper include: spe- 1. Introduction cial purpose hardware, methods for handling non- The following is an introduction to the fast-growing ®eld Cartesian data, advanced algorithm optimizations and of volume visualization for the computer graphics pro- enhancements, user interfaces, and commercial and pub- grammer. Many computer graphics techniques are used lic domain implementations. in volume visualization. The computer graphics tech- It should be kept in mind that, although not speci®cally niques themselves will not be discussed, rather the way discussed, animation is critical to the volume visualiza- these techniques are applied in fundamental volume visu- tion process. Without animating rendered volumetric alization algorithms will be explained. Advantages and images, the system user will usually have a dif®cult time disadvantages of each algorithm will be covered along discerning three-dimensional information from two- with a rough idea of the algorithm's space and time dimensional imagery. Animation is often a straight- requirements, ease of implementation, and the type of forward extension to the topics covered here. data it handles best. The following introduction to a wide range of volume Most volume visualization algorithms follow similar visualization algorithms will give the reader a solid start- steps. These steps will be discussed before any speci®c ing point for getting involved in this relatively new ®eld. algorithms are covered. The discussion will also explain Other technical perspectives at the introductory level can the terms, procedures, and heuristics most often used in be found in [Dreb88][Levo90e][Kauf91][Wilh91a]. A the ®eld of volume visualization. Although there is not good non-technical introduction is given in [Fren89]. Advanced topics in medical volume visualization are wispy, cloud-like structures are particularly dif®cult to covered in [Hohn90][Levo90c]. render. These are just a few of the hurdles yet to be dealt with in the ®eld of volume visualization. 2. Furthering scienti®c insight Despite these dif®culties, macro and micro scientists are This section introduces the reader to the ®eld of volume still ®nding many new ways to use volume visualization. visualization as a sub®eld of scienti®c visualization and Volume visualization is widely used in the medical ®eld discusses many of the current research areas in both. as well as in geoscience, astrophysics, chemistry, micros- copy, mechanical engineering, non-destructive testing, 2.1. Challenges in scienti®c visualization and many other scienti®c and engineering areas. The Scienti®c Visualization uses computer graphics tech- most common units of measure recorded in data volumes niques to help give scientists insight into their data include density, pressure, temperature, electrostatic [McCo87][Brod91]. Insight is usually achieved by charge, and velocity. Multiple values in each of these extracting scienti®cally meaningful information from measures could be stored at every gridpoint in one numerical descriptions of complex phenomena through volume. For example, atmospheric scientists often record the use of interactive imaging systems. Scientists need thirty or more parameters at every gridpoint (images that these systems not only for their own insight, but also to attempt to display more than one parameter at a time, share their results with their colleagues, the institutions however, are dif®cult to interpret). One need only look that support the scientist's research, and the general pub- around to ®nd new volumes to measure. lic. Few technical articles are published without cap- tioned data visualizations of some sort. 3. Data Characteristics The most active sub®eld of scienti®c visualization is 3.1. Sources of volume data volume visualization. Volume visualization is the process of projecting a multidimensional dataset onto a two- Scientists sometimes use volume visualization to com- dimensional image plane for the purpose of gaining an pare numerical results derived from empirical experi- understanding of the structure (or lack of structure) con- ments with results derived from simulations of the empir- tained within the volumetric data. Most often the dataset ical event. Finite-element analysis or computational ¯uid is de®ned on a three-dimensional lattice with one or more dynamics programs are often used to simulate events scalar values, and possibly one or more vector values at from nature. If an event is too big, too small, too fast, or each gridpoint on the lattice. Methods for visualizing too slow to record in nature, then only the simulated higher-dimensional grids and/or irregular grids are rela- event data volumes can be studied. tively unknown. Volume datasets are often acquired by scanning the To be useful, volume visualization techniques must offer material-of-interest using Magnetic Resonance Imaging understandable data representations, quick data manipu- (MRI), Computer-aided Tomography (CT), Positron lation, and reasonably fast rendering. Scienti®c users Emission Tomography (PET), and/or Sonogram should be able to change parameters and see the resultant machines. Laser scan confocal, and other high power image instantly. Few present day systems are capable of microscopes are also used to acquire data. this type of performance; therefore volume visualization Volume data can be generated by voxelizing geometric algorithm development and re®nement are important descriptions of objects, sculpting digital blocks of marble, areas of study. Understanding the fundamental algo- hand-painting in three-dimensions with a wand, or by rithms is requisite for such endeavors. writing programs that generate interesting volumes using stochastic methods. Some of these methods will be dis- 2.2. Applications of volume visualization cussed in more detail. Many challenges still exist in the ®eld of volume visuali- All of these datasets can be treated similarly even though zation [DeFa89]. The typical size of a volume dataset is they are generated by diverse means. The amount of several megabytes, sometimes hundreds of megabytes, structure in the dataset usually determines which volume and gigabyte datasets are just waiting for the hardware visualization algorithm will create the most informative that can handle them. Many scientists would like to be images. able to combine all of the interesting aspects of two or more volumetric datasets into one image. Creating static 3.2. Alternatives to single scalar data images from volumes of vector data is also an unsolved Vector data is sometimes visualized one slice at a time problem. Not all volume visualization techniques work with arrows at each gridpoint. The direction of the arrow well with all types of data and current data-classi®cation indicates the direction of the vector, and the color of the tools are rudimentary. Amorphous datasets describing arrow usually displays the vector's magnitude, although it could display any other scalar value. Alternatively, ani- The cell approach views a volume as a collection of hex- mations using streamers ribbons, tufts, particles, and ahedra whose corners are gridpoints and whose value other time-dependent mechanisms do an adequate job of varies between the gridpoints. This technique attempts to showing the data characteristics of a collection of slices. estimate values inside the cell by interpolating between Tensor data has also been visualized with some success. the values at the corners of the cell. Trilinear and tricubic Finding effective means for visualizing vector and tensor are the most commonly used interpolation functions. data is still, however, an open area of research. Images generated using the cell approach