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,

Volume Visualization

An investigation of the quality of surface-shading algorithms using computer-simulated test objects is reported. Test results are presented for four algorithms: z-buffer gradient, gray-level gradient, adaptive gray-level gradient, and marching cubes with two extensions. It was found that gray-level gradient shading and marching cubes did not differ greatly, except for thin objects, where adaptive gray-level gradient shading was better. Transparent visualization using transparent gray-level gradient shading is examined. It is shown that although there is no way to assure the fidelity of transparent shading, it is useful when no other surface at all can be determined. Use of a combination of shading methods appears to yield the best visualization of the respective objects. >

Investigation of medical 3D-rendering algorithms

This paper presents an introduction to the field of three-dimensional medical imaging It presents medical imaging terms and concepts, summarizes the basic operations performed in three-dimensional medical imaging, and describes sample algorithms for accomplishing these operations. The paper contains a synopsis of the architectures and algorithms used in eight machines to render three-dimensional medical images, with particular emphasis paid to their distinctive contributions. It compares the performance of the machines along several dimensions, including image resolution, elapsed time to form an image, imaging algorithms used in the machine, and the degree of parallehsm used in the architecture. The paper concludes with general trends for future developments in this field and references on three-dimensional medical imaging.

https://surface.syr.edu/cgi/viewcontent.cgi?article=1005&context=lcsmith_other

Three-dimensional medical imaging: algorithms and computer systems

Volume visualization is a method of extracting meaningful information from volumetric data using interactive graphics and imaging. It is concerned with volume data representation, modeling, manipulation, and rendering. Volume data are 3D (possibly time-varying) entities that may have information inside them, may not consist of tangible surfaces and edges, or may be too voluminous to be represented geometrically. They are obtained by sampling, simulation, or modeling techniques. When volumetric data are visualized using a surface-rendering technique, a dimension of information is essentially lost. In response to this, volume rendering techniques were developed that attempt to capture the entire 3D data in a single 2D image. Volume rendering conveys more information than surface-rendered images but at the cost of increased algorithm complexity and consequently increased rendering times. To improve interactivity in volume rendering, many optimization methods both for software and graphics-accelerator implementations as well as several special-purpose volume rendering machines have been developed.

/pdf/7-overview-of-volume-rendering-3uaii3coqa.pdf

7 – Overview of Volume Rendering

In medical 3-dimensional display, an input scene is represented by an array of volume elements (abbreviated as “voxels”), and an object in the scene is specified as a “connected” set of voxels. In such applications, surface tracking is an important, and often time-consuming, precursory step. One of the most efficient surface detection algorithms reported in the literature tracks a specified surface of a 3-dimensional object by visiting each boundary face in the surface twice. In this paper, we present a new definition of discrete objects and boundaries that leads to a modified algorithm, which, on the average, visits only one-third of the boundary faces twice (and the rest once). The algorithm has been implemented in our display software package and is found to achieve a run-time reduction of approximately 35%. This timing includes the computation of surface-normal information which is needed for the realistic rendering of surfaces. Without this computation, the saving would be about 55%.

Fast surface tracking in three-dimensional binary images

A general framework for real-time manipulation-of 3D objects from-medical data sets promises physicians a powerful new tool.

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