Volume rendering is a technique for visualizing sampled scalar or vector fields of three spatial dimensions without fitting geometric primitives to the data. A subset of these techniques generates images by computing 2-D projections of a colored semitransparent volume, where the color and opacity at each point are derived from the data using local operators. Since all voxels participate in the generation of each image, rendering time grows linearly with the size of the dataset. This paper presents a front-to-back image-order volume-rendering algorithm and discusses two techniques for improving its performance. The first technique employs a pyramid of binary volumes to encode spatial coherence present in the data, and the second technique uses an opacity threshold to adaptively terminate ray tracing. Although the actual time saved depends on the data, speedups of an order of magnitude have been observed for datasets of useful size and complexity. Examples from two applications are given: medical imaging and molecular graphics.

/pdf/efficient-ray-tracing-of-volume-data-4l5b7uzhr8.pdf

Efficient ray tracing of volume data

Ray tracing, ray casting, and other forms of point sampling are important techniques in computer graphics, but their usefulness has been undermined by aliasing artifacts. In this paper it is shown that these artifacts are not an inherent part of point sampling, but a consequence of using regularly spaced samples. If the samples occur at appropriate nonuniformly spaced locations, frequencies above the Nyquist limit do not alias, but instead appear as noise of the correct average intensity. This noise is much less objectionable to our visual system than aliasing. In ray tracing, the rays can be stochastically distributed to perform a Monte Carlo evaluation of integrals in the rendering equation. This is called distributed ray tracing and can be used to simulate motion blur, depth of field, penumbrae, gloss, and translucency.

/pdf/stochastic-sampling-in-computer-graphics-1m7ogcpixa.pdf

Stochastic sampling in computer graphics

Texture mapping is one of the most successful new techniques in high-quality image synthesis. It can enchance the visual richness of raster-scan images immensely while entailing only a relatively smann increase in computation. The technique has been applied to a number of surface attributes: surface color, surface normal, specularity, transparency, illumination, and surface displacement?to name a few. Although the list is potentially endless, the techniques of texture mapping are essentially the same in all cases. This article surveys the fundamentals of texture mapping, which can be spilt into two topics: the geometric mapping that warps a texture onto a surface, and the filtering necessary to avoid aliasing. An extensive bibliography is included.

/pdf/survey-of-texture-mapping-5exi4tv5em.pdf

Survey of Texture Mapping

A new method of farthest point strategy (FPS) for progressive image acquisition-an acquisition process that enables an approximation of the whole image at each sampling stage-is presented. Its main advantage is in retaining its uniformity with the increased density, providing efficient means for sparse image sampling and display. In contrast to previously presented stochastic approaches, the FPS guarantees the uniformity in a deterministic min-max sense. Within this uniformity criterion, the sampling points are irregularly spaced, exhibiting anti-aliasing properties comparable to those characteristic of the best available method (Poisson disk). A straightforward modification of the FPS yields an image-dependent adaptive sampling scheme. An efficient O(N log N) algorithm for both versions is introduced, and several applications of the FPS are discussed.

/pdf/the-farthest-point-strategy-for-progressive-image-sampling-15x3nqtvu0.pdf

The farthest point strategy for progressive image sampling

In this article we propose algorithms that address the two basic problems encountered in generating continuous-tone images by ray tracing: speed and aliasing. We examine previous approaches to the problem and then propose a scheme based on the coherency of an auxiliary data structure imposed on the original object domain. After investigating both simple spatial enumeration and a hybrid octree approach, we developed 3DDDA, a 3D line generator for efficient traversing of both structures. 3DDDA provides an order of magnitude improvement in processing speed compared to other known ray-tracing methods. Processing time is found to be virtually independent of the number of objects involved in the scene. For large numbers of objects, this method actully becomes faster than scan-line methods. To remove jags from edges, a scheme for identifying edge orientation and distance from pixel center to true edge has been implemented. The time required for antialiasing depends on the total length of the edges encountered, but it is normally only a fractional addition to the time needed to produce the scene without antialiasing.

ARTS: accelerated ray-tracing system

Stochastic sampling techniques, in particular Poisson and fittered sampling, are developed and analyzed. These approaches allow the construction of alias-free approximations to continuous functions using discrete calculations. Stochastic sampling scatters high frequency information into broadband noise rather than generating the false patterne produced by regular sampling. The type of randomness used in the sampling process controls the spectral character of the noise. The average sampling rate and the function being sampled determine the amount of noise that is produced. Stochastic sampling is applied adaptively so that a greater number of samples are taken where the function varies most. An estimate is used to determine how many samples to take over a given region. Noise reducing filters are used to increase the efficacy of a given sampling rate. The filter width is adaptively controlled to further improve performance. Stochastic sampling can be applied spatiotemporally as well as to other aspects of scene simulation. Ray tracing is one example of an image synthesis approach that can be antialiased by stochastic sampling.

Antialiasing through stochastic sampling

An algorithm for computing ray traced pictures is presented, which adaptively subdivides scenes into S subregions, each with roughly uniform load. It can yield speedups of O(S2/3) over the standard algorithm.This algorithm can be mapped onto a parallel architecture consisting of a three dimensional array of computers which operate autonomously. The algorithm and architecture are well matched, so that communication overhead is small with respect to the computation, for sufficiently complex scenes. This allows close to linear improvements in performance, even with thousands of computers, in addition to the improvement due to subdivision.The algorithm and architecture provide mechanisms to gracefully degrade in response to excessive load. The architecture also tolerates failures of computers without errors in the computation.

An adaptive subdivision algorithm and parallel architecture for realistic image synthesis

Stochastic sampling: theory and application

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Antialiasing through stochastic sampling

An adaptive subdivision algorithm and parallel architecture for realistic image synthesis

Stochastic sampling: theory and application