Antialiased pixel values are often computed as the mean of N point samples.Using uniformly distributed random samples, the central limit theorem predicts a variance of the mean of O(N -1 ).Stratified sampling can further reduce the variance of the mean.This paper investigates how and why stratification effects the convergence to mean value of image pixels, which are observed to converge from N -2 to N -1 , with a rate of about N -3/2 in pixels containing edges.This is consistent with results from the theory of discrepancy.The result is generalized to higher dimensions, as encountered with distributed ray tracing or form-factor computation.

Patterns used for supersampling in graphics have been analyzed from statistical and signal-processing viewpoints. We present an analysis based on a type of isotropic discrepancy—how good patterns are at estimating the area in a region of defined type. We present algorithms for computing discrepancy relative to regions that are defined by rectangles, halfplanes, and higher-dimensional figures. Experimental evidence shows that popular supersampling patterns have discrepancies with better asymptotic behavior than random sampling, which is not inconsistent with theoretical bounds on discrepancy.

Most recent rendering research has concentrated on two subproblems: modeling the reflection of light from materials, and calculating the direct and indirect illumination from light sources and other surfaces. Another key component of a rendering system is the camera model. Unfortunately, current camera models are not geometrically or radiometrically correct and thus are not sufficient for synthesizing images from physically-based rendering programs. In this paper we describe a physically-based camera model for computer graphics. More precisely, a physically-based camera model accurately computes the irradiance on the film given the incoming radiance from the scene. In our model a camera is described as a lens system and film backplane. The lens system consists of a sequence of simple lens elements, stops and apertures. The camera simulation module computes the irradiance on the backplane from the scene radiances using distributed ray tracing. This is accomplished by a detailed simulati...

A technique is presented to compute the reflected illumination from curved mirror surfaces onto other surfaces. In accordance with Fermat's principle, this is equivalent to finding extremal paths from the light source to the visible surface via the mirrors. Once pathways of illumination are found, irradiance is computed from the Gaussian curvature of the geometrical wavefront. Techniques from optics, differential geometry and interval analysis are applied to solve these problems. CR Categories and Subject Descriptions: I.3.3 [ Computer Graphics ]: Picture/Image Generation; I.3.7 [ Computer Graphics ]: Three-Dimensional Graphics and Realism General Terms: Algorithms Additional Keywords and Phrases: Caustics, Differential Geometry, Geometrical Optics, Global Illumination, Interval Arithmetic, Ray Tracing, Wavefronts 1. Introduction Ray tracing provides a straightforward means for synthesizing realistic images on the computer. A scene is first modeled, usually by a collection of implici...

Nonuniform sampling of images is a useful technique in computer graphics, because a properly designed pattern of samples can make aliasing take the form of high-frequency random noise. In this paper, the technique of nonuniform sampling is extended from two dimensions to include the extra parameter dimensions of distribution ray tracing. A condition for optimality is suggested, and algorithms for approximating optimal sampling are developed. The technique is demonstrated at low sampling densities, so the characteristics of aliasing noise are clearly visible. At supersampling rates, this technique should move noise into frequencies above the passband of the pixel-reconstruction filter.

The production of computer-generated video presents a number of difficulties not encountered with motion pictures. Interlaced scanning and the color subcarrier of NTSC video are responsible for special problems such as interline flicker, and chroma aliasing. As in motion pictures, temporal aliasing is also an issue. A renderer can sample and filter a moving image in an arbitrary manner and is not constrained to simply imitate the behavior of a television camera. This paper explores several different spatiotemporal antialiasing filters and how they affect the quality of video animation.

Problems of signal processing arise in image synthesis because of transformations between continuous and discrete representations of 2D images. Aliasing introduced by sampling has received much attention in graphics, but reconstruction of samples into a continuous representation can also cause aliasing as well as other defects in image quality. The problem of designing a filter for use on images is discussed, and a new family of piecewise cubic filters are investigated as a practical demonstration. Two interesting cubic filters are found, one having good antialiasing properties and the other having good image-quality properties. It is also shown that reconstruction using derivative as well as amplitude values can greatly reduce aliasing.

Ray tracing produces point samples of an image from a 3-D model. Constructing an antialiased digital picture from point samples is difficult without resorting to extremely high sampling densities. This paper describes a program that focuses on that problem. While it is impossible to eliminate aliasing totally, it has been shown that nonuniform sampling yields aliasing that is less conspicuous to the observer. An algorithm is presented for fast generation of nonuniform sampling patterns that are optimal in some sense. Some regions of an image may require extra sampling to avoid strong aliasing. Deciding where to do extra sampling can be guided by knowledge of how the eye perceives noise as a function of contrast and color. Finally, to generate the digital picture, the image must be reconstructed from the samples and resampled at the display pixel rate. The nonuniformity of the samples complicates this process, and a new nonuniform reconstruction filter is presented which solves this problem efficiently.

This paper presents two distributed algorithms for detecting and resolving deadlocks. By insuring that only one of the deadlock processes will detect it, the problem of resolving the deadlock is simplified. That process could simply abort itself. In one version of the algorithm, an arbitrary process detects deadlock; and in a second version, the process with the lowest priority detects deadlock.