Don P. Mitchell

Generating antialiased images at low sampling densities

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.

Reconstruction filters in computer-graphics

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.

A realistic camera model for computer graphics

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 simulation of the geometry of ray paths through the lens system, and by sampling the lens system such that the radiometry is computed accurately and efficiently. Because even the most complicated lenses have a relatively small number of elements, the simulation only increases the total rendering time slightly. CR

Spectrally optimal sampling for distribution ray tracing

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.

Illumination from curved reflectors

A technique is presented to compute the refkted illumination from curved mirror surfaces onto other surfaces. In accordance with Fermat’s principle, this is equivalent to fiiding extremal paths from the light source to the visible surface via the mirrors. Once pathways of illumination are found, h-radiance is computed from the Gaussian curvature of the geometrical wavefront. Techniques from optics, differential geometry and interval analysis are applied to this problem in global illumination. CR Categories and Subject Descriptions: 1.3.3 [ Computer Graphics ]: Picture/Image Generation; 1.3.7 [ Computer Graphics ]: Three-Dimensional Graphics and Realism

Consequences of stratified sampling in graphics

central limit theorem predicts a variance of the mean of O(N -1). Stratified sampling can further reduce the variance of the me This paper investigates how and why stratification effects t convergence to mean value of image pixels, which are obser 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 the of discrepancy. The result is generalized to higher dimensio as encountered with distributed ray tracing or form-fact computation.

20.4: Displaced Filtering for Patterned Displays

This paper describes the filtering used in Microsoft ClearType. ClearType is a software system than enhances the resolution and readability of fonts on displays that contain a repeating pattern of addressable colored sub-pixels. The filtering in ClearType is based on a perceptual model of human vision. The perceptual model leads to an optimization technique for finding the best output values. The results of the optimization can be approximated by pre-filtering each color channel of an input image and then sampling each filtered color image at the spatial locations of the same colored sub-pixels in the display. We refer to this filtering followed by displaced sampling as RGB decimation. RGB decimation eliminates the phase error caused by standard anti-aliasing. A further approximation of the optimal filter yields RGB decimation with displaced box filters. Fourier analysis demonstrates that both the optimization technique and the displaced box filter suppress frequencies that contribute most to color fringing in unfiltered displaced sampling.

Antialiasing of interlaced video animation

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.