This paper presents a new discrete approach to antialiasing called stochastic sampling. Stochastic sampling is a Monte Carlo technique in which the image is sampled at appropriate nonuniformly spaced locations rather than at regularly spaced locations. This approach is inherently different from either supersampling or adaptive sampling, though it can be combined with either of them. Stochastic sampling can eliminate all forms of aliasing, including unruly forms such as highlight aliasing. With stochastic sampling, aliasing is replaced by noise of the correct average intensity. Frequencies above the Nyquist limit are still inadequately sampled, and they still appear as artifacts in the image. But a highly objectionable artifact (aliasing) is replaced with an artifact that our visual systems tolerate very well (noise). Stochastic sampling also provides new capabilities for discrete algorithms such as ray tracing. The physical equations simulated in the rendering process involve integrals over time, lens area, specular reflection angle, etc. Image-synthesis algorithms have usually avoided performing these integrals by resorting to crude approximations that assume instantaneous shutters, pinhole cameras, mirror or diffuse reflections, etc. But these integrals can be easily evaluated by stochastically sampling them, a process called Monte Carlo integration. In a ray-tracing algorithm, this involves stochastically distributing the rays in time, lens area, reflection angle, etc. This is called probabilistic or distributed ray tracing. Distributed ray tracing allows the simulation of fuzzy phenomena, such as motion blur, depth of field, penumbrae, gloss, and translucency. Stochastic sampling is a form of stochastic sampling that can be used to approximate a Poisson disk distribution. It involves adding noise to sample locations. There are many types of jitter; among these is additive random jitter, which can eliminate aliasing completely. But the discussion in this paper is limited to one particular type of jitter: the jittering of a regular grid. This type of jitter produces good results and is particularly well suited to image-rendering algorithms. The Fourier transform of a jittered grid is similar to the Fourier transform of a Poisson disk distribution. An analysis like that in Figures 2 and 4 shows that the results are not quite so good as those obtained with Poisson disk sampling. The images are somewhat noisier and some very small amount of aliasing can remain. We now look at this noise and aliasing quantitatively. Jitter was analyzed in one dimension (time) by Balakrishnan. He calculated the effect of time jitter, in which the nth sample is jittered by an amount ζn so that it occurs at time nT + ζn, where T is the sampling period. If the ζn are uncorrelated, Balakrishnan reports that jittering has the following effects: high frequencies are attenuated. The energy lost to the attenuation appears as uniform noise. The intensity of the noise equals the intensity of the attenuatedThis paper presents a new discrete approach to antialiasing called stochastic sampling. Stochastic sampling is a Monte Carlo technique in which the image is sampled at appropriate nonuniformly spaced locations rather than at regularly spaced locations. This approach is inherently different from either supersampling or adaptive sampling, though it can be combined with either of them. Stochastic sampling can eliminate all forms of aliasing, including unruly forms such as highlight aliasing. With stochastic sampling, aliasing is replaced by noise of the correct average intensity. Frequencies above the Nyquist limit are still inadequately sampled, and they still appear as artifacts in the image. But a highly objectionable artifact (aliasing) is replaced with an artifact that our visual systems tolerate very well (noise). Stochastic sampling also provides new capabilities for discrete algorithms such as ray tracing. The physical equations simulated in the rendering process involve integrals over time, lens area, specular reflection angle, etc. Image-synthesis algorithms have usually avoided performing these integrals by resorting to crude approximations that assume instantaneous shutters, pinhole cameras, mirror or diffuse reflections, etc. But these integrals can be easily evaluated by stochastically sampling them, a process called Monte Carlo integration. In a ray-tracing algorithm, this involves stochastically distributing the rays in time, lens area, reflection angle, etc. This is called probabilistic or distributed ray tracing. Distributed ray tracing allows the simulation of fuzzy phenomena, such as motion blur, depth of field, penumbrae, gloss, and translucency. Stochastic sampling is a form of stochastic sampling that can be used to approximate a Poisson disk distribution. It involves adding noise to sample locations. There are many types of jitter; among these is additive random jitter, which can eliminate aliasing completely. But the discussion in this paper is limited to one particular type of jitter: the jittering of a regular grid. This type of jitter produces good results and is particularly well suited to image-rendering algorithms. The Fourier transform of a jittered grid is similar to the Fourier transform of a Poisson disk distribution. An analysis like that in Figures 2 and 4 shows that the results are not quite so good as those obtained with Poisson disk sampling. The images are somewhat noisier and some very small amount of aliasing can remain. We now look at this noise and aliasing quantitatively. Jitter was analyzed in one dimension (time) by Balakrishnan. He calculated the effect of time jitter, in which the nth sample is jittered by an amount ζn so that it occurs at time nT + ζn, where T is the sampling period. If the ζn are uncorrelated, Balakrishnan reports that jittering has the following effects: high frequencies are attenuated. The energy lost to the attenuation appears as uniform noise. The intensity of the noise equals the intensity of the attenuated