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Generating a synthetic image is a sampling problem. The extensive literature in signal processing provides many useful algorithms and insights for image generation. Principles from signal processing for sampling and reconstructing images have been explored by many researchers (e.g. [6],[9]). Because samples are computationally expensive for global illumination calculations, efficient techniques must be employed in selecting the original samples. However, as noted by Mitchell [10] the problem of sampling global illumination is more complicated than 2-D image sampling because it involves predicting noise in 2-D space resulting from sampling a higher dimensional space. As we will discuss in more detail in the following section, even with sophisticated sampling techniques, excessive supersampling is required to eliminate noise under many common circumstances.

Lee and Redner [8] have studied the problem of noise in stochastically sampled synthetic images. They note that the linear filters typically used in computer graphics are unsatisfactory for eliminating the spike noise encountered in images generated using stochastic sampling. Linear filters tend to blur image details that should be kept sharp, while failing to spread the spike noise adequately. To resolve this problem, Lee and Redner proposed using alpha trimmed filters. Alpha trimmed filters have proved successful for eliminating spike noise and preserving edges in image processing applications. Such filters throw out ``outlier'' sample values when computing filtered pixel values. Lee and Redner demonstrate that alpha trimmed filters produce synthetic images without noticeable noise artifacts. However, they do not address the effect of such filters on the accuracy of the resulting image, and some important features may be lost.

Alpha trimmed and similar non-linear filters (e.g. morphological filters [5]) produce good results for many types of physically recorded images. In physically recorded images, the noise in the image is frequently due to secondary inputs that corrupt the signal of interest. Examples of unwanted secondary inputs are thermal noise in a detector element, and bit errors introduced in image transmission. Throwing out samples from these extraneous sources is desirable. In synthetic images, there are no corrupting secondary inputs. All of the samples carry valid information about the signal, and their effect should be included in the final image.

Another difference between synthetic and recorded images is the confidence we have in the results for some pixels. In recorded images there is frequently a great deal of uncertainty throughout the image. The exact pixel values are often unimportant, since many applications only need to identify objects, rather than examine subtle lighting effects. For synthetic images we have a high level of confidence in the values of some pixels. A great deal of computational effort has been expended to obtain subtle effects. We don't want the values of these pixels altered by a post-process filter.

In effect, we want our rendering process to simulate a sort of ``idealized camera'' up to and possibly including the storage of our final image. In displaying the image, we may attempt to compensate for human visual response with a tone-mapping operator (as discussed in the following section), but if we do not have a valid physical result, we have nothing to offer as input to such an operator.

The differences between synthetic and recorded images introduce two constraints for a filter for synthetic images that are not usually imposed on filters for physical images - energy preservation and minimal disruption. Energy preservation comes from the consideration that we do not want to throw any samples out. If a sample is contributing to a noisy region, we want to reduce noise by spreading out the energy it carries - not by removing it from the image. Minimal disruption comes from the consideration that we do not want to alter pixels that we have a high level of confidence in. To the greatest extent possible, the radiance of these pixels should be the same in the filtered image as in the unfiltered image.

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