In 1973 Schafer and Rabiner [52] presented a frequency domain interpretation of the interpolation process, through which it becomes clear that interpolation is fundamentally a linear filtering process. They derive filters corresponding to linear interpolation and Lagrange interpolation which allows them to investigate the frequency responses of these methods. However, they conclude that linear and Lagrange interpolation leave much to be desired in a digital signal processing context.
An important step for computer graphics was done by Crow [10], who identified sampling as the cause for un-wanted artifacts in computer-generated images. The most obvious problems occur at object silhouettes, i.e., sharp edges. These often have an annoying jagged appearance. Another problem are small objects which can disappear between sampling points or appear much bigger as they really are. Also, long skinny objects can break up in several components. Further, regions of complicated details cannot be represented adequately. This gets even more problematic in animation sequences. Then the jaggies move along the edges (``Armies of ants appear to run along edges.''), small objects suddenly disappear and pop up again or larger objects appear to change shape and size.
Crow proposed three techniques to reduce these problems. The first is to increase the resolution, which is, of course, quite a brute force method, not always applicable and does not really deal with the problem. The second is to blur the output image, but then also fine detail gets lost. The third technique is to let every pixel represent not one point but a finite area in the scene. This has the effect of applying a low-pass filter before the scene is sampled, making it band-limited and therefore representable by point samples.