Let us now consider how this model applies to Computer Graphics.
All antialiasing techniques use some form of blurring or smoothening the image to reduce the effect of aliasing.
All rendering algorithms globally fall in two categories.
In the discrete algorithms, the generation and sampling of the image are interwined. There is no continuous image function that is sampled - an image value that is calculated at sample points. We cannot insert an antialiasing filter which operates in the continuous information domain.Another point we need to consider, is that the images which are function of spatial variables over a sampling grid.
The amplitude characteristic of most images peaks at the origin and decreases as the reciprocal of the spatial frequency. This may not be the case with graphics as it may result in high values of F(u,v) which is the transform of the two dimensional point, far away from the origin. We have to distinguish between theoretical transforms and the transforms of images on the screen. The spatial frequency of computer graphics abstractions can extend to infinity in both u & v.
Screen images are however limited in each direction by the resolution of the frame store and by the line rate and horizontal resolution of the display device.
The locus of equal spatial frequencies is a circle centered at the origin. So a perfect low pass filter is a cylinder centred at the origin. High frequencies contribute to the sharpness in the image. So removing these blurs the image. In the Fourier domain, the antialiasing operations are a tradeoff between artefact visibility and image blurring because we remove high spatial frequencies.
Thus we find that simple filtering cannot be applied in Graphics directly.
The errors caused by aliasing are called artefacts. Common aliasing artefacts include jagged profiles, disappearing or improperly rendered fine detail, and disintegrating textures.
The picture on the left shows the sampling grid superimposed on the original scene. The picture on the right is the rendered image. A jagged profile is quite evident in the rendered image. Also known as "jaggies", jagged silhouettes are probably the most familiar effect caused by aliasing. Jaggies are especially noticeable where there is a high contrast between the interior and the exterior of the silhouette.
Back to the main screen