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17.1. Sources of Aliasing

The human eye is extremely good at noticing edges. This is how we comprehend shape and form and how we recognize letters and words. Our eye is naturally good at it, and we spend our whole lives practicing it, so naturally it is something we do very, very well.

A computer display is limited in its capability to present an image. The display is made up of a finite number of discrete elements called pixels. At a given time, each pixel can produce only one color. This makes it impossible for a computer display to accurately represent detail that is smaller than one pixel in screen space, such as an edge.

When you combine these two things, the human eye's ability to discern edges and the computer graphics display's limitations in replicating them, you have a problem, and this problem is known as aliasing. In a nutshell, aliasing occurs when we try to reproduce a signal with an insufficient sampling frequency. With a computer graphics display, we'll always have a fixed number of samples (pixels) with which to reconstruct our image, and this will always be insufficient to provide adequate sampling, so we will always have aliasing. We can reduce it to the point that it's not noticeable, or we can transform it into some other problem that is less objectionable, like blurriness or noise.

The problem is illustrated in Figure 17.1. In this diagram, we show the results of trying to draw a gray object. The intended shape is shown in Figure 17.1 (A). The computer graphics display limits us to a discrete sampling grid. If we choose only one location within each grid square (usually the center) and determine the color to be used by sampling the desired image at that point, we see some apparent artifacts. This is called POINT SAMPLING and is illustrated in Figure 17.1 (B). The result is ugly aliasing artifacts for edges that don't line up naturally with the sampling grid (see Figure 17.1 (C)). (The drawing is idealized because pixels on a standard CRT do not produce light in the shape of a square, but the artifacts are obvious even when the sampled points are reconstructed as overlapping circles on the computer display.)

Figure 17.1. Aliasing artifacts caused by point sampling. The gray region represents the shape of the object to be rendered (A). The computer graphics display presents us with a limited sampling grid (B). The result of choosing to draw or not draw gray at each pixel results in jaggies, or aliasing artifacts (C).

Aliasing takes on other forms as well. If you are developing a sequence of images for an animation and you don't properly sample objects that are in motion, you might notice TEMPORAL ALIASING. This is caused by objects that are moving too rapidly for the sampling frequency being used. Objects may appear to stutter as they move or blink on and off. The classic example of temporal aliasing comes from the movies: A vehicle (car, truck, or covered wagon) in motion is going forward, but the spokes of its wheels appear to be rotating backwards. This effect is caused when the sampling rate (movie frames per second) is too low relative to the motion of the wheel spokes. In reality, the wheel may be rotating two- and three-quarter revolutions per frame, but on film it looks like it's rotating one-quarter revolution backwards each frame.

To render images that look truly realistic rather than computer generated, we need to develop techniques for overcoming the inherent limitations of the graphics display.

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