Figure 2.21: The most basic psychometric function. For this example, as the stimulus intensity is increased, the percentage of people detecting the phenomenon increases. The point along the curve that corresponds to 50 percent indicates a critical threshold or boundary in the stimulus intensity. The curve above corresponds to the cumulative distribution function of the error model (often assumed to be Gaussian).

Psychophysics is the scientific study of perceptual phenomena that are produced by physical stimuli. For example, under what conditions would someone call an object ``red''? The stimulus corresponds to light entering the eye, and the perceptual phenomenon is the concept of ``red'' forming in the brain. Other examples of perceptual phenomena are ``straight'', ``larger'', ``louder'', ``tickles'', and ``sour''. Figure 2.21 shows a typical scenario in a psychophysical experiment. As one parameter is varied, such as the frequency of a light, there is usually a range of values for which subjects cannot reliably classify the phenomenon. For example, there may be a region where they are not sure whether the light is red. At one extreme, they may consistently classify it as ``red'' and at the other extreme, they consistently classify it as ``not red''. For the region in between, the probability of detection is recorded, which corresponds to the frequency with which it is classified as ``red''. Section 12.4 will discuss how such experiments are designed and conducted.

Steven M LaValle 2020-11-11