Almost equivalence of combinatorial and distance processes for discrimination in multielement images

Under certain experimental conditions, visual discrimination performance in multielement images is closely related to visual identification performance: elements of the image are distinguished only insofar as they appear to have distinct, discrete, internal characterizations. This report is concerned with the detailed relationship between such internal characterizations and observable discrimination performance. Two types of general processes that might underline discrimination are considered. The first is based on computing all possible internal image characterizations that could allow a correct decision, each characterization weighted by the probability of its occurrence and of a correct decision being made. The second process is based on computing the difference between the probabilities associated with the internal characterizations of the individual image elements, the difference quantified naturally with an l(p) norm. The relationship between the two processes was investigated analytically and by Monte Carlo simulations over a plausible range of numbers n of the internal characterizations of each of the m elements in the image. The predictions of the two processes were found to be closely similar. The relationship was precisely one-to-one, however, only for n = 2, m = 3, 4, 6, and for n greater than 2, m = 3, 4, p = 2. For all other cases tested, a one-to-one relationship was shown to be impossible.