A description of discrete internal representation schemes for visual pattern discrimination

Abstract

Abstract.A general description of a class of schemes for pattern vision is outlined in which the visual system is assumed to form a discrete internal representation of the stimulus. These representations are discrete in that they are considered to comprise finite combinations of "components" which are selected from a fixed and finite repertoire, and which designate certain simple pattern properties or features. In the proposed description it is supposed that the construction of an internal representation is a probabilistic process. A relationship is then formulated associating the probability density functions governing this construction and performance in visually discriminating patterns when differences in pattern shape are small. Some questions related to the application of this relationship to the experimental investigation of discrete internal representations are briefly discussed.

Qualitative Cues in the Discrimination of Affine-Transformed Minimal Patterns

“…The data were fitted by a simple probabilistic model of discrimination performance that involved a combination of qualitative (discrete) and quantitative (continuous) cues (Foster 1980a(Foster , 1991. It was assumed that the visual system was able to extract from the two patterns estimates x , , x2 of the positions of the displaced points, defined by their distances along a diagonal from some reference position, such as the opposite point.…”

“…Although visual invariants may include continuously varying quantities such as the ratios of distances along a line, it is possible that these invariants also include discrete or 'qualitative' cues (Foster 1980a;Wagemans 1993); for example, collinearity and parallelism (Foster 1980b;Biederman 1987;Wagemans 1993), and related properties such as concavity and convexity (Koenderink 1986;Ullman 1989). In some patterndiscrimination tasks (eg Wagemans 1992(eg Wagemans , 1993) it has been found that when two patterns have the same qualitative properties they are more likely to be judged as 'same' than when this property is present in only one of the patterns.…”

Characterization of discrete and continuous modes of visual pattern discrimination

“…The framework for this study on discrete and continuous modes of visual pattern processing is based on the scheme for the description and investigation of discrete internal representations formulated by Foster (1980aFoster ( , 1980b. This scheme entailed the use of a local 1-parameter group of local transformations tp~, st J, to obtain, from a given pattern B, a continuum of patterns ~p~(B), scJ, from which pairs of perturbed patterns ~ps+~(B), lp~_~s(B) were selected and their discriminability measured as a function of the parameter s. In this paper, discrete and continuous modes of visual discrimination performance have been further analyzed to obtain a quantitative criterion typifying the two kinds of performance.…”

“…Let P~u be the conditional discrete probability density function of 6tu and let fj~ be the conditional continuous probability density function of 7j~. It was suggested in Foster (1980a) that if B~ and B 2 are two subpatterns in the visual field, sufficiently alike in shape, then the discriminability of B~ and B 2 is determined by the differences in the density functions p~u and in the density functions fj~ for the two subpatterns. To explore the effect of these differences in density functions, patterns are drawn from a smooth continuum generated from a given transformational uniformity for the continuum (Foster, 1980b).…”

Classical and Fuzzy Differential Methods in Shape Analysis

“…At the lowest, most immediate levels of image representation, there are effects of noise in sensory transduction and of limits on sampling frequency, both spatial and temporal. At higher, more removed levels of image representation (13], there are more general imprecisions to do with the specification of image qualities (40]. For the human observer it is unclear what geometrical framework is used to form the representation, and indeed whether a metric structure or the structure of Foster a normed space is part of it [11,14].…”