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For the purpose of quantifying models of letter recognition, similarities are often specified in terms of stimulus properties. In this paper, an approach is advocated based on similarities between internal letter representations or internal letter images, i.e. it is argued that optical and retinal factors play a more prominent role in letter confusions than is usually assumed. To illustrate this, letter images were calculated on the basis of earlier experimentally determined point spread functions (Blommaert et al., Spatial Vision 2, 99-115, 1987). Next, data on confusion matrices from Bouma (Vision Res. 11, 459-474, 1971) were taken to evaluate different measures which might be useful for quantifying similarities between internal letter representations. In the analysis of experimental data, Luce's (In: Handbook of Mathematical Psychology, 1963) choice model was used. It was found that if similarities were expressed in terms of differences between image contours, a fair first order approximation of Bouma's experimental results could be formulated (overall correlation coefficient of 0.95). Other measures like correlations between spatial frequency spectra of letter images were found to be less successful. The method used provides a means to relate quantitatively stimulus features and optical and early-visual factors to letter confusions.

Abstract-A point spread function, chosen to link contrast sensitivity and stimulus dimensions. can be obtained from measured thresholds by assuming small-signal-linearity and peak detection for the visual system. To that end a special case of summation of subthreshold signals (perturbation) is used. taking specific measures against the effect of sensitivity drift. The basic assumptions are tested simuitaneousl~-and confirmed. Other provisional assumptions tike radial symmetry and homogeneity were evaluated along a horizontal and a vertical meridian through the fovea. In the fovea no deviation from radial symmetry was found. The effect of inhomogeneity within the central fovea. seems to be too small to cause a significant change in the point spread function. The validity for predicting thresholds of stimuli exposing larger areas is tested. Annuli with varying radii show no significant aberration if probability summation is taken into account. Predicted disk thresholds, however, show a large discrepancy with experiment for radii larger than 2min arc. A possible extension of the model with multiple-detection units having tuned sizes is evaluated. INTRODUCfIONIn order to investigate characteristics of detail vision stimuli like Landolt C's, lines or gratings are generally used. Sometimes, radially symmetrical stimuli like disks and annuli are used to investigate lateral processing over short distances (Fiorentini and Maffei, 1970;Westheimer, 1967). The spatial processing of the visual system is rather inhomogeneously over the retina. This is demonstrated by data on visual acuity (Le Grand, 1967) and thresholds for disks (Kishto, 1970;Wilson, 1970). A review is made by van Doorn et al. (1972). The effect is also found with thresholds of lines (Hines, 1976;Wilson and Bergen, 1979; Limb and Rubinstein, 1977). Wilson and Bergen, ibid, stressing the importance of local measurement of the inhomogeneous system. used line sources instead of gratings as stimuli. However, line sources of the usual type still stimulate retinal parts with different properties. The use of point sources is an obvious further step, the more so, since it is not clear how much the discrepancy between measured thresholds and prediction based on a line spread function (e.g. Wilson and Bergen, 1979) is disguised by effects of the mentioned extension of the lines.A point spread or weighting function can be used to characterize the effect of a near-threshold-pointsource on the contrast sensitivity of neighbouring retinal points (e.g. van Meeteren, 1973;Kelly, 1975). However, the threshold changes which have to be measured to obtain such a function are very small. Consequently special measures have to be taken to eliminate the effects of unavoidable sensitivity drift in order to obtain the required precision.In this report the results of a technique to obtain a point spread function from threshold measurements is investigated and the predictive power is tested. This point spread function should represent the simple processing of the visual system, thus ...

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