We describe several experiments on contour interactions and crowding effects at the resolution limit of the visual system. As test stimuli we used characters that are often employed in optometric practice for testing visual acuity: Landolt C's, Snellen E's, and rectangular gratings. We tested several hypotheses that have been put forward to explain contour interaction and crowding effects. In Experiment 1 and Experiment 2, Landolt C's were the test stimuli, and bars, or Landolt C's, or gratings served as distractors. In Experiment 1, we showed that neither scale invariance nor spatial frequency selectivity is a characteristic of foveal crowding effects. These results allowed us to conclude that mechanisms other than lateral masking contribute to observers' performance in 'crowded' tasks. R. F. Hess, S. C. Dakin, and N. Kappor (2000) suggested that the spatial frequency band most appropriate for target recognition is shifted by the surrounding bars to higher spatial frequencies that cannot be resolved by observers. Our Experiment 2 rejects this hypothesis as the experimental data do not follow theoretical predictions. In Experiment 3, we employed Snellen E's, both as test stimuli and as distractors. The masking functions were similar to those measured in Experiment 1 when the test Landolt C was surrounded by Landolt C's. In Experiment 4, we extended the range of test stimuli to rectangular gratings; same-frequency or high-frequency gratings were distractors. In this case, if the distracting gratings had random orientation from trial to trial, the critical spacing was twice larger than in the first three experiments. If the orientation of the distractors was fixed during the whole experiment, the critical spacing was similar to that measured in the first three experiments. We suggest that the visual system can use different mechanisms for the discrimination of different test stimuli in the presence of particular surround. Different receptive fields with different spatial characteristics can be employed. To explain why crowding effects at the resolution limit of the visual system are not scale invariant, we suggest that a range of stimuli, slightly varying in size, may all be processed by the same neural channel--the channel with the smallest receptive fields of the visual system.

We calculated the two-dimensional Fourier spectrum of a Landolt C. For Landolt Cs of orthogonal orientation, the main differences in the amplitude spectrum were found at a low frequency such that 1.3 periods were equal to the size fo the Landolt C, rather than at the high frequency corresponding to the size of the gap, i.e., such that 2.5 periods were equal to the size of the Landolt C. We compared visual acuity assessments obtained with Landolt C optotypes and the cut-off of the contrast sensitivity function measured with sinusoidal gratings. We found that the frequency corresponding to the size of the gap is twice the latter frequency. We suggest that, in fact, this lower frequency can be used to determine the position of the gap.

We tested whether visual complexity can be modeled through the use of parameters relevant to known mechanisms of visual processing. In psychophysical experiments observers ranked the complexity of two groups of stimuli: 15 unfamiliar Chinese hieroglyphs and 24 outline images of well-known common objects. To predict image complexity, we considered: (i) spatial characteristics of the images, (ii) spatial-frequency characteristics, (iii) a combination of spatial and Fourier properties, and (iv) the size of the image encoded as a JPEG file. For hieroglyphs the highest correlation was obtained when complexity was calculated as the product of the squared spatial-frequency median and the image area. This measure accounts for the larger number of lines, strokes, and local periodic patterns in the hieroglyphs. For outline objects the best predictor of the experimental data was complexity estimated as the number of turns in the image, as Attneave (1957 Journal of Experimental Psychology 53 221-227) obtained for his abstract outlined images. Other predictors of complexity gave significant but lower correlations with the experimental ranking. We conclude that our modeling measures can be used to estimate the complexity of visual images but for different classes of images different measures of complexity may be required.

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