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Michelle To, P. George Lovell, Tom Troscianko, David Tolhurst; Minkowski summation of cues in complex visual discriminations using natural scene stimuli. Journal of Vision 2007;7(9):968. doi: https://doi.org/10.1167/7.9.968.
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© ARVO (1962-2015); The Authors (2016-present)
Quick's vector magnitude model (1974, Kybernetik 16, 65–67) suggests that the detectability of a compound visual stimulus can be estimated by nonlinearly summing the detectability of the component elements. We investigated whether this could be extended to suprathreshold tasks using complex natural images. In three discrimination experiments, observers made subjective ratings of the difference between many naturalistic image pairs. Each experiment comprised combination groups that were composed of three image pairs: in two pairs the images differed along different single dimensions; the third pair was a composite, differing along both dimensions (e.g. change of object colour in Pair 1; change of image blur in Pair 2; and changes of both colour and blur in Pair 3). We investigated whether the ratings for composite pairs could be predicted by combining the ratings from their respective component pairs. In Experiment 1, 11 observers were presented with a wide variety of image pairs (900) that included 136 combination sets. The ratings for component pairs accurately predicted the ratings for the 136 combination pairs using Minkowski summation with an exponent of 2.78. Similar results were obtained in Experiment 2 when repeating the procedure using colour-distorted and inverted image pairs on 11 new observers (best Minkowski exponent of 2.79). In Experiment 3, 15 observers were retested on 432 new combination sets, generated from 6 parent images by summing coupled cues in various proportions (best Minkowski exponent of 2.95). When all 704 combination sets were compiled, Minkowski summation with an exponent of 2.84 had the strongest predictive power, a value similar to that previously reported in compound grating detection experiments. The correlation coefficient between predicted and measured combination-pair ratings was 0.96. This suggests that vision theories for detecting simple stimuli can be extended to more complex types of visual processing.
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