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Charles Chubb, Charles E. Wright; A regular grid imposes a city-block metric on visual space. Journal of Vision 2005;5(8):969. doi: 10.1167/5.8.969.
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© ARVO (1962-2015); The Authors (2016-present)
Purpose. To measure the metric imposed on visual space by the processes that group a grid of points into rows and columns. Method. On each trial the observer viewed (for 200 ms) a grid of small dots (Gaussian blobs), some of which were displaced from their expected locations. On any given trial, either 84 or 108 dots were perturbed, and the subject judged, with feedback, which type of grid had been presented. Dot perturbations all had length equal to 18.75% of the horizontal inter-dot distance but varied in direction over the 16 angles, 0, 22.5, 45, …, 237.5 deg. There were thirty conditions using different histograms of displacement directions, with prescribed displacements assigned randomly to grid-dots on a given trial. From the data we estimate the average impact (in multiples of d') exerted on judgments by displacements in different directions. We take these impacts to reflect the distances in visual space traversed by different displacements. In Expt. 1 the mean grid was 16 by 16, with equal horizontal and vertical spacing. In Expt. 2, the mean grid had 11 rows and 14 columns, with rows 1.25 times farther apart than columns. Results & Conclusions. In Expt. 1, the visual distance traversed by a displaced dot was found to be equal to the sum of the separate distances traversed by the dot in the horizontal and vertical directions. Thus, for example, a diagonal displacement exerted sqrt(2) times the impact of a vertical displacement. We conclude that a regular grid of points imposes a city-block metric on visual space. When rows were 25% farther apart than columns, displacements closer to horizontal than diagonal obeyed a city-block metric as observed in Expt. 1. However, displacements ranging from diagonal up to vertical did not: the visual distance traversed by such a displacement depended only on its vertical projection.
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