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Feitong Yang, Jonathan Flombaum; Polar coordinates as the format of spatial representation in visual perception. Journal of Vision 2018;18(10):21. doi: 10.1167/18.10.21.
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© ARVO (1962-2015); The Authors (2016-present)
Does perception describe locations as orthogonal distances from an origin, a Cartesian format; or does it employ Polar descriptions, a distance from the origin with angular bearings? Are these representations even distinguishable? After all, they are isomorphic: any representation in one format can be translated to the other. As inputs to template matching routines, however, they differ in terms of which templates are described linearly vs nonlinearly. We reasoned that linear templates should be more easily matched than nonlinear. We therefore replicated and extended experiments on the identification of overlapping Glass patterns. Participants recognized circular and radial patterns more easily than line patterns, consistent with the Polar coordinate hypothesis wherein circle and radial patterns have linear descriptions. We further examined the hypothesis by considering it as an explanation for Vernier acuity performance. Across a wide range of conditions, including Vernier stimuli placed on oblique axes, we found significant biases to report alignment for stimuli that are misaligned towards the circumference of the circle defined by fixation —stimuli misaligned in Cartesian terms, but aligned (i.e. linearly related) in Polar terms. Finally, we examined noisy responses in simple localization tasks. Variances of responses were better explained by a model which drew responses from noisy Polar representations compared to Cartesian, except for localization by saccade, where the Cartesian model was better. This contrast demonstrates that Cartesian and Polar representations can be distinguished, and that different systems can rely on different representational formats. Discussing representations, Marr (1982) made the point that: "how information is represented can greatly affect how easy it is to do different things with it." Our results suggest that the format of visual-spatial representation makes it easy to do things that are linear in Polar terms.
Meeting abstract presented at VSS 2018
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