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Ellen Svarverud, Stuart J. Gilson, Andrew Glennerster; Breaking space: Intransitivity of distance judgements. Journal of Vision 2009;9(8):73. doi: 10.1167/9.8.73.
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© ARVO (1962-2015); The Authors (2016-present)
Many experiments support the idea that observers generate a distorted representation of space, but the proposed transformation between physical and perceived space is generally a simple homography (i.e. a 1:1 mapping between points). Here, we show that perceived space can ‘break’ in such a way that the perceived distances of two objects can, at the same time, obey both D1 [[gt]] D2 and D1 2. We demonstrate this in the unusual situation of an expanding virtual room (Glennerster et al, 2006, Current Biology 16(4), 428–432), which appears stable to observers despite large changes in size.
In an immersive virtual reality environment, observers in a brick-textured room viewed a reference square in one interval and judged whether a comparison square in the second interval was closer or farther away. The virtual room was visible throughout the trial and it either remained static or increased in size by a factor of 4 between intervals. The squares were placed either in the middle of the room or adjacent to the wall, where the effect of room expansion on distance judgements was greater. Interleaving 4 different psychometric functions, we determined the distances at which 4 pairs of objects were perceived to be at the same distance, allowing us to infer the relative perceived distance of two objects (O1 and O3) via two different intermediate objects. Specifically, the ordering of perceived distances of the objects was O1 [[gt]] O2a [[gt]] O3, while simultaneously O1 2b 3. Thus, our results demonstrate a paradoxical, intransitive ordering of perceived distance and challenge the idea of a single representation of visual space.
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