Terrain influences the accurate judgement of distance

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Abstract
Mathematically, three-dimensional space can be represented differently by the cartesian, polar, and other coordinate systems. However, in physical sciences, the choice of representation system is restricted by the need to simplify a machine's computation while enhancing its efficiency1. Does the brain, for the same reasons, ‘select’ the most cost-efficient way to represent the three-dimensional location of objects? As we frequentlyinteract with objects on the common ground surface, it might be beneficial for the visual system to code an object's location using a ground-surface-based reference frame2. More precisely, the brain could use a quasi-two-dimensional coordinate system (x s, y s) with respect to the ground surface (s), rather than a strictly three-dimensional coordinate system (x, y, z), thus reducing coding redundancy and simplifying computations2,3,4,5. Here we provide support for this view by studying human psychophysical performance in perceiving absolute distance and in visually directed action tasks6,7,8,9,10,11. For example, when an object was seen on a continuous, homogeneous texture ground surface, the observer judged the distance to the object accurately. However, when similar surface information was unavailable, for example, when the object was seen across a gap in the ground, or across distinct texture regions, distance judgement was impaired.

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