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Silvio Savarese, Fei Fei Li, Pietro Perona; Can we see the shape of a mirror?. Journal of Vision 2003;3(9):74. doi: 10.1167/3.9.74.
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© 2016 Association for Research in Vision and Ophthalmology.
The three-dimensional shape of a surface may be perceived from a monocular static image. Contours, shading, texture gradients, perspective and occlusion are well-studied cues to this percept. When looking at the surface of a smooth reflecting object, such as a well washed car, one additional cue is potentially available: the surrounding scene is reflected, and the deformation of this reflection is a function of the shape of the object's surface. Is this cue used by the human visual system? May it be used in isolation, i.e. when other visual cues are not available?
In order to investigate this question we asked a number of human observers to discriminate between images of mirror surfaces of qualitatively different shapes: a sphere, a cylinder and the neck of a vase. Such shapes have positive, zero and negative Gaussian curvature and reflect the same scene with distinctly different distortions. The experimental stimuli were 144 photographs of large patches of each mirror surface reflecting one of six regular patterns which had been shown to the subjects in advance. Each patch was obtained by vignetting one of the photographs using irregularly shaped boundaries, in order to eliminate occluding boundary information. It was viewed monocularly and centrally on a standard computer monitor for 1 second. Each patch subtended in average a visual angle of 20 degrees. The subjects were instructed to respond to three forced alternative choices (sphere, cylinder, vase).
Our subjects are only slightly better than chance in discriminating such shape differences. Our ideal observer analysis indicates that mirror reflections allow recovery of depth, tangent plane and surface curvature when the surrounding world has a known shape.
However, when the surrounding world is (partially) unknown, the problem is underconstrained and many solutions are possible. Our experiments confirm this analysis indicating that mirror reflections are a weak cue for most human observers when additional information is not available.
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