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J. Amati, J. H. Elder; Factors affecting the discrimination and perceived attitude of multiple transparent surfaces. Journal of Vision 2001;1(3):430. doi: https://doi.org/10.1167/1.3.430.
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OBJECTIVE: In the natural world, each region of an image typically projects from a unique surface in the scene. This rule is broken when surfaces are transparent, as for water or glass. Surfaces with many gaps or holes, either at a fine scale (sheer cloth) or at a course scale (a wire fence), approximate transparency in that patches of multiple surfaces may be interleaved in the image in a complex way. While the necessary conditions for perceived transparency are well studied, little is known about how the visual system extracts the 3D geometry of these surfaces. In this study, we examine visual perception of 3-D attitude from texture for multiple, overlaid transparent surfaces. METHODS: In each trial, observers monocularly viewed transparent planar surfaces rendered in perspective within a circular window of diameter 45 degrees. Two surfaces were painted with different textures and rendered at identical slants but systematically different tilts. Subjects were asked to: i) indicate whether 1 or 2 different planar surfaces were perceived, and ii) use a mouse-controlled visual gauge figure to indicate the attitude of the perceived surface(s).
RESULTS: Data were partitioned into two groups based on whether 1 or 2 surfaces were perceived. The latter group was used to estimate statistical distributions of estimated tilt error for each textured surface in the presence of each of the other textured surfaces. Based on these data, a statistical model was constructed to predict, as a function of the surface textures and the tilt difference between the 2 surfaces, i) the incidence with which 1 vs 2 surfaces are perceived, and ii) the mean and variance of the tilt estimates for those cases in which a single fused surface is perceived. CONCLUSION: The fusion and discrimination of multiple transparent surfaces can be understood within the framework of statistical decision theory, based on estimated uncertainties in the attitude judgement of the individual surfaces.
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