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Andrew Watson, Albert Ahumada; The pyramid of visibilty. Journal of Vision 2016;16(12):567. doi: 10.1167/16.12.567.
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© ARVO (1962-2015); The Authors (2016-present)
A fundamental limit to human vision is our ability to sense variations in light intensity over space and time. A half century ago, these limits were first described systematically in a series of three seminal papers. de Lange (1958), van Nes and Bouman (1967), and Robson (1966) measured the visibility of temporal, spatial, and joint spatio-temporal sinusoidal variations. Additionally, the first two papers described the dependence of sensitivity on the the light level from which the deviations occurred. These results provided an enduring foundation for all subsequent studies of contrast sensitivity. We have recently reanalyzed these reports and discovered a remarkable simplification. At moderate to high frequencies the log of contrast sensitivity is a linear function of spatial frequency, temporal frequency, and the log of adapting luminance. As a surface in the space defined by spatial and temporal frequency, log sensitivity thus forms a rectangular pyramid. Almost 40 years ago, Kulikowski (1971) also noted these linear relationships in his own data, but his result appears not to have been widely appreciated. Elsewhere we have described the intersection of this surface with a plane at a contrast of 1 as the "window of visibility." (Watson, Ahumada & Farrell 1986; Watson 2013). The new linear formulation allows us to describe the complete surface as the "pyramid of visibility." The height of the pyramid rises linearly with the log of adapting luminance. As a result, the window of visibility is always a diamond that grows and shrinks, linearly, with the log of adapting luminance. This result has both theoretical significance and practical utility. The independence of spatial, temporal, and light level effects constrains models of visual processing, while the limits defined by the pyramid of visibility determine the ultimate spatial and temporal resolution required in electronic displays of static or moving imagery.
Meeting abstract presented at VSS 2016
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