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Yaniv Morgenstern, Richard F. Murray, Wilson S. Geisler; A low-dimensional statistical model of natural lighting. Journal of Vision 2011;11(11):377. doi: https://doi.org/10.1167/11.11.377.
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© ARVO (1962-2015); The Authors (2016-present)
The visual system has shape and lightness constancy over a wide range of lighting conditions. The visual system is thought to achieve constancy partially by relying on assumptions about regularities in natural lighting. Natural light is complex, but for some purposes, such as understanding shading of Lambertian objects, only low-frequency lighting patterns are relevant (Basri and Jacobs, 2001; Ramamoorthi and Hanrahan, 2001). METHODS: We used a multidirectional photometer to make measurements of real-world lighting. The multidirectional photometer is a 20 cm diameter aluminum sphere, mounted with 64 approximately evenly spaced photodiodes. We modelled the lighting measurements as a sum of the first three orders of spherical harmonics, and then decomposed them into the scalar, vector, and tensor representation developed by Mury, Pont, and Koenderink (2007). The latter representation gives a principled way of visualizing the light field with a scalar component that describes ambient illumination, a light vector that describes the magnitude and direction of maximum light transfer, and a tensor component that varies in shape and direction. RESULTS: We find several new regularities in natural illumination. The power of the vector and tensor components are strongly correlated. The vector and tensor components usually peak in approximately the same direction, and the difference in their directions is strongly correlated with the power of the vector. The shape of the tensor has a strong tendency to be a small subset of its theoretically possible shapes, and within this subset the shape of the tensor is strongly correlated with the power of the vector. CONCLUSIONS: Our findings reveal significant new structures in natural lighting that the visual system can rely on to solve underconstrained problems like perception of shape, reflectance, and material. We will discuss what properties of real-world scenes may be responsible for these strong regularities in natural lighting.
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