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Issue No.12 - December (2011 vol.33)
pp: 2506-2520
Ping Tan , National University of Singapore, Singapore
Long Quan , Hong Kong University of Science and Technology, Hong Kong
Todd Zickler , Harvard University, Cambridge
ABSTRACT
Different materials reflect light in different ways, and this reflectance interacts with shape, lighting, and viewpoint to determine an object's image. Common materials exhibit diverse reflectance effects, and this is a significant source of difficulty for image analysis. One strategy for dealing with this diversity is to build computational tools that exploit reflectance symmetries, such as reciprocity and isotropy, that are exhibited by broad classes of materials. By building tools that exploit these symmetries, one can create vision systems that are more likely to succeed in real-world, non-Lambertian environments. In this paper, we develop a framework for representing and exploiting reflectance symmetries. We analyze the conditions for distinct surface points to have local view and lighting conditions that are equivalent under these symmetries, and we represent these conditions in terms of the geometric structure they induce on the Gaussian sphere and its abstraction, the projective plane. We also study the behavior of these structures under perturbations of surface shape and explore applications to both calibrated and uncalibrated photometric stereo.
INDEX TERMS
Reflectance symmetry, projective geometry, autocalibration, photometric stereo.
CITATION
Ping Tan, Long Quan, Todd Zickler, "The Geometry of Reflectance Symmetries", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.33, no. 12, pp. 2506-2520, December 2011, doi:10.1109/TPAMI.2011.35
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