A Theory of Specular Surface Geometry

13 years 7 months ago

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Atheoreticalframeworkisintroducedfortheperceptionofspecularsurfacegeometry.Whenanobserver moves in three-dimensional space, real scene features such as surface markings remain stationary with respect to the surfaces they belong to. In contrast, a virtual feature which is the specular reﬂection of a real feature, travels on the surface. Based on the notion of caustics, a feature classiﬁcation algorithm is developed that distinguishes real and virtual features from their image trajectories that result from observer motion. Next, using support functions of curves, a closed-form relation is derived between the image trajectory of a virtual feature and the geometry of the specular surface it travels on. It is shown that, in the 2D case, where camera motion and the surface proﬁle are coplanar, the proﬁle is uniquely recovered by tracking just two unknown virtual features. Finally, these results are generalized to the case of arbitrary 3D surface proﬁles that are traveled by virtual...

Michael Oren, Shree K. Nayar

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