A Theory of Specular Surface Geometry

  • Authors:
  • Michael Oren;Shree K. Nayar

  • Affiliations:
  • Department of Computer Science, Columbia University, New York, N.Y. 10027. E-mail: oren@cs.columbia.edu, nayar@cs.columbia.edu;Department of Computer Science, Columbia University, New York, N.Y. 10027. E-mail: oren@cs.columbia.edu, nayar@cs.columbia.edu

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 1997

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Abstract

A theoretical framework is introduced for the perception of specularsurface geometry. When an observer moves in three-dimensional space,real scene features such as surface markings remain stationary withrespect to the surfaces they belong to. In contrast, a virtualfeature which is the specular reflection of a real feature, travelson the surface. Based on the notion of caustics, a featureclassification algorithm is developed that distinguishes real andvirtual features from their image trajectories that result fromobserver motion. Next, using support functions of curves, aclosed-form relation is derived between the image trajectory of avirtual feature and the geometry of the specular surface it travelson. It is shown that, in the 2D case, where camera motion and thesurface profile are coplanar, the profile is uniquely recovered bytracking just two unknown virtual features. Finally, these resultsare generalized to the case of arbitrary 3D surface profiles that aretraveled by virtual features when camera motion is not confined to aplane. This generalization includes a number of mathematical resultsthat substantially enhance the present understanding of specularsurface geometry. An algorithm is developed that uniquely recovers 3Dsurface profiles using a single virtual feature tracked from theoccluding boundary of the object. All theoretical derivations andproposed algorithms are substantiated by experiments.