What Is the Set of Images of an Object Under All Possible Illumination Conditions?

  • Authors:

  • Peter N. Belhumeur;David J. Kriegman

  • Affiliations:

  • Center for Comp. Vision and Control, Dept. of Electrical Engineering, Yale University, New Haven CT 06520;Center for Comp. Vision and Control, Dept. of Electrical Engineering, Yale University, New Haven CT 06520

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 1998

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Abstract

The appearance of an object depends on both the viewpoint from whichit is observed and the light sources by which it is illuminated. If theappearance of two objects is never identical for any pose or lightingconditions, then–in theory–the objects can always bedistinguished or recognized. The question arises: What is the set of imagesof an object under all lighting conditions and pose? In this paper, weconsider only the set of images of an object under variable illumination,including multiple, extended light sources and shadows. We prove that theset of n-pixel images of a convex object with aLambertian reflectance function, illuminated by an arbitrary number of pointlight sources at infinity, forms a convex polyhedral cone in R^n and that the dimension of this illuminationcone equals the number of distinct surface normals. Furthermore, theillumination cone can be constructed from as few as three images. Inaddition, the set of n-pixel images of an object of any shapeand with a more general reflectance function, seen under all possibleillumination conditions, still forms a convex cone in R^n. Extensions of these results to color images are presented.These results immediately suggest certain approaches to object recognition.Throughout, we present results demonstrating the illumination conerepresentation.