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  • 1
    ISSN: 1573-1405
    Keywords: variable illumination ; object representation ; object recognition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract The appearance of an object depends on both the viewpoint from which it is observed and the light sources by which it is illuminated. If the appearance of two objects is never identical for any pose or lighting conditions, then–in theory–the objects can always be distinguished or recognized. The question arises: What is the set of images of an object under all lighting conditions and pose? In this paper, we consider only the set of images of an object under variable illumination, including multiple, extended light sources and shadows. We prove that the set of n-pixel images of a convex object with a Lambertian reflectance function, illuminated by an arbitrary number of point light sources at infinity, forms a convex polyhedral cone in IRn and that the dimension of this illumination cone equals the number of distinct surface normals. Furthermore, the illumination cone can be constructed from as few as three images. In addition, the set of n-pixel images of an object of any shape and with a more general reflectance function, seen under all possible illumination conditions, still forms a convex cone in IRn. 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 cone representation.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1573-1405
    Keywords: variable illumination ; shadows ; shape ambiguity ; object representation ; object recognition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract When an unknown object with Lambertian reflectance is viewed orthographically, there is an implicit ambiguity in determining its 3-d structure: we show that the object's visible surface f(x, y) is indistinguishable from a “generalized bas-relief” transformation of the object's geometry, $$ {\bar f} $$ (x, y) = λf(x, y) + μx + νy, and a corresponding transformation on the object's albedo. For each image of the object illuminated by an arbitrary number of distant light sources, there exists an identical image of the transformed object illuminated by similarly transformed light sources. This result holds both for the illuminated regions of the object as well as those in cast and attached shadows. Furthermore, neither small motion of the object, nor of the viewer will resolve the ambiguity in determining the flattening (or scaling) λ of the object's surface. Implications of this ambiguity on structure recovery and shape representation are discussed.
    Type of Medium: Electronic Resource
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