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Impossible Shaded Images
February 1993 (vol. 15 no. 2)
pp. 166-170

It is shown that shaded images that cannot have originated from a uniformly illuminated, smooth continuous surface with uniform albedo exist. The typical condition where this occurs is when a dark area (corresponding to a region of high gradient) is surrounded by a lighter region (with low gradient). For this to correspond to a real surface, it must be established that there is a local extremum or area of lower gradient inside the dark region. This, in turn, will show up as either a light area in the image or an orientation discontinuity in the surface (thus violating either intensity or smoothness constraints). The impossibility of a shaded image can be established by counting the number of extrema inside a region corresponding to an isolated surface patch.

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Index Terms:
shaded images; local extremum; lower gradient; light area; orientation discontinuity; isolated surface patch; image recognition
B.K.P. Horn, R.S. Szeliski, A.L. Yuille, "Impossible Shaded Images," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 2, pp. 166-170, Feb. 1993, doi:10.1109/34.192489
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