Recent uniqueness results in shape from shading

  • Ryszard Kozera
Conference paper
Part of the Advances in Computing Science book series (ACS)


The main purpose of this paper is to discuss briefly two topics. The first one is to show that Sneddon’s claim ([9, Section 7 pp. 61]) about representability of any solution to a given first-order partial differential equation in terms of either a complete or a general or a singular integral is erroneous. The literature on complete integrals is a bewildering collection of incomplete and false statements (see e.g. Dou [6] or [9]). Recent results by Chojnacki [3] and Kozera [8] shed new light on this topic and fill a gap in the literature. The second goal of this paper is to critically inspect uniqueness results (see Brooks [1, 2]) concerning the images of a Lambertian hemisphere and a Lambertian plane, which resort to Sneddon’s erroneous assertion and as such are invalid. Finally, we adopt a different approach so that the results claimed in [1, 2], subject to minor reformulations, become valid. For a more detailed analysis an interested reader is also referred to [3] or [8].


Gaussian Curvature Singular Integral Eikonal Equation Complete Integral False Statement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag/Wien 1997

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  • Ryszard Kozera

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