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A Note on Existence and Uniqueness in Shape from Shading

Ryszard Kozera
ICCV 1993 pp. 507-511
doi:10.1109/ICCV.1993.378171 /iccv/1993/kozera1993iccv-note/

Abstract

Shape recovery of a smooth Lambertian surface illuminated by one, two, or three distant light sources is discussed. In the case of three light-sources, it is shown that the corresponding system of three first-order nonlinear partial differential equations has a unique solution. In the case of one overhead light-source, the existence and uniqueness of solutions to the corresponding eikonal equation are discussed. With regard to existence, two classes of shading patterns are shown for which no genuine shapes exist. In connection with uniqueness, circularly symmetric eikonal equations are revealed for which there exist circularly symmetric and non-circularly symmetric smooth solutions of special form.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

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Cite

Text

Kozera. "A Note on Existence and Uniqueness in Shape from Shading." IEEE/CVF International Conference on Computer Vision, 1993. doi:10.1109/ICCV.1993.378171

Markdown

[Kozera. "A Note on Existence and Uniqueness in Shape from Shading." IEEE/CVF International Conference on Computer Vision, 1993.](https://mlanthology.org/iccv/1993/kozera1993iccv-note/) doi:10.1109/ICCV.1993.378171

BibTeX

@inproceedings{kozera1993iccv-note,
  title     = {{A Note on Existence and Uniqueness in Shape from Shading}},
  author    = {Kozera, Ryszard},
  booktitle = {IEEE/CVF International Conference on Computer Vision},
  year      = {1993},
  pages     = {507-511},
  doi       = {10.1109/ICCV.1993.378171},
  url       = {https://mlanthology.org/iccv/1993/kozera1993iccv-note/}
}