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Journal of Mathematical Physics / Volume 23 / Issue 5

J. Math. Phys. 23, 890 (1982); http://dx.doi.org/10.1063/1.525441 (7 pages)

The eikonal equation: some results applicable to computer vision

Anna R. Bruss

Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

In this paper we investigate certain first order partial differential equations which formulate the relationship between the light reflected from a surface and its shape. Particular emphasis is given to eikonal equations. Two results are presented. First, we prove that a special type of eikonal equation has only one convex and positive C2 solution in some neighborhood of a singular point. Using this result, we show that a restricted form of this equation has exactly two solutions. These results have application in scanning electron microscopy.

KEYWORDS and PACS

Keywords

SURFACES, IMAGE PROCESSING, LIGHT TRANSMISSION, REFLECTION, DIFFERENTIAL EQUATIONS, EIKONAL APPROXIMATION, ANALYTICAL SOLUTION, USES, ELECTRON MICROSCOPY, ELECTRON SCANNING

PACS

  • 42.25.Gy

    Edge and boundary effects; reflection and refraction

  • 42.30.Va

    Image forming and processing

  • 74.20.-z

    Theories and models of superconducting state

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.525441

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

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