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**Circularly symmetric eikonal equations and non-uniqueness in computer vision.**
*(English)*
Zbl 0799.35036

Authors’ introduction: The eikonal equation
\[
\Bigl( {{\partial u} \over {\partial x}}\Bigr)^ 2 + \Bigl( {{\partial u} \over {\partial y}} \Bigr)^ 2 = {\mathcal E}(x,y),
\]
which arises naturally in wavefront analysis and in the development of special methods for integrating Hamilton’s equations (the Jacobi-Hamilton method), has long attracted the attention of physicists and mathematicians. More recently, there has been a resurgence of interest in the eikonal equation as a result of its applicability in an area of computer vision. One of the issues considered in the latter context has been that of determining whether or not a particular eikonal equation exhibits many solutions defined over a given domain. In this paper, we offer insight into this issue by presenting a non-uniqueness result of significance for the foundations of computer vision.

### MSC:

35F20 | Nonlinear first-order PDEs |

### Keywords:

eikonal equation; wavefront analysis; Hamilton’s equations; computer vision; non-uniqueness result
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\textit{M. J. Brooks} et al., J. Math. Anal. Appl. 165, No. 1, 192--215 (1992; Zbl 0799.35036)

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### References:

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[3] | Bruss, A. R., The eikonal equation: Some results applicable to computer vision, J. Math. Phys., 23, 890-896 (1982) · Zbl 0502.35079 |

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