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.


35F20 Nonlinear first-order PDEs
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