Brooks, Michael J.; Chojnacki, Wojciech; Kozera, Ryszard Circularly symmetric eikonal equations and non-uniqueness in computer vision. (English) Zbl 0799.35036 J. Math. Anal. Appl. 165, No. 1, 192-215 (1992). 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. Cited in 5 Documents MSC: 35F20 Nonlinear first-order PDEs Keywords:eikonal equation; wavefront analysis; Hamilton’s equations; computer vision; non-uniqueness result × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Brooks, M. J., Two results concerning ambiguity in shape from shading, (Proceedings of the National Conference on Artificial Intelligence. Proceedings of the National Conference on Artificial Intelligence, Washington, DC (August 22-26, 1983)), 36-39, (The American Association for Artificial Intelligence, sponsor) [2] Brooks, M. J.; Chojnacki, W.; Kozera, R., Shading without shape, Quart. Appl. Math., 50, 27-38 (1992) · Zbl 0763.35103 [3] Bruss, A. R., The eikonal equation: Some results applicable to computer vision, J. Math. Phys., 23, 890-896 (1982) · Zbl 0502.35079 [4] Deift, P.; Sylvester, J., Some remarks on the shape-from-shading problem in computer vision, J. Math. Anal. Appl., 34, 235-248 (1981) · Zbl 0485.35081 [5] Hartman, P., Ordinary Differential Equations (1973), Wiley: Wiley New York · Zbl 0125.32102 [6] Horn, B. K.P, Obtaining shape from shading information, (Winston, P. H., The Psychology of Computer Vision (1975), McGraw-Hill: McGraw-Hill New York), 115-155 [7] (Horn, B. K.P; Brooks, M. J., Shape from Shading (1989), MIT Press: MIT Press Cambridge, MA) · Zbl 0629.65125 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.