Gradually varied surface and its optimal uniform approximation

Li Chen

doi:10.1117/12.171078

23 March 1994 Gradually varied surface and its optimal uniform approximation

Li Chen

Proceedings Volume 2182, Image and Video Processing II; (1994) https://doi.org/10.1117/12.171078
Event: IS&T/SPIE 1994 International Symposium on Electronic Imaging: Science and Technology, 1994, San Jose, CA, United States

Abstract

A new digital surface called the gradually varied surface is introduced and studied in digital spaces, especially in digital manifolds. In this paper, we have proved a constructive theorem: Let i_(Sigma) _m be an indirectly adjacent grid space. Given a subset J of D and a mapping f_J : J yields i_(Sigma) _m, if the distance of any two points p and q in J is not less than the distance of f_J(p) and f_J(q) in i_(Sigma) _m, then there exists an extension mapping f of f_J, such that the distance of any two points p and q in D is not less than the distance of f(p) and f(q) in i_(Sigma) _m, we call such f a gradually varied surface. We also show that any digital manifold (graph) can normally immerse an arbitrary tree T. Furthermore, we discuss the gradually varied function. An envelop theorem, a uniqueness theorem, and an extension theorem concerned with having the same norm are obtained. Finally, we show an optimal uniform approximation theorem of gradually varied functionals and develop an efficient algorithm for the approximation.

Citation Download Citation

Li Chen "Gradually varied surface and its optimal uniform approximation", Proc. SPIE 2182, Image and Video Processing II, (23 March 1994); https://doi.org/10.1117/12.171078

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