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On the numerical approximation of the length of (implicit) level curves. (English) Zbl 1203.65040
Summary: The evaluation of the length of a curve, represented in an Eulerian way as the zero level set of an implicit function, depends mainly on the representation of the curve. We propose a parameter to measure the complexity of the curve, and therefore the accuracy of the evaluation, based on the evolution of the representation in different scales. We analyze this parameter, its properties and its relations with the regularity of the curve.

MSC:
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
68W40 Analysis of algorithms
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