An axiomatic approach to scalar data interpolation on surfaces |
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Authors: | V Caselles L Igual O Sander |
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Institution: | 1. Dept. de Tecnologia, University of Pompeu-Fabra, Passeig de Circumval.lació, 8, 08003, Barcelona, Spain 2. Institut für Mathematik II, Freie Universit?t Berlin, Arnimallee 2-6, 14195, Berlin, Germany
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Abstract: | We discuss possible algorithms for interpolating data given on a set of curves in a surface of ℝ3. We propose a set of basic assumptions to be satisfied by the interpolation algorithms which lead to a set of models in terms
of possibly degenerate elliptic partial differential equations. The Absolutely Minimizing Lipschitz Extension model (AMLE)
is singled out and studied in more detail. We study the correctness of our numerical approach and we show experiments illustrating
the interpolation of data on some simple test surfaces like the sphere and the torus. |
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Keywords: | 68U10 35J60 65D05 65N06 |
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