An axiomatic approach to scalar data interpolation on surfaces

by: V Caselles, L Igual, O Sander

Numerische Mathematik, Vol. 102, No. 3. (20 January 2006), pp. 383-411.

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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.

@article{citeulike:2964530, 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.}, author = {Caselles, V. and Igual, L. and Sander, O. }, citeulike-article-id = {2964530}, doi = {10.1007/s00211-005-0656-8}, journal = {Numerische Mathematik}, keywords = {interpolation, manifold}, month = {January}, number = {3}, pages = {383--411}, posted-at = {2008-07-04 15:57:33}, priority = {2}, title = {An axiomatic approach to scalar data interpolation on surfaces}, url = {http://dx.doi.org/10.1007/s00211-005-0656-8}, volume = {102}, year = {2006} }

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TY - JOUR ID - citeulike:2964530 L3 - citeulike-article-id:2964530 TI - An axiomatic approach to scalar data interpolation on surfaces JF - Numerische Mathematik VL - 102 IS - 3 SP - 383 EP - 411 N2 - 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. KW - interpolation KW - manifold AU - Caselles, V AU - Igual, L AU - Sander, O PY - 2006/01/20/ UR - http://dx.doi.org/10.1007/s00211-005-0656-8 ER -

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