We discuss possible algorithms for interpolating data given in a set of curves and/or points in the plane. 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 Absolute Minimal Lipschitz Extension model (AMLE) is singled out and studied in more detail. We show experiments suggesting a possible application, the restoration of images with poor dynamic range. We also analyse the problem of unsmooth interpolation and show how it permits a subsidiary variational method.
@article{SEDP_1997-1998____A12_0,
author = {Caselles, Vicent and Masnou, Simon and Morel, Jean-Michel and Sbert, Catalina},
title = {Image {Interpolation}},
journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
note = {talk:12},
pages = {1--15},
publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {1997-1998},
zbl = {1058.65020},
mrnumber = {1660525},
language = {en},
url = {http://archive.numdam.org/item/SEDP_1997-1998____A12_0/}
}
TY - JOUR AU - Caselles, Vicent AU - Masnou, Simon AU - Morel, Jean-Michel AU - Sbert, Catalina TI - Image Interpolation JO - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:12 PY - 1997-1998 SP - 1 EP - 15 PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://archive.numdam.org/item/SEDP_1997-1998____A12_0/ LA - en ID - SEDP_1997-1998____A12_0 ER -
%0 Journal Article %A Caselles, Vicent %A Masnou, Simon %A Morel, Jean-Michel %A Sbert, Catalina %T Image Interpolation %J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" %Z talk:12 %D 1997-1998 %P 1-15 %I Centre de mathématiques Laurent Schwartz, École polytechnique %U http://archive.numdam.org/item/SEDP_1997-1998____A12_0/ %G en %F SEDP_1997-1998____A12_0
Caselles, Vicent; Masnou, Simon; Morel, Jean-Michel; Sbert, Catalina. Image Interpolation. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1997-1998), Exposé no. 12, 15 p. http://archive.numdam.org/item/SEDP_1997-1998____A12_0/
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