A proof of equivalence between level lines shortening and curvature motion in image processing

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

3 Scopus Citations
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Original languageEnglish
Pages (from-to)1047-1067
Journal / PublicationSIAM Journal on Mathematical Analysis
Issue number3
Publication statusPublished - 2013
Externally publishedYes


In this paper we define the continuous Level Lines Shortening evolution of a twodimensional image as the curve shortening operator acting simultaneously and independently on all the level lines of the initial data, and we show that it computes a viscosity solution for the mean curvature motion. This provides an exact analytical framework for its numerical implementation, which runs on line on any image at http://www.ipol.im. Analogous results hold for its affine variant version, the Level Lines Affine Shortening. © 2013 Society for Industrial and Applied Mathematics.

Research Area(s)

  • Affine curvature motion, Affine shortening, Curve shortening, Level lines, Mean curvature motion, Partial differential equations, Topographic maps

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