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
View graph of relations

Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)1047-1067
Journal / PublicationSIAM Journal on Mathematical Analysis
Volume45
Issue number3
Publication statusPublished - 2013
Externally publishedYes

Abstract

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

Bibliographic Note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to lbscholars@cityu.edu.hk.