Calculus of Variations and Geometric Measure Theory

R. March - G. Riey

Analysis of a variational model for motion compensated inpainting

created by march on 26 Jun 2017
modified on 14 Feb 2018


Published Paper

Inserted: 26 jun 2017
Last Updated: 14 feb 2018

Journal: Inverse Problems and Imaging
Volume: 11
Number: 6
Pages: 997-1025
Year: 2017
Doi: 10.3934/ipi.2017046


We study a variational problem for simultaneous video inpainting and motion estimation. We consider a functional proposed by Lauze and Nielsen $[25]$ and we study, by means of the relaxation method of the Calculus of Variations, a slightly modified version of this functional. The domain of the relaxed functional is constituted of functions of bounded variation and we compute a representation formula of the relaxed functional. The representation formula shows the role of discontinuities of the various functions involved in the variational model. The present study clarifies the variational properties of the functional proposed in $[25]$ for motion compensated video inpainting.