Inserted: 26 jun 2017
Last Updated: 26 jun 2017
We study a variational problem for simultaneous video inpainting and motion estimation. We consider a functional proposed by Lauze and Nielsen $$ and we study, by means of the relaxation method of the Calculus of Variations, a slightly modified version of this functional. The domain of the relaxed functional is constituted of functions of bounded variation and we compute a representation formula of the relaxed functional. The representation formula shows the role of discontinuities of the various functions involved in the variational model. The present study clarifies the variational properties of the functional proposed in $$ for motion compensated video inpainting.