We consider a functional proposed by Lauze and Nielsen (2004) for motion compensated inpainting and recently applied by the same authors to problems of video deinterlacing (2008) and video super-resolution (2011). We modify their model in order to achieve better variational properties and we study the corresponding relaxed functional, wich gives information about numerical algorithms designed for the original functional. Minimizers of the relaxed functional are vector valued functions of bounded variation, so that a video content which is discontinuous along the boundaries of moving objects can be reconstructed. Moreover, we find a representation formula of the relaxed functional which shows explicitly the role of discontinuities of the various functions involved in the variational model. Joint work with R. March.

This presentation is part of Contributed Presentation “CP5 - Contributed session 5”

Authors:

Giuseppe Riey (University of Calabria)

Keywords:

calculus of variations, computer vision, image deblurring, image reconstruction, image segmentation, motion estimation, partial differential equation models, video inpainting