Navier-stokes, fluid dynamics, and image and video inpainting

Abstract

Image inpainting involves filling in part of an image or video using information from the surrounding area. Ap- plications include the restoration of damaged photographs and movies and the removal of selected objects. In this pa- per, we introduce a class of automated methods for digital inpainting. The approach uses ideas from classical fluid dy- namics to propagate isophote lines continuously from the exterior into the region to be inpainted. The main idea is to think of the image intensity as a 'stream function' for a two-dimensionalincompressible flow. The Laplacian of the image intensity plays the role of the vorticity of the fluid; it is transported into the region to be inpainted by a vec- tor field defined by the stream function. The resulting al- gorithm is designed to continue isophotes while matching gradient vectors at the boundary of the inpainting region. The methodis directly based on the Navier-Stokes equations for fluid dynamics, which has the immediate advantage of well-developed theoretical and numerical results. This is a new approach for introducing ideas from computational fluid dynamics into problems in computer vision and image analysis.