Geodesic path based digital inpainting

The filling-in technique has been used since the Renascence period and its main goal is to reconstruct missing parts or damaged areas in an image in such a way as to restore its harmony. In artwork restoration, this process is called inpainting. After the original work of Bertalmio, Sapiro, Caselles and Ballester several different approaches have been used to tackle the digital inpainting problem. Some are based on Partial Differential Equations to model a transportation process and a diffusion process, others are based on the Euler elastica functional. This paper presents a model for completing missing parts using the geodesic path continuation to perform the filling-in of the inpainting domain D. The model is proposed in a way as to satisfy the “Connectivity Principle”. The image u(x,y) is represented by a family of level lines and the missing part of the image is filled-in by the propagation of the available surrounding information, from outside to inside of the inpainting domain D along the geodesic paths of the image. After defining the domain D the restoration process becomes automatic and the final result u(x,y,tn) is carried out by the evolutionary process starting with the initial degraded image u(x,y,0). In the proposed model, no limitations are imposed on the topology of the domain D, even permitting holes within the domain. Examples on real and textured images show the performance of this proposed model.