Inpainting digital models have been since the late 1990's a powerful image reconstruction tool for missing data. After the original work of Bertalmio, Sapiro, Caselles and Ballester [Image Inpainting] several different approaches have been used to tackle the problem. Some are based on Partial Differential Equations to model a transport process and a diffusion process, others are based on the Euler elastica functional. This paper presents a model using the level lines 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 level lines of the image. After defining the domain D the restoration process becomes automatic and the final result u(x; y; t_n) is carried out by the evolutionary process starting with the initial degraded image u(x; y; 0). Examples on real and textured images show the performance of this proposed model.