Inpainting of surfaces and Images

Inpainting of images, represented on surfaces, was previously considered successfully by the application of a two-dimensional Laplacian operator, including in the context of the discrete representation on surfaces. Considering the shortcoming of errors and computational complexity of the strictly-two-dimensional approaches, we propose a one-dimensional-based multi-line approach, wherein the set of lines cover the region of inpainting and its boundaries. The multi-line framework is implemented on smooth and non-smooth surfaces and on images and the results are found to be superior to the previously published results. Additional possible one-dimensional representations are discussed.