M.Sc Thesis

M.Sc StudentKrengel Ofir
SubjectInpainting of Surfaces and Images
DepartmentDepartment of Electrical and Computer Engineering
Supervisor PROFESSOR EMERITUS Yehoshua Zeevi
Full Thesis textFull thesis text - English Version


Inpainting, the technique of modifying an image in an undetectable from, is as ancient as art itself. Inpainting of images, represented as surfaces, has been studied extensively by the application of a two-dimensional Laplacian operator, including in the context of its discrete representation on surfaces. Considering the shortcomings with regard to errors and computational complexity of the strictly-two-dimensional approaches, we propose a one-dimensional-based multi-line approach, wherein the set of lines covers the region of inpainting and its boundaries. Similarly to other inpainting techniques, after the user selects the regions to be completed, the algorithm fills-in these regions with information determined by what is found on their boundaries. Like other smooth surface completion methods, the multi-line uses the Laplacian kernel. But, unlike diffusion method, the multi-line approach uses the Laplacian in its one-dimensional form. Furthermore, unlike diffusion methods, the multi-line approach is guaranteed to be stable and to converge. Instead of using an iterative process, the proposed method requires a simple matrix inversion that can be executed easily with minimal effort. This renders the algorithm to be suitable for real-time applications. We present the implementation of the proposed approach and address its limitations. We also compare it with some other common approaches. Next, we calculate and compare the computational complexity with those that are characteristic of other approaches and show that our approach has the lowest computational complexity. The multi-line framework is implemented on smooth surfaces and on images where the results, with and without noise, are found to be superior to the previously published results. Finally, additional promising directions for future work, such as different one-dimensional representations, are discussed.