The goal of this project is the mathematical investigation of smoothness and self-similarity principles in generating natural images, the mathematical formulation and unification of both ideas in a variational form, and its application to develop models and algorithms for image processing tasks.

The proposed research will lead to the formulation and mathematical analysis of new variational principles for image and movie processing, the analysis of their underlying geometric measure theory and partial differential equations, unifying local and nonlocal approaches as respective mathematical expressions of the ideas of regularity and self-similarity. Our research will be guided by a thorough investigation of the inpainting problem (including images, video and stereo video inpainting), as a very suitable model for testing the proposed ideas.

The first practical impact will be the development of models and algorithms for 2D and 3D image and video editing and manipulation, enabling the deletion and insertion of objects. As a second impact we will provide the theoretical background and implementation of a set of algorithms for 2D to 3D conversion of video data enabling the generation of 3D content for 3D TV from existing 2D video. Due to its fundamental nature, the proposed models may impact other image and video processing areas such as denoising, restoration, optical flow computation, or stereo, that share similar challenges. 

Post-doc and PhD positions are opened in the context of this project. Interested candidates should contact Vicent Caselles (email: [email protected])