Guy Gilboa (Mathematics, UCLA)
Variational and PDE-based methods have been extensively used for vision and image-processing tasks such as denoising, segmentation, inpainting, optical flow and more. An underlying assumption is the (piecewise) local correlation between pixels in typical images.
Images also exhibit nonlocal correlations in repetitive structures and textures. A coherent mathematical framework for nonlocal regularization will be presented in this talk, which stems from graph theory. The notions of nonlocal derivatives, diffusion processes and regularizers will be defined and used for various image processing applications.