Four-Dimensional Anisotropic Diffusion Framework With PDEs for Light Field Regularization and Inverse Problems

In this paper, we consider the problem of vector-valued regularization of light fields based on PDEs. We propose a regularization method operating in the four-dimensional (4-D) ray space that does not require prior estimation of disparity maps. The method performs a PDE-based anisotropic diffusion along directions defined by local structures in the 4-D ray space. We analyze light field regularization in the 4-D ray space using the proposed 4-D anisotropic diffusion framework by first considering a light field toy example, i.e., a tesseract. This simple light field example allows an in-depth analysis of how each eigenvector influences the diffusion process. We then illustrate the diffusion effect for several light field processing applications: denoising, angular, and spatial interpolation, regularization for enhancing disparity estimation as well as inpainting.