Parallel Algorithm for a Nonlocal Diffusion Model Applied to a 3D Input Domain

In this paper we analyze two methods to optimize the numerical computations for the diffusion term in a nonlocal reaction-diffusion equation in case of a 3D input domain. The results are studied in the context of applying the equation to 3D image processing tasks like image restoration and segmentation. It is important to find an optimal way of computing the numerical approximation for diffusion term because, due to its integral formulation, the diffusion is computational intensive especially if the numerical analysis takes place on a large input domain with three dimensions.