Approximating Non-linear Diffusion

We assess the feasibility of approximating non-linear diffusion processes with simple local Gaussian filters. The purpose of doing this is twofold. Firstly, the theoretical implications are by themselves interesting. Secondly, a successful method would reduce the need for computationally expensive implementations of non-linear diffusion schemes. We evaluate using isotropic and affine Gaussian filters for the task of approximating the local diffusion for a number of non-linear diffusion schemes. The approximations are firstly explored using an information theoretical approach and secondly evaluated based on their performance on a multi-scale segmentation application.

The results show that while the approximations do not perform quite as well as the original non-linear scheme, the decrease in performance is acceptable for the evaluated task. Furthermore, the affine approximations perform significantly better than the isotropic.