Efficient anisotropic α-Kernels decompositions and flows

Abstract

The Laplacian raised to fractional powers can be used to generate scale spaces as was shown in recent literature. This was later extended for inhomogeneous diffusion processes and more general functions of the Laplacian and studied for the Perona-Malik case. In this paper we extend the results to the truly anisotropic Beltrami flow. We additionally introduce a technique for splitting up the work into smaller patches of the image which greatly reduce the computational complexity and allow for the parallelization of the algorithm. Important issues involved in the numerical implementation are discussed.