Anisotropic Diffusion Stencils: From Simple Derivations over Stability Estimates to ResNet Implementations

arXiv:2309.05575v3 Announce Type: replace-cross
Abstract: Anisotropic diffusion processes with a diffusion tensor are important in image analysis, physics, and engineering. However, their numerical approximation has a strong impact on dissipative artefacts and deviations from rotation invariance. In this work, we study a large family of finite difference discretisations on a 3 x 3 stencil. We derive it by splitting 2-D anisotropic diffusion into four 1-D diffusions. The resulting stencil class involves one free parameter and covers a wide range of …

abstract analysis approximation arxiv cs.lg cs.na difference diffusion eess.iv engineering family however image impact math.na numerical physics processes resnet rotation simple stability study tensor type work