Lie group of transformations to study anisotropic diffusion of scalar images
Jasobanta Jena · Lobachevskii Journal of Mathematics · 2012
Lie group of transformations associated with anisotropic diffusion equation is derived using the invariance properties. The equation is of great importance in the study of geometrical diffusion of scalar images. Infinitesimals of Lie group of transformations with respect to independent and dependent variables along with invariant surface conditions are used to obtain a general form of edge stopping function. The edge stopping functions used by Perona & Malik and their successors are obtained in particular cases. The equation in three independent variables reduced in terms of fewer independent variables.