Finite volume schemes for the affine morphological scale space (AMSS) model (Q2068667)

The authors consider an affine curvature evolution equation. It is nonlinear and degenerate. In addition to the use of the so-called Evans-Spruck regularization, they use another one. This is done to avoid zero values in denominator. The space discretization is performed using the finite volume mesh introduced in [\textit{R. Eymard} et al., in: Solution of equations in \(\mathbb{R}^n\) (Part 3). Techniques of scientific computing (Part 3). Amsterdam: North-Holland/ Elsevier. 713--1020 (2000; Zbl 0981.65095)]. Four schemes are considered, namely explicit, semi-implicit, fully-implicit and Crank-Nicolson. The stability is proved for explicit and implicit schemes. However, the stability has not yet proved for the Crank-Nicolson scheme. Some numerical examples are presented to support the convergence and convergence order.