We analyze the discrete maximum principle for the Beltrami color flow. The Beltrami flow can display linear as well as nonlinear behavior according to the values of a parameter β, which represents the ratio between spatial and color distances. In general, the standard schemes fail to satisfy the discrete maximum principle. In this work we show that a nonnegative second order difference scheme can be built for this flow only for small β, i.e. linear-like diffusion. Since this limitation is too severe, we construct a novel finite difference scheme, which is not nonnegative and satisfies the discrete maximum principle for all values of β. Numerical results support the analysis.
- Color image analysis
- Discrete maximum principle
- Nonlinear parabolic differential equations
- Nonnegative finite difference scheme