Semi-implicit complementary volume scheme for solving level set like equations in image processing and curve evolution. (English) Zbl 1065.65105

Handlovičová, Angela; Mikula, Karol; Sgallari, Fiorella

Numer. Math. 93, No. 4, 675-695 (2003).

The authors introduce a linear semi-implicit complementarity volume numerical scheme for solving a level-set like nonlinear diffusion equation arising from image processing and curvature evolution problems. The equation is first linearized and by using a finite difference scheme in time \(t\), and the finite volume discretization in space is then applied to the linearized equation. Stability and existence of the generalized solution are proved mathematically. Various numerical examples are also presented to demonstrate the usefulness of the method.

Reviewer: Song Wang (Nedlands)

MSC:

65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35K55	Nonlinear parabolic equations
94A08	Image processing (compression, reconstruction, etc.) in information and communication theory

Keywords:

semi-implicit complementarity volume scheme; nonlinear degenerate diffusion equations; image processing; level set; mean curvature flow; finite difference scheme; stability; numerical examples