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

##### 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
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