Error estimates of a fully discrete linear approximation scheme for Stefan problem.
Error estimates of a linear approximation scheme for nonlinear diffusion problems.
Two approaches for the approximation of the nonlinear smoothing term in the image segmentation
Purpose of the paper is to study nonlinear smoothing term initiated in [3], [4], [6] and [7] for problems of image segmentation and missing boundaries completion. The generalization of approach presented in [1] is proposed and applied in the field of image segmentation. So called regularised Riemannian mean curvature flow equation is studied and the construction of the numerical scheme based on the finite volume method approach is explained. The principle of the level set, for the first time given...
Perona-Malik equation: properties of explicit finite volume scheme
The Perona–Malik nonlinear parabolic problem, which is widely used in image processing, is investigated in this paper from the numerical point of view. An explicit finite volume numerical scheme for this problem is presented and consistency property is proved.
Nonlinear Tensor Diffusion in Image Processing
This paper presents and summarize our results concerning the nonlinear tensor diffusion which enhances image structure coherence. The core of the paper comes from [3, 2, 4, 5]. First we briefly describe the diffusion model and provide its basic properties. Further we build a semi-implicit finite volume scheme for the above mentioned model with the help of a co-volume mesh. This strategy is well-known as diamond-cell method owing to the choice of co-volume as a diamondshaped polygon, see [1]. We...
Stability and consistency of the semi-implicit co-volume scheme for regularized mean curvature flow equation in level set formulation
We show stability and consistency of the linear semi-implicit complementary volume numerical scheme for solving the regularized, in the sense of Evans and Spruck, mean curvature flow equation in the level set formulation. The numerical method is based on the finite volume methodology using the so-called complementary volumes to a finite element triangulation. The scheme gives the solution in an efficient and unconditionally stable way.
Numerical analysis of a semi-implicit DDFV scheme for the regularized curvature driven level set equation in 2D
Stability and convergence of the linear semi-implicit discrete duality finite volume (DDFV) numerical scheme in 2D for the solution of the regularized curvature driven level set equation is proved. Numerical experiments concerning comparison with exact solution and image filtering problem using proposed scheme are included.
Applications of approximate gradient schemes for nonlinear parabolic equations
We develop gradient schemes for the approximation of the Perona-Malik equations and nonlinear tensor-diffusion equations. We prove the convergence of these methods to the weak solutions of the corresponding nonlinear PDEs. A particular gradient scheme on rectangular meshes is then studied numerically with respect to experimental order of convergence which shows its second order accuracy. We present also numerical experiments related to image filtering by time-delayed Perona-Malik and tensor diffusion...
Special issue: Editorial
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