Papers by Angela Handlovicova
Computer Methods in Material Science
Tensor diffusion equation represents an important model in many fields of science. We focused our... more Tensor diffusion equation represents an important model in many fields of science. We focused our attention to the problem which arises in financial mathematics and is known as 2D Heston model. Stability estimates for discrete duality finite volume scheme for proposed model is presented. Numerical experiments using proposed method and comparing it with previous numerical scheme are included
summary:Purpose of the paper is to study nonlinear smoothing term initiated in [3], [4], [6] and ... more summary: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 in [2], is used. We mention two different approaches for the approximation of the nonlinear smoothing term in the equation and known theoretical results for both of them. We provide the numerical tests for both schemes. It the last section we discuss obtained results and propose possibilities for the future research
Tatra Mountains Mathematical Publications, 2020
We propose a new finite volume numerical scheme for the approximation of the Affine Morphological... more We propose a new finite volume numerical scheme for the approximation of the Affine Morphological Scale Space (AMSS) model. We derive the basic scheme and its iterative improvement. For both schemes, several numerical experiments using examples where the exact solution is known are presented. Then the numerical errors and experimental order of convergence of the proposed schemes is studied.
Stability estimates and convergence for the numerical scheme based on the Finite volume method in... more Stability estimates and convergence for the numerical scheme based on the Finite volume method in space together with the average of n + 1 and n − 1 time step diffusion is investigated. Experiments using exact solution in 2D case are included. The computed experimental order of convergence (EOC) is of second order for proposed experiments.
Special issue: Editorial
Kybernetika, 2007
The main goal of the paper is to contribute to the area of acoustical simulations. Authors deal w... more The main goal of the paper is to contribute to the area of acoustical simulations. Authors deal with the approach of numerical methods, particularly the Finite volume method. The boundary conditions used are of Robin type, and they include rigid piston on one side of the domain, and changing boundary conditions on other sides. Further the numerical solution of one case is compared with the analytical one.
where Ω ⊂ R is a polygonal convex domain with the boundary Γ, T <∞, ν is the outward normal to... more where Ω ⊂ R is a polygonal convex domain with the boundary Γ, T <∞, ν is the outward normal to Γ, the functions f, g, β, k are Lipschitz continuous, β : R → R is nondecreasing and k(s) is a positive definite symmetric d × d-matrix for any s ∈ R. The use of linear approximation schemes for solving these problems from both the theoretical and numerical point of view has been extensively studied. A linear approximation scheme based on the so-called nonlinear Chernoff formula with constant relaxation parameter μ was studied in [1], [12], [14], [8]. Another linear approximation scheme was investigated in [5], [6], [7], [3]. There the authors used an approximation scheme of the type
Mathematical Modelling and Analysis, 2005
Error estimates in the L2 norm for the explicit fully discrete numerical finite volume scheme are... more Error estimates in the L2 norm for the explicit fully discrete numerical finite volume scheme are derived and proved for Perona‐Malik equation. Numerical example is also presented.
Tatra Mountains Mathematical Publications, 2018
The aim of the paper is to study problem of image segmentation and missing boundaries completion ... more The aim of the paper is to study problem of image segmentation and missing boundaries completion introduced in [Mikula, K.—Sarti, A.––Sgallarri, A.: Co-volume method for Riemannian mean curvature flow in subjective surfaces multiscale segmentation, Comput. Vis. Sci. 9 (2006), 23–31], [Mikula, K.—Sarti, A.—Sgallari, F.: Co-volume level set method in subjective surface based medical image segmentation, in: Handbook of Medical Image Analysis: Segmentation and Registration Models (J. Suri et al., eds.), Springer, New York, 583–626, 2005], [Mikula, K.—Ramarosy, N.: Semi-implicit finite volume scheme for solving nonlinear diffusion equations in image processing, Numer. Math. 89 (2001), 561–590] and [Tibenský, M.: VyužitieMetód Založených na Level Set Rovnici v Spracovaní Obrazu, Faculty of mathematics, physics and informatics, Comenius University, Bratislava, 2016]. We generalize approach presented in [Eymard, R.—Handlovičová, A.—Mikula, K.: Study of a finite volume scheme for regularised...
Letter Numerical solution of parabolic equations related to level set formulation of mean curvature flow
Computing and Visualization in Science, 1998
Kybernetika -Praha-
The Perona-Malik nonlinear parabolic problem, which is widely used in image process- ing, is inve... more The Perona-Malik nonlinear parabolic problem, which is widely used in image process- ing, 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.
2010 3rd International Congress on Image and Signal Processing, 2010
We present new numerical scheme for solving regularised mean curvature flow level set equation an... more We present new numerical scheme for solving regularised mean curvature flow level set equation and show its behavior in image filtering examples. The scheme is based on finite volume space discretization and semi-implicit time discretization [9], it is unconditionally stable and very weakly diffusive. Such properties are important in image filtering where they guarantee correct reconstruction of shapes deteriorated by high level of noise in stable and computationally efficient way. We compare the filtering capabilities of our new scheme with the standard explicit finite difference approximation of the mean curvature level set equation [15] and show appropriate behavior of the new method.
There is presented a Perona-Malik nonlinear image selective smoothing equation (modified in the s... more There is presented a Perona-Malik nonlinear image selective smoothing equation (modified in the sense of Catté, Lions, Morel and Coll) which is investigated especially from numerical point of view. Error estimates in L 2 norms for fully discrete numerical finite volume scheme are derived and proved. Some numerical examples are presented.
Applications of approximate gradient schemes for nonlinear parabolic equations
Applications of Mathematics, 2015
Springer Proceedings in Mathematics, 2011
We present a gradient scheme (which happens to be similar to the MPFA finite volume O-scheme) for... more We present a gradient scheme (which happens to be similar to the MPFA finite volume O-scheme) for the approximation to the solution of the Perona-Malik model regularized by a time delay and to the solution of the nonlinear tensor anisotropic diffusion equation. Numerical examples showing properties of the method and applications in image filtering are discussed.
Tatra Mountains Mathematical Publications, 2014
Stability of the linear semi-implicit discrete duality finite volume (DDFV) numerical scheme for ... more Stability of the linear semi-implicit discrete duality finite volume (DDFV) numerical scheme for the solution of the regularized curvature driven level set equation is proved. Our scheme is linear, it is efficient regarding computational times. Numerical experiments confirm accuracy of the proposed scheme
We introduce a new stabilized finite volume method for solving tensor diffusion equations. The ne... more We introduce a new stabilized finite volume method for solving tensor diffusion equations. The new scheme is based on the classical diamond-cell finite volume method and on the idea of inflow-implicit/outflow-explicit (or forward-backward diffusion) splitting accompanied by a suitable stabilization. Comparisons with known exact solution and numerical experiments investigating stability of the proposed method in case of highly anisotropic diffusion tensor are discussed.
We discuss two different semi-implicit numerical schemes based on the finite volume method for ap... more We discuss two different semi-implicit numerical schemes based on the finite volume method for approximation of the regularised mean curvature flow level set equation. The first, CVS scheme, is based on co-volume strategy and nonlinear terms, given by absolute value of gradient, are evaluated on pixel sides using splitted diamond-cell approach [11, 7, 8, 2, 6]. In the second, EHM scheme, the absolute values of gradients are evlauated inside the pixels by the Stokes formula and the scheme is obtained by imposing the continuity of fluxes on pixel sides [4]. Results concerning numerical analysis of the schemes are presented and a comparison of these numerical approximations on several representative examples are discussed including performance in image filtering. On testing examples with exact solutions the schemes behave similarly in solution error, but the EHM scheme has higher precision in gradient error. Finite volume numerical schemes also perform better in the filtering of a strong salt & pepper noise as the results obtained using finite difference method [10].
Numerical approximation of a nonlinear diffusion equation of mean curvature flow type is discusse... more Numerical approximation of a nonlinear diffusion equation of mean curvature flow type is discussed. Convergence and error analysis of a regularized problem is presented.
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Papers by Angela Handlovicova