9 citations · 31 across the 14 of their papers we have counts for
15 papers
Mathematical and numerical methods for accurate aorta segmentation from non-enhanced CT Data yielding reliable identification and evaluation of large vessel vasculitis
Konan A. Allaly, Jozef Urban, Karol Mikula
Segmentation of the aorta is crucial for various medical analyses, such as the diagnosis and treatment of cardiovascular diseases. This work presents mathematical models and method…
Laplacian regularized eikonal equation with Soner boundary condition on polyhedral meshes
Jooyoung Hahn, Karol Mikula, Peter Frolkovič
In this paper, we propose a numerical algorithm based on a cell-centered finite volume method to compute a distance from given objects on a three-dimensional computational domain d…
Segmentation based tracking of cells in 2D+time microscopy images of macrophages
Seol Ah Park, Tamara Sipka, Zuzana Kriva +3
The automated segmentation and tracking of macrophages during their migration are challenging tasks due to their dynamically changing shapes and motions. This paper proposes a new…
Macrophages trajectories smoothing by evolving curves
Giulia Lupi, Karol Mikula, Seol Ah Park
When analyzing cell trajectories, we often have to deal with noisy data due to the random motion of the cells and possible imperfections in cell center detection. To smooth these t…
Direct simple computation of middle surface between 3D point clouds and/or discrete surfaces by tracking sources in distance function calculation algorithms
Balazs Kosa, Karol Mikula
In this paper, we introduce novel methods for computing middle surfaces between various 3D data sets such as point clouds and/or discrete surfaces. Traditionally the middle surface…
4D Segmentation Algorithm with application to 3D+time Image Segmentation
Markjoe Olunna Uba, Karol Mikula, Seol Ah Park
In this paper, we introduce and study a novel segmentation method for 4D images based on surface evolution governed by a nonlinear partial differential equation, the generalized su…
Natural Numerical Networks for Natura 2000 habitats classification by satellite images
Karol Mikula, Michal Kollar, Aneta A. Ozvat +5
Natural numerical networks are introduced as a new classification algorithm based on the numerical solution of nonlinear partial differential equations of forward-backward diffusio…
What was the river Ister in the time of Strabo? A mathematical approach
Karol Mikula, Martin Ambroz, Renata Mokosova
In this paper, we introduce a novel method for map registration and apply it to transformation of the river Ister from Strabo's map of the World to the current map in the World Geo…
Design and analysis of finite volume methods for elliptic equations with oblique derivatives; application to Earth gravity field modelling
Jerome Droniou, Matej Medla, Karol Mikula
We develop and analyse finite volume methods for the Poisson problem with boundary conditions involving oblique derivatives. We design a generic framework, for finite volume discre…
Semi-implicit second order schemes for numerical solution of level set advection equation on Cartesian grids
Peter Frolkovič, Karol Mikula
A new parametric class of semi-implicit numerical schemes for a level set advection equation on Cartesian grids is derived and analyzed. An accuracy and a stability study is provid…
Higher order semi-implicit schemes for linear advection equation on Cartesian grids with numerical stability analysis
Peter Frolkovič, Karol Mikula
A new class of semi-implicit numerical schemes for linear advection equation on Cartesian grids is derived that is inspired by so-called -schemes used with fully explicit discre…
Numerical aspects of evolution of plane curves satisfying the fourth order geometric equation
Karol Mikula, Daniel Sevcovic
In this review paper we present a stable Lagrangian numerical method for computing plane curves evolution driven by the fourth order geometric equation. The numerical scheme and co…
A simple, fast and stabilized flowing finite volume method for solving general curve evolution equations
Karol Mikula, Daniel Sevcovic, Martin Balazovjech
A new simple Lagrangian method with favorable stability and efficiency properties for computing general plane curve evolutions is presented. The method is based on the flowing fini…
On tangential stabilization in curvature driven flows of planar curves
Karol Mikula, Daniel Sevcovic
We discuss the role of tangential stabilization in a curvature driven flow of planar curves. The governing system of nonlinear parabolic equations includes a nontrivial tangential…
Comparison study for Level set and Direct Lagrangian methods for computing Willmore flow of closed planar curves
Michal Benes, Karol Mikula, Tomas Oberhuber +1
The main goal of this paper is to present results of comparison study for the level set and direct Lagrangian methods for computing evolution of the Willmore flow of embedded plana…