Edit Profile (opens in new tab) Mikula, Karol Co-Author Distance Author ID: mikula.karol Published as: Mikula, Karol; Mikula, K. Documents Indexed: 116 Publications since 1995, including 5 Additional arXiv Preprints 8 Contributions as Editor · 1 Further Contribution Co-Authors: 87 Co-Authors with 117 Joint Publications 861 Co-Co-Authors all top 5 Co-Authors 6 single-authored 19 Frolkovič, Peter 18 Handlovičová, Angela 16 Ševčovič, Daniel 10 Remešiková, Mariana 8 Balazovjech, Martin 8 Čunderliḱ, Róbert 8 Hahn, Jooyoung 8 Krivá, Zuzana 8 Urbán, Jozef 7 Basara, Branislav 7 Sgallari, Fiorella 6 Ambroz, Martin 6 Medl’a, Matej 6 Peyriéras, Nadine 4 Beneš, Michal 4 Eymard, Robert 4 Kacur, Jozef 4 Macák, Marek 4 Minarechová, Zuzana 4 Sarti, Alessandro 4 Tomek, Lukáš 3 Kollár, Michal 3 Kósa, Balázs 3 Kútik, Pavol 3 Ohlberger, Mario 3 Park, Seol Ah 3 Smíšek, Michal 3 Špir, Róbert 2 Bänsch, Eberhard 2 Bourgine, Paul 2 Corsaro, Stefania 2 Drblíková, Olga 2 Herbin, Raphaèle 2 Húska, Martin 2 Jarolímek, Ivan 2 Kratochvil, Jan 2 Minárik, Vojtěch 2 Mojzeš, Matej 2 Novysedlák, Peter 2 Oberhuber, Tomás 2 Olunna Uba, Markjoe 2 Preusser, Tobias 2 Rizzi, Barbara 2 Rumpf, Martin 2 Šibík, Jozef 2 Šibíková, Mária 2 Stašová, Olga 1 Albers, Wulf 1 Bamberg, Günter 1 Beran, Branislav 1 Campana, Matteo 1 Chalupecký, Vladimír 1 Chi, Mai Nguyen 1 Christodoulou, Neophytos 1 Crott 1 Daniel, Patrik 1 De Simone, Valentina 1 Drblíková-Stašová, Olga 1 Droniou, Jérôme 1 Erdélyi, Ján 1 Fašková, Zuzana 1 Faure, Emmanuel 1 Fraštia, Marek 1 Frolkovič, Richard 1 Güth, Werner 1 Honti, Richard 1 Janák, Juraj 1 Kollár, Jozef 1 Komornikova, Magda 1 Lamberti, Carlo 1 Lupi, Giulia 1 Lutfalla, Georges 1 Marčiš, Marián 1 Martin, Dirk 1 Melani, Camilo 1 Mokošová, Renáta 1 Morigi, Serena 1 Okock, Polycarp Omondi 1 Opitz, Otto 1 Petrášová, Mária 1 Peyriéeras, N. 1 Priesching, Peter 1 Ramarosy, Narisoa 1 Rosenmüller, Joachim 1 Sanguinetti, Gonzalo 1 Sarkoci, Peter 1 Sarti, Alex 1 Schader, Martin 1 Selten, Reinhard 1 Sipka, Tamara 1 Šprlál, Michal 1 Ungvarský, Cyril 1 Weberling, Antonia 1 Zanella, Cecilia 1 Zernicka-Goetz, Magdalena all top 5 Serials 11 Computing and Visualization in Science 9 Applied Numerical Mathematics 9 Discrete and Continuous Dynamical Systems. Series S 6 Acta Mathematica Universitatis Comenianae. New Series 6 Tatra Mountains Mathematical Publications 6 SIAM Journal on Scientific Computing 4 Kybernetika 3 Applications of Mathematics 3 Advances in Computational Mathematics 3 Journal of Electrical Engineering 2 Computers & Mathematics with Applications 2 Numerische Mathematik 2 Japan Journal of Industrial and Applied Mathematics 1 Applicable Analysis 1 IMA Journal of Numerical Analysis 1 Journal of Computational Physics 1 Mathematical Methods in the Applied Sciences 1 Applied Mathematics and Computation 1 International Journal for Numerical Methods in Engineering 1 Journal of Computational and Applied Mathematics 1 SIAM Journal on Numerical Analysis 1 Journal of Scientific Computing 1 SIAM Journal on Applied Mathematics 1 Computational and Applied Mathematics 1 Journal of Geodesy 1 Computational Geosciences 1 IEEE Transactions on Image Processing 1 Communications on Pure and Applied Analysis 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Mathematical Systems in Economics 1 Communications in Computational Physics 1 RIMS Kôkyûroku Bessatsu 1 GEM - International Journal on Geomathematics all top 5 Fields 105 Numerical analysis (65-XX) 79 Partial differential equations (35-XX) 28 Information and communication theory, circuits (94-XX) 25 Computer science (68-XX) 18 Biology and other natural sciences (92-XX) 17 Differential geometry (53-XX) 11 Fluid mechanics (76-XX) 9 Geophysics (86-XX) 8 General and overarching topics; collections (00-XX) 6 Mechanics of deformable solids (74-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 History and biography (01-XX) 1 Dynamical systems and ergodic theory (37-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 83 Publications have been cited 595 times in 290 Documents Cited by ▼ Year ▼ Geometrical image segmentation by the Allen-Cahn equation. Zbl 1055.94502 Beneš, Michal; Chalupecký, Vladimír; Mikula, Karol 70 2004 Evolution of plane curves driven by a nonlinear function of curvature and anisotropy. Zbl 0980.35078 Mikula, Karol; Sevcovic, Daniel 34 2001 A direct method for solving an anisotropic mean curvature flow of plane curves with an external force. Zbl 1049.35019 Mikula, Karol; Ševčovič, Daniel 29 2004 Semi-implicit complementary volume scheme for solving level set like equations in image processing and curve evolution. Zbl 1065.65105 Handlovičová, Angela; Mikula, Karol; Sgallari, Fiorella 26 2003 High-resolution flux-based level set method. Zbl 1141.76041 Frolkovič, Peter; Mikula, Karol 19 2007 Semi-implicit finite volume scheme for solving nonlinear diffusion equations in image processing. Zbl 1013.65094 Mikula, Karol; Ramarosy, Narisoa 19 2001 Solution of nonlinear diffusion appearing in image smoothing and edge detection. Zbl 0823.65089 Kačur, Jozef; Mikula, Karol 18 1995 Flux-based level set method: A finite volume method for evolving interfaces. Zbl 1120.65093 Frolkovič, Peter; Mikula, Karol 17 2007 Semi-implicit covolume method in 3D image segmentation. Zbl 1126.65088 Corsaro, S.; Mikula, K.; Sarti, A.; Sgallari, F. 17 2006 Inflow-implicit/outflow-explicit finite volume methods for solving advection equations. Zbl 1310.65103 Mikula, Karol; Ohlberger, Mario; Urbán, Jozef 16 2014 Study of a finite volume scheme for the regularized mean curvature flow level set equation. Zbl 1241.65072 Eymard, Robert; Handlovičová, Angela; Mikula, Karol 14 2011 Convergence analysis of finite volume scheme for nonlinear tensor anisotropic diffusion in image processing. Zbl 1233.65063 Drblíková, Olga; Mikula, Karol 14 2008 A higher-order scheme for a tangentially stabilized plane curve shortening flow with a driving force. Zbl 1276.65048 Balažovjech, Martin; Mikula, Karol 13 2011 Evolution of curves on a surface driven by the geodesic curvature and external force. Zbl 1097.35084 Mikula, Karol; Ševčovič, Daniel 13 2006 Manifold evolution with tangential redistribution of points. Zbl 1328.53086 Mikula, Karol; Remešíková, Mariana; Sarkoci, Peter; Ševčovič, Daniel 13 2014 A coarsening finite element strategy in image selective smoothing. Zbl 0971.65084 Bänsch, Eberhard; Mikula, Karol 12 1997 Lagrangean method with topological changes for numerical modelling of forest fire propagation. Zbl 1278.65131 Balažovjech, Martin; Mikula, Karol; Petrášová, Mária; Urbán, Jozef 12 2012 A new level set method for motion in normal direction based on a semi-implicit forward-backward diffusion approach. Zbl 1223.65072 Mikula, Karol; Ohlberger, Mario 11 2010 Inflow-implicit/outflow-explicit scheme for solving advection equations. Zbl 1246.65167 Mikula, Karol; Ohlberger, Mario 10 2011 Simulation of anisotropic motion by mean curvature – comparison of phase field and sharp interface approaches. Zbl 0963.80004 Beneš, M.; Mikula, K. 9 1998 Cells segmentation from 3-D confocal images of early zebrafish embryogenesis. Zbl 1371.94449 Zanella, Cecilia; Campana, Matteo; Rizzi, Barbara; Melani, Camilo; Sanguinetti, Gonzalo; Bourgine, Paul; Mikula, Karol; Peyriéras, Nadine; Sarti, Alessandro 9 2010 Comparison study for level set and direct Lagrangian methods for computing Willmore flow of closed planar curves. Zbl 1213.35033 Beneš, Michal; Mikula, Karol; Oberhuber, Tomáš; Ševčovič, Daniel 9 2009 Semi-implicit finite volume level set method for advective motion of interfaces in normal direction. Zbl 1320.65124 Frolkovič, Peter; Mikula, Karol; Urbán, Jozef 8 2015 Slow and fast diffusion effects in image processing. Zbl 0971.65085 Kacur, Jozef; Mikula, Karol 7 2001 3D embryogenesis image segmentation by the generalized subjective surfaces method using the finite volume technique. Zbl 1374.94259 Mikula, K.; Peyriéras, N.; Remešíková, M.; Sarti, A. 7 2008 A simple, fast and stabilized flowing finite volume method for solving general curve evolution equations. Zbl 1364.65175 Mikula, Karol; Sevcovic, Daniel; Balazovjech, Martin 7 2010 Numerical solution of nonlinear diffusion with finite extinction phenomenon. Zbl 0852.35080 Mikula, K. 6 1995 Finite volume schemes for the generalized subjective surface equation in image segmentation. Zbl 1209.68473 Mikula, Karol; Remešíková, Mariana 6 2009 Adaptivity in 3D image processing. Zbl 0996.65104 Bänsch, Eberhard; Mikula, Karol 6 2001 Error estimates of the finite volume scheme for the nonlinear tensor-driven anisotropic diffusion. Zbl 1172.65052 Drblíková, Olga; Handlovičová, Angela; Mikula, Karol 6 2009 Co-volume method for Riemannian mean curvature flow in subjective surfaces multiscale segmentation. Zbl 1511.65104 Mikula, Karol; Sarti, Alessandro; Sgallari, Fiorella 6 2006 Numerical modeling of wildland surface fire propagation by evolving surface curves. Zbl 1415.65206 Ambroz, Martin; Balažovjech, Martin; Medl’a, Matej; Mikula, Karol 6 2019 Solution of nonlinearly curvature driven evolution of plane curves. Zbl 0938.65145 Mikula, Karol; Ševčovič, Daniel 5 1999 Evolution of convex plane curves describing anisotropic motions of phase interfaces. Zbl 0868.35063 Mikula, Karol; Kačur, Jozef 5 1996 Finite volume schemes for solving nonlinear partial differential equations in financial mathematics. Zbl 1246.91150 Kútik, Pavol; Mikula, Karol 5 2011 Applications of approximate gradient schemes for nonlinear parabolic equations. Zbl 1340.65187 Eymard, Robert; Handlovičová, Angela; Herbin, Raphaèle; Mikula, Karol; Stašová, Olga 5 2015 Semi-implicit level set method with inflow-based gradient in a polyhedron mesh. Zbl 1365.65204 Hahn, Jooyoung; Mikula, Karol; Frolkovič, Peter; Basara, Branislav 5 2017 Inflow-based gradient finite volume method for a propagation in a normal direction in a polyhedron mesh. Zbl 1371.65092 Hahn, Jooyoung; Mikula, Karol; Frolkovič, Peter; Basara, Branislav 5 2017 Iterative inflow-implicit outflow-explicit finite volume scheme for level-set equations on polyhedron meshes. Zbl 1442.65196 Hahn, Jooyoung; Mikula, Karol; Frolkovič, Peter; Medl’a, Matej; Basara, Branislav 5 2019 Counting number of cells and cell segmentation using advection-diffusion equations. Zbl 1140.35468 Frolkovič, Peter; Mikula, Karol; Peyriéras, Nadine; Sarti, Alex 4 2007 Stability and consistency of the semi-implicit co-volume scheme for regularized mean curvature flow equation in level set formulation. Zbl 1199.35197 Handlovičová, Angela; Mikula, Karol 4 2008 Image processing with partial differential equations. Zbl 1065.94502 Mikula, Karol 4 2002 4D numerical schemes for cell image segmentation and tracking. Zbl 1246.65166 Mikula, K.; Peyriéeras, N.; Remešíková, M.; Smíšek, M. 4 2011 A new tangentially stabilized 3D curve evolution algorithm and its application in virtual colonoscopy. Zbl 1296.65030 Mikula, Karol; Urbán, Jozef 4 2014 Computational and qualitative aspects of evolution of curves driven by curvature and external force. Zbl 1522.53008 Mikula, Karol; Ševčovič, Daniel 4 2004 Solving the oblique derivative boundary-value problem by the finite volume method. Zbl 1278.65166 Macák, Marek; Mikula, Karol; Minarechová, Zuzana 4 2012 4D embryogenesis image analysis using PDE methods of image processing. Zbl 1198.94020 Bourgine, Paul; Čunderlík, Róbert; Drblíková-Stašová, Olga; Mikula, Karol; Remešíková, Mariana; Peyriéras, Nadine; Rizzi, Barbara; Sarti, Alessandro 4 2010 Semi-implicit second order schemes for numerical solution of level set advection equation on Cartesian grids. Zbl 1427.65162 Frolkovič, Peter; Mikula, Karol 4 2018 Semi-implicit finite volume scheme for image processing in 3D cylindrical geometry. Zbl 1042.65069 Mikula, Karol; Sgallari, Fiorella 3 2003 Numerical simulation of dislocation dynamics. Zbl 1163.65309 Minárik, Vojtěch; Kratochvíl, Jan; Mikula, Karol; Beneš, Michal 3 2004 Numerical simulation of dislocation dynamics by means of parametric approach. Zbl 1312.74022 Minárik, Vojtěch; Kratochvíl, Jan; Mikula, Karol 3 2005 Flux balanced approximation with least-squares gradient for diffusion equation on polyhedral mesh. Zbl 1465.65116 Frolkovič, Peter; Mikula, Karol; Hahn, Jooyoung; Martin, Dirk; Basara, Branislav 3 2021 Numerical solution of the linearized fixed gravimetric boundary-value problem. Zbl 1162.86306 Čunderlík, R.; Mikula, K.; Mojzeš, M. 2 2008 An adaptive finite volume method in processing of color images. Zbl 1012.35002 Krivá, Zuzana; Mikula, Karol 2 2001 Solution of nonlinear curvature driven evolution of plane convex curves. Zbl 0877.65068 Mikula, Karol 2 1997 Gradient schemes for image processing. Zbl 1246.65163 Eymard, Robert; Handlovičová, Angela; Herbin, Raphaèle; Mikula, Karol; Stašová, Olga 2 2011 Semi-implicit diamond-cell finite volume scheme for 3D nonlinear tensor diffusion in coherence enhancing image filtering. Zbl 1374.94088 Drblíková, Olga; Mikula, Karol 2 2008 Distance function and extension in normal direction for implicitly defined interfaces. Zbl 1321.76045 Frolkovič, Peter; Mikula, Karol; Urbán, Jozef 2 2015 Diamond-cell finite volume scheme for the Heston model. Zbl 1317.35103 Kútik, Pavol; Mikula, Karol 2 2015 Parameter estimation for the forest fire propagation model. Zbl 1475.35346 Ambroz, Martin; Mikula, Karol; Fraštia, Marek; Marčiš, Marián 2 2020 The finite element method as a tool to solve the oblique derivative boundary value problem in geodesy. Zbl 1475.65198 Macák, Marek; Minarechová, Zuzana; Čunderlík, Róbert; Mikula, Karol 2 2020 Design and analysis of finite volume methods for elliptic equations with oblique derivatives; application to Earth gravity field modelling. Zbl 1453.65389 Droniou, Jérôme; Medla, Matej; Mikula, Karol 2 2019 Semi-automatic segmentation of NATURA 2000 habitats in sentinel-2 satellite images by evolving open curves. Zbl 1468.35215 Mikula, Karol; Urbán, Jozef; Kollár, Michal; Ambroz, Martin; Jarolímek, Ivan; Šibík, Jozef; Šibíková, Mária 2 2021 Approximation of nonlinear parabolic equations using a family of conformal and non-conformal schemes. Zbl 1264.65159 Eymard, Robert; Handlovičová, Angela; Mikula, Karol 2 2012 Gravimetric quasigeoid in Slovakia by the finite element method. Zbl 1205.86041 Fašková, Zuzana; Mikula, Karol; Čunderliḱ, Róbert; Janák, Juraj; Šprlál, Michal 1 2007 Computing minimal surfaces by mean curvature flow with area-oriented tangential redistribution. Zbl 1413.53024 Tomek, L.; Remešíková, M.; Mikula, K. 1 2018 The boundary element method applied to the determination of the global quasigeoid. Zbl 1056.86500 Čunderlík, R.; Mikula, K.; Mojzeš, M. 1 2001 Numerical solution of parabolic equations related to level set formulation of mean curvature flow. Zbl 0912.68210 Handlovičová, Angela; Mikula, Karol; Sarti, Alessandro 1 1998 Tangentially stabilized Lagrangian algorithm for elastic curve evolution driven by intrinsic Laplacian of curvature. Zbl 1180.65019 Mikula, Karol; Ševčovič, Daniel 1 2005 Adaptive diamond cell finite volume method in image processing. Zbl 1173.94322 Krivá, Zuzana; Mikula, Karol 1 2009 Semi-implicit second order accurate finite volume method for advection-diffusion level set equation. Zbl 1320.65123 Balažovjech, Martin; Frolkovič, Peter; Frolkovič, Richard; Mikula, Karol 1 2014 3D Lagrangian segmentation with simultaneous mesh adjustment. Zbl 1320.65037 Mikula, Karol; Remešíková, Mariana 1 2014 Nonlinear PDE based numerical methods for cell tracking in zebrafish embryogenesis. Zbl 1320.65126 Mikula, Karol; Špir, Róbert; Smíšek, Michal; Faure, Emmanuel; Peyriéras, Nadine 1 2015 Numerical algorithm for tracking cell dynamics in 4D biomedical images. Zbl 1325.35238 Peyriéras, Nadine; Špir, Róbert; Mikula, Karol 1 2015 Macrophage image segmentation by thresholding and subjective surface method. Zbl 1475.65095 Park, Seol Ah; Sipka, Tamara; Krivá, Zuzana; Ambroz, Martin; Kollár, Jozef; Kósa, Balázs; Chi, Mai Nguyen; Lutfalla, Georges; Mikula, Karol 1 2020 Finite volume method with the Soner boundary condition for computing the signed distance function on polyhedral meshes. Zbl 07767258 Hahn, Jooyoung; Mikula, Karol; Frolkovič, Peter; Basara, Branislav 1 2022 Reconstruction of surfaces from point clouds using a Lagrangian surface evolution model. Zbl 1450.65017 Daniel, Patrik; Medl’a, Matej; Mikula, Karol; Remešíková, Mariana 1 2015 Cell-centered finite volume method for regularized mean curvature flow on polyhedral meshes. Zbl 1451.65119 Hahn, Jooyoung; Mikula, Karol; Frolkovič, Peter; Balažovjech, Martin; Basara, Branislav 1 2020 A new form-finding method based on mean curvature flow of surfaces. Zbl 1278.53014 Húska, Martin; Medl’a, Matej; Mikula, Karol; Novysedlák, Peter; Remešíková, Mariana 1 2012 Parallel algorithms for segmentation of cellular structures in 2D+time and 3D morphogenesis data. Zbl 1278.65210 Mikula, Karol; Smíšek, Michal; Špir, Róbert 1 2012 3D image segmentation supported by a point cloud. Zbl 1471.65148 Kósa, Balázs; Mikula, Karol; Olunna Uba, Markjoe; Weberling, Antonia; Christodoulou, Neophytos; Zernicka-Goetz, Magdalena 1 2021 Computational optimization in solving the geodetic boundary value problems. Zbl 1460.65107 Macák, Marek; Čunderlík, Róbert; Mikula, Karol; Minarechová, Zuzana 1 2021 An automated segmentation of NATURA 2000 habitats from sentinel-2 optical data. Zbl 1468.35214 Mikula, Karol; Urbán, Jozef; Kollár, Michal; Ambroz, Martin; Jarolímek, Ivan; Šibík, Jozef; Šibíková, Mária 1 2021 Finite volume method with the Soner boundary condition for computing the signed distance function on polyhedral meshes. Zbl 07767258 Hahn, Jooyoung; Mikula, Karol; Frolkovič, Peter; Basara, Branislav 1 2022 Flux balanced approximation with least-squares gradient for diffusion equation on polyhedral mesh. Zbl 1465.65116 Frolkovič, Peter; Mikula, Karol; Hahn, Jooyoung; Martin, Dirk; Basara, Branislav 3 2021 Semi-automatic segmentation of NATURA 2000 habitats in sentinel-2 satellite images by evolving open curves. Zbl 1468.35215 Mikula, Karol; Urbán, Jozef; Kollár, Michal; Ambroz, Martin; Jarolímek, Ivan; Šibík, Jozef; Šibíková, Mária 2 2021 3D image segmentation supported by a point cloud. Zbl 1471.65148 Kósa, Balázs; Mikula, Karol; Olunna Uba, Markjoe; Weberling, Antonia; Christodoulou, Neophytos; Zernicka-Goetz, Magdalena 1 2021 Computational optimization in solving the geodetic boundary value problems. Zbl 1460.65107 Macák, Marek; Čunderlík, Róbert; Mikula, Karol; Minarechová, Zuzana 1 2021 An automated segmentation of NATURA 2000 habitats from sentinel-2 optical data. Zbl 1468.35214 Mikula, Karol; Urbán, Jozef; Kollár, Michal; Ambroz, Martin; Jarolímek, Ivan; Šibík, Jozef; Šibíková, Mária 1 2021 Parameter estimation for the forest fire propagation model. Zbl 1475.35346 Ambroz, Martin; Mikula, Karol; Fraštia, Marek; Marčiš, Marián 2 2020 The finite element method as a tool to solve the oblique derivative boundary value problem in geodesy. Zbl 1475.65198 Macák, Marek; Minarechová, Zuzana; Čunderlík, Róbert; Mikula, Karol 2 2020 Macrophage image segmentation by thresholding and subjective surface method. Zbl 1475.65095 Park, Seol Ah; Sipka, Tamara; Krivá, Zuzana; Ambroz, Martin; Kollár, Jozef; Kósa, Balázs; Chi, Mai Nguyen; Lutfalla, Georges; Mikula, Karol 1 2020 Cell-centered finite volume method for regularized mean curvature flow on polyhedral meshes. Zbl 1451.65119 Hahn, Jooyoung; Mikula, Karol; Frolkovič, Peter; Balažovjech, Martin; Basara, Branislav 1 2020 Numerical modeling of wildland surface fire propagation by evolving surface curves. Zbl 1415.65206 Ambroz, Martin; Balažovjech, Martin; Medl’a, Matej; Mikula, Karol 6 2019 Iterative inflow-implicit outflow-explicit finite volume scheme for level-set equations on polyhedron meshes. Zbl 1442.65196 Hahn, Jooyoung; Mikula, Karol; Frolkovič, Peter; Medl’a, Matej; Basara, Branislav 5 2019 Design and analysis of finite volume methods for elliptic equations with oblique derivatives; application to Earth gravity field modelling. Zbl 1453.65389 Droniou, Jérôme; Medla, Matej; Mikula, Karol 2 2019 Semi-implicit second order schemes for numerical solution of level set advection equation on Cartesian grids. Zbl 1427.65162 Frolkovič, Peter; Mikula, Karol 4 2018 Computing minimal surfaces by mean curvature flow with area-oriented tangential redistribution. Zbl 1413.53024 Tomek, L.; Remešíková, M.; Mikula, K. 1 2018 Semi-implicit level set method with inflow-based gradient in a polyhedron mesh. Zbl 1365.65204 Hahn, Jooyoung; Mikula, Karol; Frolkovič, Peter; Basara, Branislav 5 2017 Inflow-based gradient finite volume method for a propagation in a normal direction in a polyhedron mesh. Zbl 1371.65092 Hahn, Jooyoung; Mikula, Karol; Frolkovič, Peter; Basara, Branislav 5 2017 Semi-implicit finite volume level set method for advective motion of interfaces in normal direction. Zbl 1320.65124 Frolkovič, Peter; Mikula, Karol; Urbán, Jozef 8 2015 Applications of approximate gradient schemes for nonlinear parabolic equations. Zbl 1340.65187 Eymard, Robert; Handlovičová, Angela; Herbin, Raphaèle; Mikula, Karol; Stašová, Olga 5 2015 Distance function and extension in normal direction for implicitly defined interfaces. Zbl 1321.76045 Frolkovič, Peter; Mikula, Karol; Urbán, Jozef 2 2015 Diamond-cell finite volume scheme for the Heston model. Zbl 1317.35103 Kútik, Pavol; Mikula, Karol 2 2015 Nonlinear PDE based numerical methods for cell tracking in zebrafish embryogenesis. Zbl 1320.65126 Mikula, Karol; Špir, Róbert; Smíšek, Michal; Faure, Emmanuel; Peyriéras, Nadine 1 2015 Numerical algorithm for tracking cell dynamics in 4D biomedical images. Zbl 1325.35238 Peyriéras, Nadine; Špir, Róbert; Mikula, Karol 1 2015 Reconstruction of surfaces from point clouds using a Lagrangian surface evolution model. Zbl 1450.65017 Daniel, Patrik; Medl’a, Matej; Mikula, Karol; Remešíková, Mariana 1 2015 Inflow-implicit/outflow-explicit finite volume methods for solving advection equations. Zbl 1310.65103 Mikula, Karol; Ohlberger, Mario; Urbán, Jozef 16 2014 Manifold evolution with tangential redistribution of points. Zbl 1328.53086 Mikula, Karol; Remešíková, Mariana; Sarkoci, Peter; Ševčovič, Daniel 13 2014 A new tangentially stabilized 3D curve evolution algorithm and its application in virtual colonoscopy. Zbl 1296.65030 Mikula, Karol; Urbán, Jozef 4 2014 Semi-implicit second order accurate finite volume method for advection-diffusion level set equation. Zbl 1320.65123 Balažovjech, Martin; Frolkovič, Peter; Frolkovič, Richard; Mikula, Karol 1 2014 3D Lagrangian segmentation with simultaneous mesh adjustment. Zbl 1320.65037 Mikula, Karol; Remešíková, Mariana 1 2014 Lagrangean method with topological changes for numerical modelling of forest fire propagation. Zbl 1278.65131 Balažovjech, Martin; Mikula, Karol; Petrášová, Mária; Urbán, Jozef 12 2012 Solving the oblique derivative boundary-value problem by the finite volume method. Zbl 1278.65166 Macák, Marek; Mikula, Karol; Minarechová, Zuzana 4 2012 Approximation of nonlinear parabolic equations using a family of conformal and non-conformal schemes. Zbl 1264.65159 Eymard, Robert; Handlovičová, Angela; Mikula, Karol 2 2012 A new form-finding method based on mean curvature flow of surfaces. Zbl 1278.53014 Húska, Martin; Medl’a, Matej; Mikula, Karol; Novysedlák, Peter; Remešíková, Mariana 1 2012 Parallel algorithms for segmentation of cellular structures in 2D+time and 3D morphogenesis data. Zbl 1278.65210 Mikula, Karol; Smíšek, Michal; Špir, Róbert 1 2012 Study of a finite volume scheme for the regularized mean curvature flow level set equation. Zbl 1241.65072 Eymard, Robert; Handlovičová, Angela; Mikula, Karol 14 2011 A higher-order scheme for a tangentially stabilized plane curve shortening flow with a driving force. Zbl 1276.65048 Balažovjech, Martin; Mikula, Karol 13 2011 Inflow-implicit/outflow-explicit scheme for solving advection equations. Zbl 1246.65167 Mikula, Karol; Ohlberger, Mario 10 2011 Finite volume schemes for solving nonlinear partial differential equations in financial mathematics. Zbl 1246.91150 Kútik, Pavol; Mikula, Karol 5 2011 4D numerical schemes for cell image segmentation and tracking. Zbl 1246.65166 Mikula, K.; Peyriéeras, N.; Remešíková, M.; Smíšek, M. 4 2011 Gradient schemes for image processing. Zbl 1246.65163 Eymard, Robert; Handlovičová, Angela; Herbin, Raphaèle; Mikula, Karol; Stašová, Olga 2 2011 A new level set method for motion in normal direction based on a semi-implicit forward-backward diffusion approach. Zbl 1223.65072 Mikula, Karol; Ohlberger, Mario 11 2010 Cells segmentation from 3-D confocal images of early zebrafish embryogenesis. Zbl 1371.94449 Zanella, Cecilia; Campana, Matteo; Rizzi, Barbara; Melani, Camilo; Sanguinetti, Gonzalo; Bourgine, Paul; Mikula, Karol; Peyriéras, Nadine; Sarti, Alessandro 9 2010 A simple, fast and stabilized flowing finite volume method for solving general curve evolution equations. Zbl 1364.65175 Mikula, Karol; Sevcovic, Daniel; Balazovjech, Martin 7 2010 4D embryogenesis image analysis using PDE methods of image processing. Zbl 1198.94020 Bourgine, Paul; Čunderlík, Róbert; Drblíková-Stašová, Olga; Mikula, Karol; Remešíková, Mariana; Peyriéras, Nadine; Rizzi, Barbara; Sarti, Alessandro 4 2010 Comparison study for level set and direct Lagrangian methods for computing Willmore flow of closed planar curves. Zbl 1213.35033 Beneš, Michal; Mikula, Karol; Oberhuber, Tomáš; Ševčovič, Daniel 9 2009 Finite volume schemes for the generalized subjective surface equation in image segmentation. Zbl 1209.68473 Mikula, Karol; Remešíková, Mariana 6 2009 Error estimates of the finite volume scheme for the nonlinear tensor-driven anisotropic diffusion. Zbl 1172.65052 Drblíková, Olga; Handlovičová, Angela; Mikula, Karol 6 2009 Adaptive diamond cell finite volume method in image processing. Zbl 1173.94322 Krivá, Zuzana; Mikula, Karol 1 2009 Convergence analysis of finite volume scheme for nonlinear tensor anisotropic diffusion in image processing. Zbl 1233.65063 Drblíková, Olga; Mikula, Karol 14 2008 3D embryogenesis image segmentation by the generalized subjective surfaces method using the finite volume technique. Zbl 1374.94259 Mikula, K.; Peyriéras, N.; Remešíková, M.; Sarti, A. 7 2008 Stability and consistency of the semi-implicit co-volume scheme for regularized mean curvature flow equation in level set formulation. Zbl 1199.35197 Handlovičová, Angela; Mikula, Karol 4 2008 Numerical solution of the linearized fixed gravimetric boundary-value problem. Zbl 1162.86306 Čunderlík, R.; Mikula, K.; Mojzeš, M. 2 2008 Semi-implicit diamond-cell finite volume scheme for 3D nonlinear tensor diffusion in coherence enhancing image filtering. Zbl 1374.94088 Drblíková, Olga; Mikula, Karol 2 2008 High-resolution flux-based level set method. Zbl 1141.76041 Frolkovič, Peter; Mikula, Karol 19 2007 Flux-based level set method: A finite volume method for evolving interfaces. Zbl 1120.65093 Frolkovič, Peter; Mikula, Karol 17 2007 Counting number of cells and cell segmentation using advection-diffusion equations. Zbl 1140.35468 Frolkovič, Peter; Mikula, Karol; Peyriéras, Nadine; Sarti, Alex 4 2007 Gravimetric quasigeoid in Slovakia by the finite element method. Zbl 1205.86041 Fašková, Zuzana; Mikula, Karol; Čunderliḱ, Róbert; Janák, Juraj; Šprlál, Michal 1 2007 Semi-implicit covolume method in 3D image segmentation. Zbl 1126.65088 Corsaro, S.; Mikula, K.; Sarti, A.; Sgallari, F. 17 2006 Evolution of curves on a surface driven by the geodesic curvature and external force. Zbl 1097.35084 Mikula, Karol; Ševčovič, Daniel 13 2006 Co-volume method for Riemannian mean curvature flow in subjective surfaces multiscale segmentation. Zbl 1511.65104 Mikula, Karol; Sarti, Alessandro; Sgallari, Fiorella 6 2006 Numerical simulation of dislocation dynamics by means of parametric approach. Zbl 1312.74022 Minárik, Vojtěch; Kratochvíl, Jan; Mikula, Karol 3 2005 Tangentially stabilized Lagrangian algorithm for elastic curve evolution driven by intrinsic Laplacian of curvature. Zbl 1180.65019 Mikula, Karol; Ševčovič, Daniel 1 2005 Geometrical image segmentation by the Allen-Cahn equation. Zbl 1055.94502 Beneš, Michal; Chalupecký, Vladimír; Mikula, Karol 70 2004 A direct method for solving an anisotropic mean curvature flow of plane curves with an external force. Zbl 1049.35019 Mikula, Karol; Ševčovič, Daniel 29 2004 Computational and qualitative aspects of evolution of curves driven by curvature and external force. Zbl 1522.53008 Mikula, Karol; Ševčovič, Daniel 4 2004 Numerical simulation of dislocation dynamics. Zbl 1163.65309 Minárik, Vojtěch; Kratochvíl, Jan; Mikula, Karol; Beneš, Michal 3 2004 Semi-implicit complementary volume scheme for solving level set like equations in image processing and curve evolution. Zbl 1065.65105 Handlovičová, Angela; Mikula, Karol; Sgallari, Fiorella 26 2003 Semi-implicit finite volume scheme for image processing in 3D cylindrical geometry. Zbl 1042.65069 Mikula, Karol; Sgallari, Fiorella 3 2003 Image processing with partial differential equations. Zbl 1065.94502 Mikula, Karol 4 2002 Evolution of plane curves driven by a nonlinear function of curvature and anisotropy. Zbl 0980.35078 Mikula, Karol; Sevcovic, Daniel 34 2001 Semi-implicit finite volume scheme for solving nonlinear diffusion equations in image processing. Zbl 1013.65094 Mikula, Karol; Ramarosy, Narisoa 19 2001 Slow and fast diffusion effects in image processing. Zbl 0971.65085 Kacur, Jozef; Mikula, Karol 7 2001 Adaptivity in 3D image processing. Zbl 0996.65104 Bänsch, Eberhard; Mikula, Karol 6 2001 An adaptive finite volume method in processing of color images. Zbl 1012.35002 Krivá, Zuzana; Mikula, Karol 2 2001 The boundary element method applied to the determination of the global quasigeoid. Zbl 1056.86500 Čunderlík, R.; Mikula, K.; Mojzeš, M. 1 2001 Solution of nonlinearly curvature driven evolution of plane curves. Zbl 0938.65145 Mikula, Karol; Ševčovič, Daniel 5 1999 Simulation of anisotropic motion by mean curvature – comparison of phase field and sharp interface approaches. Zbl 0963.80004 Beneš, M.; Mikula, K. 9 1998 Numerical solution of parabolic equations related to level set formulation of mean curvature flow. Zbl 0912.68210 Handlovičová, Angela; Mikula, Karol; Sarti, Alessandro 1 1998 A coarsening finite element strategy in image selective smoothing. Zbl 0971.65084 Bänsch, Eberhard; Mikula, Karol 12 1997 Solution of nonlinear curvature driven evolution of plane convex curves. Zbl 0877.65068 Mikula, Karol 2 1997 Evolution of convex plane curves describing anisotropic motions of phase interfaces. Zbl 0868.35063 Mikula, Karol; Kačur, Jozef 5 1996 Solution of nonlinear diffusion appearing in image smoothing and edge detection. Zbl 0823.65089 Kačur, Jozef; Mikula, Karol 18 1995 Numerical solution of nonlinear diffusion with finite extinction phenomenon. Zbl 0852.35080 Mikula, K. 6 1995 all cited Publications top 5 cited Publications all top 5 Cited by 456 Authors 48 Mikula, Karol 23 Frolkovič, Peter 14 Beneš, Michal 14 Kim, Junseok 11 Handlovičová, Angela 10 Li, Yibao 10 Ševčovič, Daniel 9 Garcke, Harald 8 Hahn, Jooyoung 8 Sgallari, Fiorella 7 Basara, Branislav 7 Jeong, Darae 7 Nürnberg, Robert 7 Yazaki, Shigetoshi 6 Lee, Chaeyoung 6 Morigi, Serena 6 Remešiková, Mariana 6 Urbán, Jozef 6 Wei, Guowei 5 Barrett, John William 5 Choi, Yongho 5 Čunderliḱ, Róbert 5 Dehghan Takht Fooladi, Mehdi 5 Droniou, Jérôme 5 Eymard, Robert 5 Herbin, Raphaèle 5 Medl’a, Matej 5 Oberhuber, Tomás 5 Qian, Xu 5 Reichel, Lothar 5 Song, Songhe 5 Weng, Zhifeng 5 Yang, Junxiang 4 Jacobs, Byron A. 4 Kolář, Miroslav 4 Lee, Dongsun 4 Lee, Hyun Geun 4 Peyriéras, Nadine 4 Yi, Dokkyun 4 Zhang, Hong 3 Ambroz, Martin 3 Balazovjech, Martin 3 Chen, Zhan 3 Jia, Hongen 3 Kim, Hyundong 3 Kollár, Michal 3 Krivá, Zuzana 3 Strachota, Pavel 3 Tomek, Lukáš 3 Wang, Danxia 2 Abedian, Rooholah 2 Aizinger, Vadym 2 Andreianov, Boris 2 Baker, Nathan A. 2 Bendahmane, Mostafa 2 Benninghoff, Heike 2 Blank, Luise 2 Bradji, Abdallah 2 Bungert, Leon 2 Chabiniok, Radomír 2 Chen, Yaoyao 2 Dechaumphai, Pramote 2 Deng, Yangfang 2 Drblíková, Olga 2 Du, Qingqing 2 Feng, Xinlong 2 Gallouët, Thierry 2 Goto, Maika 2 Huang, Yunqing 2 Illangasekare, Tissa H. 2 Insall, R. H. 2 Jarolímek, Ivan 2 Kacur, Jozef 2 Karasözen, Bülent 2 Kim, Eunyoun 2 Kovacs, Balazs A. 2 Kuwana, Kazunori 2 Kwak, Soobin 2 Lai, Mingchih 2 Lantarón, Sagrario 2 Lee, June-Yub 2 Llanas, Bernardo 2 Macák, Marek 2 Mackenzie, J. A. 2 Minarechová, Zuzana 2 Momoniat, Ebrahim 2 Novysedlák, Peter 2 Olunna Uba, Markjoe 2 Phongthanapanich, Sutthisak 2 Pozzi, Paola 2 Prasath, V. B. Surya 2 Sakakibara, Koya 2 Sarbu, Lavinia 2 Sarti, Alessandro 2 Seol, Yunchang 2 Šibík, Jozef 2 Šibíková, Mária 2 Smíšek, Michal 2 Špir, Róbert 2 Stašová, Olga ...and 356 more Authors all top 5 Cited in 91 Serials 19 Applied Mathematics and Computation 18 Applied Numerical Mathematics 16 Computers & Mathematics with Applications 16 Kybernetika 15 Discrete and Continuous Dynamical Systems. Series S 13 Journal of Computational Physics 13 Journal of Computational and Applied Mathematics 11 Journal of Scientific Computing 9 Computing and Visualization in Science 7 Numerical Methods for Partial Differential Equations 6 Japan Journal of Industrial and Applied Mathematics 6 Applications of Mathematics 6 SIAM Journal on Scientific Computing 5 Numerische Mathematik 5 Journal of Mathematical Imaging and Vision 5 Advances in Computational Mathematics 4 Computational and Applied Mathematics 3 Bulletin of Mathematical Biology 3 Mathematics and Computers in Simulation 3 Applied Mathematics Letters 3 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 3 Numerical Algorithms 3 Applied Mathematical Modelling 3 Mathematical Problems in Engineering 3 Computational Geosciences 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Inverse Problems and Imaging 2 Computer Physics Communications 2 Journal of Mathematical Biology 2 Mathematical Methods in the Applied Sciences 2 Physica A 2 BIT 2 Tatra Mountains Mathematical Publications 2 International Journal of Computer Vision 2 Abstract and Applied Analysis 2 Interfaces and Free Boundaries 2 Discrete and Continuous Dynamical Systems. Series B 2 Advances in Applied Mathematics and Mechanics 2 SMAI Journal of Computational Mathematics 1 Applicable Analysis 1 Archive for Rational Mechanics and Analysis 1 Computer Methods in Applied Mechanics and Engineering 1 Communications on Pure and Applied Mathematics 1 International Journal for Numerical Methods in Fluids 1 Inverse Problems 1 Journal of Fluid Mechanics 1 International Journal for Numerical Methods in Engineering 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 SIAM Journal on Numerical Analysis 1 Tôhoku Mathematical Journal. Second Series 1 Circuits, Systems, and Signal Processing 1 European Journal of Applied Mathematics 1 The Journal of Geometric Analysis 1 International Journal of Computer Mathematics 1 SIAM Journal on Applied Mathematics 1 SIAM Journal on Mathematical Analysis 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Physics of Fluids 1 Journal of Mathematical Sciences (New York) 1 Engineering Analysis with Boundary Elements 1 Differential Equations and Dynamical Systems 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Vietnam Journal of Mathematics 1 European Journal of Mechanics. B. Fluids 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Communications in Nonlinear Science and Numerical Simulation 1 The ANZIAM Journal 1 Nonlinear Analysis. Real World Applications 1 Archives of Computational Methods in Engineering 1 Journal of Systems Science and Complexity 1 Journal of Applied Mathematics 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Journal of Applied Mathematics and Computing 1 International Journal of Computational Methods 1 Journal of Hyperbolic Differential Equations 1 Mediterranean Journal of Mathematics 1 International Journal of Numerical Analysis and Modeling 1 GAMM-Mitteilungen 1 Acta Mechanica Sinica 1 Communications in Computational Physics 1 GEM - International Journal on Geomathematics 1 JSIAM Letters 1 Journal of Computational Dynamics 1 Journal of Mathematics 1 East Asian Journal on Applied Mathematics 1 Sahand Communications in Mathematical Analysis 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Bollettino dell’Unione Matematica Italiana 1 AIMS Mathematics 1 International Journal on Finite Volumes all top 5 Cited in 30 Fields 230 Numerical analysis (65-XX) 162 Partial differential equations (35-XX) 50 Information and communication theory, circuits (94-XX) 39 Differential geometry (53-XX) 37 Computer science (68-XX) 35 Fluid mechanics (76-XX) 32 Biology and other natural sciences (92-XX) 19 Mechanics of deformable solids (74-XX) 11 Statistical mechanics, structure of matter (82-XX) 9 Classical thermodynamics, heat transfer (80-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 7 Geophysics (86-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Probability theory and stochastic processes (60-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Systems theory; control (93-XX) 3 Statistics (62-XX) 2 Ordinary differential equations (34-XX) 2 Approximations and expansions (41-XX) 2 Operations research, mathematical programming (90-XX) 1 Combinatorics (05-XX) 1 Algebraic geometry (14-XX) 1 Real functions (26-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Algebraic topology (55-XX) 1 Optics, electromagnetic theory (78-XX) 1 Quantum theory (81-XX) Citations by Year