Giulia Lupi, Karol Mikula, Seol Ah Park, Macrophages trajectories smoothing by evolving curves, Tatra Mountains Mathematical Publications, Vol. 86, Article 1 (2023) ( pdf file ).
(Some papers can be downloaded from this web page. The Copyright of published versions has been transferred to publishers.)
Jooyoung Hahn, Karol Mikula, Peter Frolkovic, Laplacian regularized eikonal equation with Soner boundary condition on polyhedral meshes, Computers & Mathematics with Applications, Volume 156 (2024) pp. 74-86 ( pdf file ).
Balazs Kosa, Karol Mikula, Direct simple computation of middle surface between 3D point clouds and/or discrete surfaces by tracking sources in distance function calculation algorithms, Tatra Mountains Mathematical Publications (2023) ( pdf file ).
Giulia Lupi, Karol Mikula, Seol Ah Park, Macrophages trajectories smoothing by evolving curves, Tatra Mountains Mathematical Publications, Vol. 86, Article 1 (2023) ( pdf file ).
Robert Cunderlik, Michal Kollar, Karol Mikula, 1D along-track pre-processing of the GOCE gravity gradients and nonlinear filtering of the radial components Vzz in spatial domain, Contributions to Geophysics and Geodesy, Volume 53, Number 4 (2023) pp. 333-351 ( pdf file ).
Lukas Tomek, Branislav Beran, Jan Erdelyi, Richard Honti, Karol Mikula, Multichannel segmentation of planar point clouds using evolving curves, Computational and Applied Mathematics, Volume 42 (2023) Article No. 332 ( pdf file ).
Marek Macak, Zuzana Minarechova, Robert Cunderlik, Karol Mikula, Gravity field modelling in mountainous areas by solving the nonlinear satellite-fixed geodetic boundary value problem with the finite element method, Acta Geodaetica et Geophysica, Volume 58 (2023) pp. 305–320 ( pdf file ).
Marek Macak, Zuzana Minarechova, Lukas Tomek, Robert Cunderlik, Karol Mikula, Solving the fixed gravimetric boundary value problem by the finite element method using mapped infinite elements, Computational Geosciences, Volume 27 (2023) pp. 649–662 ( pdf file ).
Jooyoung Hahn, Karol Mikula, Peter Frolkovic, Peter Priesching, Martin Balazovjech, Branislav Basara, Second-order accurate finite volume method for G-equation on polyhedral meshes, Japan Journal of Industrial and Applied Mathematics, Volume 40 (2023) pp. 1053–1082 ( pdf file ).
Karol Mikula, Michal Kollar, Aneta A. Ozvat, Martin Ambroz, Lucia Cahojova, Ivan Jarolimek, Jozef Sibik, Maria Sibikova, Natural numerical networks for Natura 2000 habitats classification by satellite images, Applied Mathematical Modelling, Volume 116 (2023) pp. 209-235 ( pdf file ).
Seol Ah Park, Tamara Sipka, Zuzana Kriva, Georges Lutfalla, Mai Nguyen-Chi, Karol Mikula, Segmentation-based tracking of macrophages in 2D + time microscopy movies inside a living animal, Computers in Biology and Medicine, Volume 153 (2023) 106499 ( pdf file ).
Markjoe Olunna Uba, Karol Mikula, Seol Ah Park, 4D segmentation algorithm with application to 3D+time image segmentation, Japan Journal of Industrial and Applied Mathematics, Volume 40 (2023) pp. 109–139 ( pdf file ).
Karol Mikula, Michal Kollar, Aneta A. Ozvat, Lucia Cahojova, Maria Sibikova, Natural Numerical Networks on Directed Graphs in Satellite Image Classification, In: Calatroni, L., Donatelli, M., Morigi, S., Prato, M., Santacesaria, M. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2023. Lecture Notes in Computer Science, vol 14009. Springer, Cham, 2023 ( pdf file ).
Tamara Sipka, Seol Ah Park, Resul Ozbilgic, Laurence Balas, Thierry Durand, Karol Mikula, Georges Lutfalla, Mai Nguyen-Chi, Macrophages undergo a behavioural switch during wound healing in zebrafish, Free Radical Biology and Medicine, Volume 192 (2022)pp. 200-212 ( pdf file ).
Lucia Cahojova, Martin Ambroz, Ivan Jarolimek, Michal Kollar, Karol Mikula, Jozef Sibik, Maria Sibikova, Exploring Natura 2000 habitats by satellite image segmentation combined with phytosociological data: a case study from the Čierny Balog area (Central Slovakia), Scientific Reports (Nature Portfolio), Volume 12, Article number: 18375 (2022) ( pdf file ).
Jooyoung Hahn, Karol Mikula, Peter Frolkovic, Branislav Basara, Finite volume method with the Soner boundary condition for computing the signed distance function on polyhedral meshes, International Journal for Numerical Methods in Engineering, Volume 123, Issue 4 (2022) pp. 1057-1077 ( pdf file ).
Zuzana Minarechova, Marek Macak, Robert Cunderlik, Karol Mikula, On the finite element method for solving the oblique derivative boundary value problems and its application in local gravity field modelling, Journal of Geodesy 95(6) (2001) Article number: 70 ( pdf file ).
K.Mikula, M.Sibikova, M.Ambroz, M.Kollar, A.A.Ozvat, J.Urban, I.Jarolimek, J.Sibik, NaturaSat—A Software Tool for Identification, Monitoring and Evaluation of Habitats by Remote Sensing Techniques, Remote Sensing, 2021, 13(17), 3381 ( pdf file ).
M.Huska, M.Medla, K.Mikula, S.Morigi, Lagrangian evolution approach to surface quadrangulation, Applications of Mathematics, Vol. 66, Issue 4 (2021) pp. 509-551 ( pdf file ).
K.Mikula, M.Ambroz, R.Mokosova, What was the river Ister in the time of Strabo? A mathematical approach, Tatra Mountains Mathematical Publications, Vol. 80 (2021) pp. 71-118 ( pdf file ), ( pdf file of a slightly more detailed arXiv version).
A.Handlovicova, K.Mikula, Finite volume schemes for the affine morphological scale space (AMSS) model, Tatra Mountains Mathematical Publications, Vol. 80 (2021) pp. 53-70 ( pdf file ).
P.Okock, J.Urban, K.Mikula, Improvement and handling of the segmentation model with an inflation term, Tatra Mountains Mathematical Publications, Vol. 80 (2021) pp. 119-134 ( pdf file ).
K.Mikula, J.Urban, M.Kollar, M.Ambroz, I.Jarolimek, J.Sibik, M.Sibikova, Semi-automatic segmentation of NATURA 2000 habitats in Sentinel-2 satellite images by evolving open curves, Discrete and Continuous Dynamical Systems - Series S, 2021, 14(3): 1033-1046 ( pdf file ).
K.Mikula, J.Urban, M.Kollar, M.Ambroz, I.Jarolimek, J.Sibik, M.Sibikova, An automated segmentation of NATURA 2000 habitats from Sentinel-2 optical data, Discrete and Continuous Dynamical Systems - Series S, 2021, 14(3): 1017-1032 ( pdf file ).
B.Kosa, K.Mikula, M.Uba, A.Weberling, N.Christodoulou, M.Zernicka-Goetz, 3D image segmentation supported by a point cloud, Discrete and Continuous Dynamical Systems - Series S, 2021, 14(3): 971-985 ( pdf file ).
Peter Frolkovic, Karol Mikula, Jooyoung Hahn, Dirk Martin and Branislav Basara, Flux balanced approximation with least-squares gradient for diffusion equation on polyhedral mesh, Discrete and Continuous Dynamical Systems - Series S, 2021, 14(3): 865-879 ( pdf file ).
Marek Macak, Róbert Cunderlik, Karol Mikula and Zuzana Minarechova, Computational optimization in solving the geodetic boundary value problems, Discrete and Continuous Dynamical Systems - Series S, 2021, 14(3): 987-999
( pdf file ).
K.Mikula, M.Kollar, A.A.Ozvat, M.Ambroz, L.Cahojova, I.Jarolimek, J.Sibik, M.Sibikova, Natural Numerical Networks for Natura 2000 habitats classification by satellite images, arXiv:2108.04327( pdf file ).
Balazs Kosa, Karol Mikula, Direct simple computation of middle surface between 3D point clouds and/or discrete surfaces by tracking sources in distance function calculation algorithms, arXiv:2112.09808( pdf file ).
R.Cunderlik, M.Medla, K.Mikula, Local quasigeoid modelling in Slovakia using the finite volume method on the discretized Earth's topography, Contributions to Geophysics and Geodesy, Vol 50, No 3 (2020) pp. 287-302 ( pdf file ).
M.Ambroz, K.Mikula, M.Frastia, M.Marcis, Parameter estimation for the forest fire propagation model, Tatra Mountains Mathematical Publications, Vol 75 (2020) pp. 1-22 ( pdf file ).
M.Macak, Z.Minarechova, R.Cunderlik, K.Mikula, The finite element method as a tool to solve the oblique derivative boundary value problem in geodesy, Tatra Mountains Mathematical Publications, Vol 75 (2020) pp. 63-80 ( pdf file ).
Polycarp Omondi Okock, Jozef Urban, Karol Mikula, Efficient 3D shape registration by using distance maps and stochastic gradient descent method, Tatra Mountains Mathematical Publications, Vol 75 (2020) pp. 81-102 ( pdf file ).
Seol Ah Park, T.Sipka, Z.Kriva, M.Ambroz, M.Kollar, B.Kosa, Mai Nguyen-Chi, G.Lutfalla, K.Mikula, Macrophage image segmentation by thresholding and subjective surface method, Tatra Mountains Mathematical Publications, Vol 75 (2020) pp. 103-120 ( pdf file ).
M.Uba, K.Mikula, Z.Kriva, H.Nguyen, T.Savy, E.Kardash, N.Peyrieras, 3D Cell Image Segmentation by Modified
Subjective Surface Method, Tatra Mountains Mathematical Publications, Vol 75 (2020) pp. 147-162 ( pdf file ).
Georgo Ibolya, Karol Mikula, Numerical solution of the 1D viscous Burgers' and traffic flow equations by the inflow-implicit/outflow-explicit finite volume method, ALGORITMY 2020 - 21st Conference on Scientific Computing, Vysoké Tatry - Podbanské, Slovakia, September 10 - 15, 2020. Proceedings of contributed papers, Editors: P.Frolkovič, K.Mikula and D. Ševčovič, Vydavateľstvo SPEKTRUM STU, 2020, ISBN: 978-80-227-5032-5, pp. 191-200
( pdf file ).
Martin Ambroz, Michal Kollar, Karol Mikula, Semi-implicit scheme for semi-automatic segmentation in NaturaSat software , ALGORITMY 2020 - 21st Conference on Scientific Computing, Vysoké Tatry - Podbanské, Slovakia, September 10 - 15, 2020. Proceedings of contributed papers, Editors: P.Frolkovič, K.Mikula and D. Ševčovič, Vydavateľstvo SPEKTRUM STU, 2020, ISBN: 978-80-227-5032-5, pp. 171-180
( pdf file ).
Markjoe Olunna Uba, Karol Mikula, Zuzana Kriva, Nguyen Hanh, Thierry Savy, Elena Kardash, Nadine Peyrieras, Application of Modified Subjective Surface Method to 3D Cell Membrane Image Segmentation, ALGORITMY 2020 - 21st Conference on Scientific Computing, Vysoké Tatry - Podbanské, Slovakia, September 10 - 15, 2020. Proceedings of contributed papers, Editors: P.Frolkovič, K.Mikula and D. Ševčovič, Vydavateľstvo SPEKTRUM STU, 2020, ISBN: 978-80-227-5032-5, pp. 51-60
( pdf file ).
J.Hahn, K.Mikula, P.Frolkovic, M.Balazovjech, B.Basara,
Cell-Centered Finite Volume Method for Regularized Mean Curvature Flow on Polyhedral Meshes. FVCA 9, Bergen, Norway, June 2020, Springer Proceedings in Mathematics & Statistics, vol 323. Springer International Publishing (2020) pp. 755-763
( pdf file ).
J.Droniou, M.Medla, K.Mikula, Design and analysis of finite volume methods for elliptic equations with oblique derivatives; application to Earth gravity field modelling, Journal of Computational Physics, Volume 398, 1 December 2019, 108876
( pdf file , link to the paper).
L.Tomek, K.Mikula, Discrete duality finite volume method with tangential redistribution of points for surfaces evolving by mean curvature, ESAIM: M2AN Mathematical modelling and numerical analysis, Volume 53, Number 6, November-December 2019, pp. 1797-1840
( pdf file ).
M.Ambroz, M.Balazovjech, M.Medla, K.Mikula, Numerical modeling of wildland surface fire propagation by evolving surface curves, Advances in Computational Mathematics, April 2019, Volume 45, Issue 2, pp 1067–1103
( pdf file ).
J.Hahn, K.Mikula, P.Frolkovic, M.Medla, B.Basara, Iterative inflow-implicit outflow-explicit finite volume scheme for level-set equations on polyhedron meshes, Computers & Mathematics with Applications, Volume 77, Issue 6, 15 March 2019, Pages 1639-1654
( pdf file ).
R.Cundelik, K.Mikula, Z.Minarechova, M.Macak, Numerical Methods for Solving the Oblique Derivative Boundary Value Problems in Geodesy,
In: Freeden W., Rummel R. (eds) Handbuch der Geodäsie. Springer Reference Naturwissenschaften. Springer Spektrum, Berlin, Heidelberg, pp. 1-48 ( pdf file , link to the paper).
R.Cundelik, M.Macak, M.Medla, K.Mikula, Z.Minarechova, Computational Methods for High-Resolution Gravity Field Modeling,
In: Grafarend E. (eds) Encyclopedia of Geodesy. Encyclopedia of Earth Sciences Series. Springer, Cham, 2018, ISBN: 978-3-319-02370-0 ( pdf file , link to the paper).
P.Frolkovic, K.Mikula,
Semi-implicit second order schemes for numerical solution of level set advection equation on Cartesian grids, Applied Mathematics and Computation,
Volume 329 (2018) pp. 129-142
( pdf file ).
L.Tomek, M.Remesikova, K.Mikula, Computing minimal surfaces by mean curvature flow with area-oriented tangential redistribution, Acta Mathematica Universitatis Comemianae (AMUC), Volume 87, No. 1 (2018) pp. 55-72 ( pdf file ).
M. Medla, K.Mikula, R.Cunderlik, M.Macak, Numerical solution to the oblique derivative boundary value
problem on non-uniform grids above the Earth topography, Journal of Geodesy, Volume 92, Issue 1 (2018) pp. 1–19 ( pdf file , link to the paper).
K.Mikula, R.Spir, N.Peyrieras, Parallelization and validation of algorithms for
zebrafish cell lineage tree reconstruction from big
4D image data, Acta Polytechnica Hungarica, Vol. 14/5 (2017) pp. 65-84 ( pdf file ).
J.Hahn, K.Mikula, P.Frolkovic, B.Basara, Inflow-Based Gradient Finite Volume Method for a Propagation in a Normal Direction in a Polyhedron Mesh, Journal of Scientific Computing, July 2017, Volume 72, Issue 1, pp 442–465, doi:10.1007/s10915-017-0364-4
( pdf file , link to the paper).
S.Dyballa, T.Savy, P.Germann, K.Mikula, M.Remesikova, R.Spir, A.Zecca, N.Peyrieras, C.Pujades, Distribution of neurosensory progenitor pools during inner ear morphogenesis unveiled by cell lineage reconstruction, eLife 2017;6:e22268, January 2017 ( pdf file , link to the paper ).
B.Kosa, J.Halickova-Brehovska, K.Mikula, New efficient numerical method for 3D point cloud surface reconstruction by using level set methods, Proceedings of Equadiff 2017 Conference, Bratislava, July 24-28, 2017, K. Mikula, D. Ševčovič and J. Urbán, Eds. Published by Slovak University of Technology, SPEKTRUM STU Publishing, 2017, ISBN: 978-80-227-4757-8 (2017) pp. 387-396
( pdf file ).
M.Medla, K.Mikula, Gaussian curvature based tangential redistribution of points on evolving surfaces, Proceedings of Equadiff 2017 Conference, Bratislava, July 24-28, 2017, K. Mikula, D. Ševčovič and J. Urbán, Eds. Published by Slovak University of Technology, SPEKTRUM STU Publishing, 2017, ISBN: 978-80-227-4757-8 (2017) pp. 255-264
( pdf file ).
R.Spir, K.Mikula, N.Peyrieras, Cell Lineage Tree Reconstruction from Time Series of 3D Images of Zebrafish Embryogenesis. In: Chen CS., Lu J., Ma KK. (eds) Computer Vision – ACCV 2016 Workshops. ACCV 2016. Lecture Notes in Computer Science, vol 10117. Springer, Cham (2017) pp. 539-554 ( pdf file , link to the paper ).
J.Hahn, K.Mikula, P.Frolkovic, B.Basara,
Semi-implicit Level Set Method with Inflow-Based Gradient in a Polyhedron Mesh. In: Cances C., Omnes P. (eds) Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems. FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 200. Springer, Cham (2017) pp. 81-89 ( pdf file , link to the paper ).
Emmanuel Faure, Thierry Savy, Barbara Rizzi, Camilo Melani, Olga Stašová, Dimitri Fabreges, Robert Spir, Mark Hammons, Robert Cunderlik, Gaëlle Recher, Benoît Lombardot, Louise Duloquin, Ingrid Colin, Jozef Kollár, Sophie Desnoulez, Pierre Affaticati, Benoît Maury, Adeline Boyreau, Jean-Yves Nief, Pascal Calvat, Philippe Vernier, Monique Frain, Georges Lutfalla, Yannick Kergosien, Pierre Suret, Mariana Remešíková, René Doursat, Alessandro Sarti, Karol Mikula, Nadine Peyriéras & Paul Bourgine, A workflow to process 3D+time microscopy images of developing organisms and reconstruct their cell lineage, Nature Communications 7, Article number: 8674, doi:10.1038/ncomms9674, February 2016 ( pdf file of main article , link to all material).
R. Cunderlik, M. Kollar, K. Mikula, Filters for geodesy data based on linear and nonlinear diffusion, GEM - International Journal on Geomathematics, Vol. 7 (2016) pp. 239-274( pdf file ).
L. Sanchez, R. Cunderlik, N. Dayoub, K. Mikula, Z. Minarechova, Z. Sima, V. Vatrt, M. Vojtiskova, A conventional value for the geoid reference potential W0, Journal of Geodesy, Volume 90, Issue 9 (2016) pp. 815–835 ( pdf file ).
J.Halickova, K.Mikula, Level set method for surface reconstruction and its application in surveying, (ASCE) Journal of Surveying Engineering, 10.1061/(ASCE)SU.1943-5428.0000159, 04016007, February 2016( pdf file ).
Z.Kriva, A.Handlovicova, K.Mikula, Adaptive cell-centered finite volume method for diffusion equations on a consistent quadtree grid, Advances in Computational Mathematics, Volume 42, Issue 2, pp 249-277, April 2016,
( pdf file ).
M.Macak, K.Mikula, Z.Minarechova, R.Cunderlik, On an iterative approach to
solving the nonlinear satellite-fixed geodetic boundary-value problem, VIII Hotine-Marussi Symposium on Mathematical Geodesy,
Volume 142 of the series International Association of Geodesy Symposia, pp 185-192, 2016
( pdf file ).
L.Tomek, K.Mikula, M.Remesikova, Discrete duality finite volume method for mean curvature flow of surfaces, ALGORITMY 2016 - 20th Conference on Scientific Computing, Vysoké Tatry - Podbanské, Slovakia, March 14 - 18, 2016. Proceedings of contributed papers, Editors: A. Handlovičová and D. Ševčovič, Publishing House of Slovak University of Technology in Bratislava, 2016, ISBN: 978-80-227-4544-4, pp. 33-43
( pdf file ).
M.Kollar, K.Mikula, R.Cunderlik, Nonlinear diffusion filtering influenced by mean curvature, ALGORITMY 2016 - 20th Conference on Scientific Computing, Vysoké Tatry - Podbanské, Slovakia, March 14 - 18, 2016. Proceedings of contributed papers, Editors: A. Handlovičová and D. Ševčovič, Publishing House of Slovak University of Technology in Bratislava, 2016, ISBN: 978-80-227-4544-4, pp. 183-193
( pdf file ).
M.Medla, K.Mikula, New Second Order Up-wind Scheme for Oblique Derivative Boundary Value Problem, ALGORITMY 2016 - 20th Conference on Scientific Computing, Vysoké Tatry - Podbanské, Slovakia, March 14 - 18, 2016. Proceedings of contributed papers, Editors: A. Handlovičová and D. Ševčovič, Publishing House of Slovak University of Technology in Bratislava, 2016, ISBN: 978-80-227-4544-4, pp. 254-263
( pdf file ).
K.Mikula, J.Urban, Fully automatic affine registration of planar parametric curves, ALGORITMY 2016 - 20th Conference on Scientific Computing, Vysoké Tatry - Podbanské, Slovakia, March 14 - 18, 2016. Proceedings of contributed papers, Editors: A. Handlovičová and D. Ševčovič, Publishing House of Slovak University of Technology in Bratislava, 2016, ISBN: 978-80-227-4544-4, pp. 343-352
( pdf file ).
M.Macak, R.Cunderlik, K.Mikula, Z.Minarechova, An upwind-based scheme for solving the oblique derivative boundary-value problem related to physical geodesy, Journal of Geodetic Sciences, Vol. 5 (2015) pp. 180-188
( pdf file ).
K.Mikula, N.Peyrieras, R.Spir,
Numerical algorithm for tracking cell dynamics in 4D biomedical images,
Discrete and Continuous Dynamical Systems - Series S (DCDS-S)
Volume 8, Number 5 (2015) pp. 953 - 967
( pdf file ).
P.Kutik, K.Mikula, Diamond-cell finite volume scheme for the Heston model,
Discrete and Continuous Dynamical Systems - Series S (DCDS-S)
Volume 8, Number 5 (2015) pp. 913 - 931
( pdf file ).
K.Mikula, M.Remesikova, P.Novysedlak, Truss structure design using a
length-oriented surface remeshing technique,
Discrete and Continuous Dynamical Systems - Series S (DCDS-S)
Volume 8, Number 5 (2015) pp. 933 - 951
( pdf file ).
P.Frolkovic, K.Mikula, J.Urban, Distance function and extension in normal
direction for implicitly defined interfaces,
Discrete and Continuous Dynamical Systems - Series S (DCDS-S)
Volume 8, Number 5 (2015) pp. 871 - 880
( pdf file ).
Z.Minarechova, M.Macak, R.Cunderlik, K.Mikula, High-resolution global
gravity field modelling by the finite volume method,
Studia Geophysica et Geodaetica, Vol. 59 (2015) pp. 1-20
( pdf file ).
K.Mikula, R.Spir, M.Smisek, E.Faure, N.Peyrieras, Nonlinear PDE based numerical methods for cell tracking in zebrafish embryogenesis,
Applied Numerical Mathematics, Vol. 95 (2015) pp. 250-266 ( pdf file ).
P.Frolkovic, K.Mikula, J.Urban, Semi-implicit finite volume level set method
for advective motion of interfaces in normal direction,
Applied Numerical Mathematics, Vol. 95 (2015) pp. 214-228 ( pdf file ).
R.Eymard, A.Handlovicova, R.Herbin, K.Mikula, O.Stasova, Applications of approximate
gradient schemes for nonlinear parabolic equations, Applications of
Mathematics, Vol. 60, No. 2 (2015) pp. 135-156
( pdf file ).
P.Daniel, M.Medla, K.Mikula, M.Remesikova,
Reconstruction of surfaces from point clouds using a Lagrangian surface evolution model, J.-F. Aujol et al. (Eds.): SSVM 2015, LNCS 9087, Springer, (2015) pp. 589–600
( pdf file ).
K.Mikula, M.Ohlberger, J.Urban, Inflow-Implicit/Outflow-Explicit
finite volume methods for solving advection equations,
Applied Numerical Mathematics, Vol. 85 (2014) pp. 16-37
( pdf file ).
K.Mikula, M.Remesikova, P.Sarkoci, D.Sevcovic, Manifold evolution with
tangential redistribution of points, SIAM J. Scientific
Computing, Vol. 36, No.4 (2014), pp. A1384-A1414
( pdf file ).
K.Mikula, J.Urban, A new tangentially stabilized 3D curve evolution
algorithm and its application in virtual colonoscopy, Advances in
Computational Mathematics, Vol. 40, Issue 4 (2014) pp. 819-837
( pdf file ).
M.Macak, Z.Minarechova, K.Mikula, A novel scheme for solving the oblique
derivative boundary-value problem,
Studia Geophysica et Geodaetica, Vol. 58 (2014) pp. 556-570
( pdf file ).
K.Mikula, M.Remesikova, 3D Lagrangian Segmentation with Simultaneous Mesh
Adjustment, Finite Volumes for Complex Applications VII -
Methods and Theoretical Aspects,
Proceedings of FVCA 7, Berlin, June 2014 (Eds. J.Fuhrmann, M.Ohlberger,
C.Rohde), Springer Proceedings in Mathematics and Statistics,
Vol. 77, 2014, pp. 685-694
( pdf file ).
Z.Kriva, A.Handlovicova, K.Mikula, Gradient Evaluation on a Quadtree Based
Finite Volume Grid, Finite Volumes for Complex Applications VII -
Methods and Theoretical Aspects,
Proceedings of FVCA 7, Berlin, June 2014 (Eds. J.Fuhrmann, M.Ohlberger,
C.Rohde), Springer Proceedings in Mathematics and Statistics,
Vol. 77, 2014, pp. 675-684
( pdf file ).
M.Balazovjech, P.Frolkovic, R.Frolkovic, K.Mikula, Semi-implicit Second
Order Accurate Finite Volume Method for Advection-Diffusion Level Set Equation,
Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects,
Proceedings of FVCA 7, Berlin, June 2014 (Eds. J.Fuhrmann, M.Ohlberger,
C.Rohde), Springer Proceedings in Mathematics and Statistics,
Vol. 77, 2014, pp. 479-488
( pdf file ).
R.Cunderlik, K.Mikula, M.Tunega,
Nonlinear diffusion filtering of data on the Earth's surface,
Journal of Geodesy, Vol. 87 (2013) pp. 143-160
( pdf file ).
R.Mikut, T.Dickmeis, W.Driever, P.Geurts, F.A.Hamprecht, B.X.Kausler,
M.J.Ledesma-Carbayo, R.Maree, K.Mikula, P.Pantazis, O.Ronneberger,
A.Santos, R.Stotzka, U.Strahle, N.Peyrias,
Automated Processing of Zebrafish Imaging Data: A Survey,
Zebrafish, Vol. 10, No. 3 (2013) pp. 401-421
(
link ).
R.Eymard, A.Handlovicova, K.Mikula,
Approximation of nonlinear parabolic equations using a family of conformal
and non-conformal schemes, Communications in Pure and Applied
Analysis, Volume 11, Issue 1 (2012) pp. 147-172 (pdf file ).
K. Mikula, J. Urban,
New fast and stable Lagrangean method for image segmentation,
Proceedings of the 5th International congress on image and signal processing (CISP 2012), Chongquing, China, October 16-18, 2012,
ISBN-978-1-4673-9/10,pp. 834-842
( pdf file).
M. Balazovjech, K. Mikula, M. Petrasova, J. Urban,
Lagrangean method with topological changes for numerical modelling of forest
fire propagation,
ALGORITMY 2012, 19th Conference on Scientific Computing,
Podbanske, Slovakia, September 9-14, 2012, Proceedings of contributed papers
and posters (Eds. A.Handlovicova, Z.Minarechova, D.Sevcovic), ISBN
978-80-227-3742-5, Publishing House of STU, 2012, pp. 42-52
( pdf file).
M. Macak, K. Mikula, Z. Minarechova, Solving the oblique derivative
boundary-value problem by the finite volume method,
ALGORITMY 2012, 19th Conference on Scientific Computing,
Podbanske, Slovakia, September 9-14, 2012, Proceedings of contributed papers
and posters (Eds. A.Handlovicova, Z.Minarechova, D.Sevcovic), ISBN
978-80-227-3742-5, Publishing House of STU, 2012, pp. 75-84
( pdf file).
M. Huska, M. Medla, K. Mikula, P. Novysedlak, M. Remesikova,
A new form-finding method based on mean curvature flow of surfaces,
ALGORITMY 2012, 19th Conference on Scientific Computing,
Podbanske, Slovakia, September 9-14, 2012, Proceedings of contributed papers
and posters (Eds. A.Handlovicova, Z.Minarechova, D.Sevcovic), ISBN
978-80-227-3742-5, Publishing House of STU, 2012, pp. 120-131
( pdf file).
K. Mikula, M. Smisek, R. Spir,
Parallel algorithms for segmentation of cellular structures in 2D+Time and
3D morphogenesis data,
ALGORITMY 2012, 19th Conference on Scientific Computing,
Podbanske, Slovakia, September 9-14, 2012, Proceedings of contributed papers
and posters (Eds. A.Handlovicova, Z.Minarechova, D.Sevcovic), ISBN
978-80-227-3742-5, Publishing House of STU, 2012, pp. 416-426
( pdf file).
A. Handlovicova, P. Kutik, K. Mikula,
Stabilized semi-implicit finite volume scheme for parabolic tensor diffusion
equations,
ALGORITMY 2012, 19th Conference on Scientific Computing,
Podbanske, Slovakia, September 9-14, 2012, Proceedings of contributed papers
and posters (Eds. A.Handlovicova, Z.Minarechova, D.Sevcovic), ISBN
978-80-227-3742-5, Publishing House of STU, 2012, pp. 438-477
( pdf file).
K.Mikula, M.Ohlberger, J.Urban, Inflow-Implicit/Outflow-Explicit Finite Volume Methods for Solving Advection Equations,
Technical Report 01/12 - N , FB 10 , Universitaet Muenster, Number 01/12 - N - February 2012
( pdf file ).
D.Sevcovic, B.Stehlikova, K.Mikula, Analytical and numerical methods for pricing financial derivatives, Nova Science Publishers, New York, 2011, 309 pages
M.Balazovjech, K.Mikula,
A higher order scheme for a tangentially stabilized plane curve shortening
flow with a driving force, SIAM Journal on Scientific Computing, Vol. 33, No. 5, pp. 2277-2294
(2011) (pdf file).
K.Mikula, N.Peyrieras, M.Remesikova, O.Stasova, Segmentation of 3D cell membrane images by PDE methods and its applications, Computers in Biology and Medicine, Vol. 41, No. 6 (2011) pp. 326-339 (pdf file).
R.Eymard, A.Handlovicova, K.Mikula,
Study of a finite volume scheme for the regularised mean curvature flow level set equation, IMA Journal on Numerical Analysis, Vol. 31 (2011) pp. 813-846 ( pdf file).
M.Sprlák, Z.Faskova, K.Mikula, On the application of the coupled finite-infinite element method to the geodetic boundary value problem, Studia Geophysica et Geodaetica, Vol. 55 (2011) pp. 479-487 ( pdf file).
Y.Bellaiche, F.Bosveld, F.Graner, K.Mikula, M.Remesikova, M.Smisek, New Robust Algorithm for Tracking Cells in Videos of Drosophila Morphogenesis Based on Finding an Ideal Path in Segmented Spatio-Temporal Cellular Structures, Proceeding of the 33rd Annual International IEEE EMBS Conference, Boston Marriott Copley Place, Boston, MA, USA, August 30 - September 3, 2011, IEEE Press, 2011, 4 pages ( pdf file).
K.Mikula, J.Urban, 3D curve evolution algorithm with tangential redistribution for a fully automatic finding of an ideal camera path in virtual colonoscopy, in Proceedings of the Third International
Conference on Scale Space Methods and Variational Methods in Computer
Vision, May 29th - June 2nd, 2011, Ein Gedi, Dead Sea, Israel, Lecture
Notes in Computer Science Series, Springer, 2011 ( pdf file).
K.Mikula, M.Ohlberger, Inflow-Implicit/Outflow-Explicit Scheme for Solving Advection Equations, in Finite Volumes in Complex Applications VI, Problems & Perspectives, Eds. J.Fořt et al. (Proceedings of the Sixth International Conference on Finite Volumes in Complex Applications, Prague, June 6-10, 2011), Springer Verlag, 2011, pp. 683-692
( pdf file).
K.Mikula, N.Peyrieras, M.Remesikova, M.Smisek, 4D numerical schemes for cell image
segmentation and tracking,
in Finite Volumes in Complex Applications VI, Problems & Perspectives, Eds. J.Fořt et al. (Proceedings of the Sixth International Conference on Finite Volumes in Complex Applications, Prague, June 6-10, 2011), Springer Verlag, 2011, pp. 693-702 ( pdf file).
P.Kutik, K.Mikula, Finite Volume Schemes for Solving Nonlinear
Partial Differential Equations in Financial
Mathematics,
in Finite Volumes in Complex Applications VI, Problems & Perspectives, Eds. J.Fořt et al. (Proceedings of the Sixth International Conference on Finite Volumes in Complex Applications, Prague, June 6-10, 2011), Springer Verlag, 2011, pp. 643-652 ( pdf file).
R.Eymard, A.Handlovicova, R.Herbin, K.Mikula, O.Stasova, Gradient Schemes for Image Processing,
in Finite Volumes in Complex Applications VI, Problems & Perspectives, Eds. J.Fořt et al. (Proceedings of the Sixth International Conference on Finite Volumes in Complex Applications, Prague, June 6-10, 2011), Springer Verlag, 2011, pp. 429-438
( pdf file).
K.Mikula, M.Ohlberger, A new level set method for motion in normal direction
based on a semi-implicit forward-backward diffusion approach,
SIAM Journal on Scientific Computing, Vol. 32, No. 3 (2010) pp. 1527-1544
( pdf file of the preprint version with more
figures than in the accepted version).
P.Bourgine, R.Cunderlik, O.Drblikova, K.Mikula, N.Peyrieras, M.Remesikova,
B.Rizzi, A.Sarti, 4D embryogenesis image analysis using PDE methods of image
processing, Kybernetika, Vol. 46, No. 2 (2010) pp. 226-259
( pdf file)
Z.Kriva, K.Mikula, N.Peyrieras, B.Rizzi, A.Sarti, O.Stasova,
3D Early Embryogenesis Image Filtering by Nonlinear Partial Differential
Equations, Medical Image Analysis, Vol. 14, No. 4 (2010) pp.
510-526
( pdf file)
C.Zanella, M.Campana, B.Rizzi, C.Melani, G.Sanguinetti, P.Bourgine,
K.Mikula, N.Peyrieras, A.Sarti,
Cells Segmentation from 3-D Confocal Images of Early Zebrafish
Embryogenesis, IEEE Transactions on Image Processing, Vol.19, No.3 (2010)
pp. 770-781
(
abstract)( pdf file)
R.Cunderlik, K.Mikula,
Direct BEM for high-resolution gravity field modelling,
Studia Geophysica et Geodetica,
Vol. 54, No. 2 (2010) pp. 219-238
( pdf file)
Z.Faskova, R.Cunderlik, K.Mikula,
Finite element method for solving geodetic boundary value problems,
Journal of Geodesy, Vol. 84, Issue 2 (2010) pp 135-144
( pdf file)
K.Mikula, D.Sevcovic, M.Balazovjech, A simple, fast and stabilized flowing
finite volume method
for solving general curve evolution equations,
Communications in Computational Physics, Vol. 7, No. 1 (2010) pp. 195-211
( pdf file)
K.Mikula, N.Peyrieras, M.Remesikova, O.Stasova,
Segmentation and analysis of 3D zebrafish cell image data,
Proceeding of the 3rd International Congress on Image and Signal Processing CISP-BMEI 2010,
Yantai, China, Vol. 3 (2010) pp. 1444-1448
(pdf file)
R.Eymard, A.Handlovicova, K.Mikula, Non-diffusive numerical scheme for
regularized mean curvature flow level set equation in image processing,
Proceedings of the 3rd International Congress on Image and Signal Processing CISP-BMEI 2010, Yantai,
China, Vol. 2 (2010) pp. 748-753
(pdf file)
K.Mikula, M.Ohlberger, A new Inflow-Implicit/Outflow-Explicit Finite
Volume Method for Solving Variable Velocity Advection Equations,
Preprint 01/10 - N, Angewandte Mathematik und Informatik,
Universitaet Muenster, June 2010
( pdf file).
R.Eymard, A.Handlovicova, K.Mikula,
Approximation of nonlinear parabolic equations using a family of conformal
and non-conformal schemes, January 2010 (
pdf file ).
D.Sevcovic, B.Stehlikova, K.Mikula, Analyticke a numericke metody ocenovania
financnych derivatov (in Slovak, Analytical and numerical methods for
pricing derivative securities),
Publishing
House of the Slovak University of Technology in Bratislava, ISBN
978-80-227-3014-3 (2009) 200 pages
( pdf file containing selected pages)
O.Drblikova, A.Handlovicova, K.Mikula,
Error estimates of the finite volume scheme for the
nonlinear tensor-driven anisotropic diffusion,
Applied Numerical Mathematics, Vol. 59, No. 10
(2009) pp. 2548-2570
( pdf file - preprint version)
K.Mikula, M.Remesikova, Finite volume schemes for the generalized subjective
surface equation in image segmentation, Kybernetika, Vol. 45, No. 4 (2009)
pp. 646-656
( pdf file)
M.Benes, K.Mikula, T.Oberhuber, D.Sevcovic,
Comparison study for Level set and Direct Lagrangian methods
for computing Willmore flow of closed planar curves,
Computing and Visualization in Science, Vol. 12, No. 6 (2009) pp. 307-317
(pdf file)
P.Bourgine, P.Frolkovic, K.Mikula, N.Peyrieras, M.Remesikova,
Extraction of the intercellular skeleton from 2D microscope images of early
embryogenesis, in
Lecture Notes in Computer Science 5567 (Proceeding of the 2nd International
Conference on Scale Space and Variational Methods in Computer Vision, Voss,
Norway, June 1-5,2009), Springer (2009) pp. 38-49
(pdf file)
O.Drblikova, K.Mikula, N.Peyrieras,
The nonlinear tensor diffusion in segmentation of meaningful biological
structures from image sequences of zebrafish embryogenesis,
in Lecture Notes in Computer Science 5567 (Proceeding of the 2nd International
Conference on Scale Space and Variational Methods in Computer Vision, Voss,
Norway, June 1-5,2009), Springer (2009)
(pdf file)
M.Balazovjech, K.Mikula,
A higher order scheme for the curve shortening flow of plane curves,
Proceedings of contributed papers and posters,
ALGORITMY 2009 -
18th Conference on Scientific Computing, Vysoke Tatry-Podbanske, Slovakia,
March 15-20, 2009, Publishing
House of the Slovak University of Technology in Bratislava, ISBN
978-80-227-3032-7 (2009) pp. 165-175
(pdf file)
Z.Kriva, K.Mikula,
Adaptive diamond cell finite volume method in image processing,
Proceedings of contributed papers and posters,
ALGORITMY 2009 -
18th Conference on Scientific Computing, Vysoke Tatry-Podbanske, Slovakia,
March 15-20, 2009, Publishing
House of the Slovak University of Technology in Bratislava, ISBN
978-80-227-3032-7 (2009) pp. 121-133
(pdf file)
J.Urban, K.Mikula,
Segmentacia medicinskych dat pomocou pohybujucich sa rovinnych
kriviek (Segmentation of medical data using evolving plane curves),
Proceedings of the conference Mathematics, Geometry and their Applications
MAGIA 2009, Kocovce, Slovakia (2009)
(pdf file in Slovak)
(video)
R.Spir, R.Cunderlik, K.Mikula,
Riesenie geodetickej okrajovej ulohy so sikmou derivaciou
metodou okrajovych prvkov (Solution of the geodetic boundary value problem
with the oblique derivative using the boundary element method),
Proceedings of the conference Mathematics, Geometry and their Applications
MAGIA 2009, Kocovce, Slovakia (2009)
(pdf file in Slovak)
M.Tunega, R.Cunderlik, K.Mikula,
Filtracia geodetickych dat na povrchu Zeme pomocou nelinearnych difuznych
rovnic (Filtration of geodetic data on the Earth surface using nonlinear
diffusion equations),
Proceedings of the conference Mathematics, Geometry and their Applications
MAGIA 2009, Kocovce, Slovakia (2009)
(pdf file in Slovak)
K.Mikula, M.Ohlberger, A new level set method for motion in normal direction
based on a forward-backward diffusion formulation,
Technical Report 05/09 - N, FB 10 , Universitaet Muenster, Number 05/09 - N -
May 2009
( pdf file), see also
link .
R.Eymard, A.Handlovicova, K.Mikula,
Study of a finite volume scheme for the regularised mean curvature flow
level set equation, July 2009
pdf file .
A.Handlovicova, K.Mikula,
Stability and consistency of the semi-implicit co-volume scheme for
regularized mean curvature flow equation in level set formulation,
Applications of Mathematics, Vol. 53, No. 2 (2008) pp. 105-129
(pdf file)
R.Cunderlik, K.Mikula, M.Mojzes,
Numerical solution of the linearized fixed gravimetric boundary value
problem, Journal of Geodesy,
Vol. 82, No. 1 (2008) pp. 15-29
(pdf file)
K.Mikula, N.Peyrieras, M.Remesikova, A.Sarti,
3D embryogenesis image segmentation by the generalized subjective surface
method using the finite volume technique, in
Finite Volumes for Complex Applications V: Problems and Perspectives (Eds.
R.Eymard, J.M.Herard), ISTE and WILEY, London, 2008, pp. 585-592
(pdf file)
O.Drblikova, K.Mikula, Semi-implicit diamond-cell finite volume scheme for
3D nonlinear tensor diffusion in coherence enhancing image filtering,
in
Finite Volumes for Complex Applications V: Problems and Perspectives (Eds.
R.Eymard, J.M.Herard), ISTE and WILEY, London, 2008, pp. 343-350
(pdf file)
K.Mikula, A.Sarti,
Parallel co-volume subjective surface method for 3D medical image
segmentation, in: Parametric and Geometric Deformable Models: An
application in Biomaterials and Medical Imagery, Volume-II, Springer
Publishers, (Eds. Jasjit S. Suri and Aly Farag), ISBN: 0-387-31204-8, 2007,
pp. 123-160
(pdf file)
O.Drblikova, K.Mikula,
Convergence analysis of finite volume scheme for nonlinear tensor
anisotropic diffusion in image processing,
SIAM Journal on Numerical Analysis, Vol. 46, No.1 (2007) pp. 37-60
( version with fully detailed convergence
proof)
P.Frolkovic, K.Mikula,
High-resolution flux-based level set method,
SIAM Journal on Scientific Computing, Vol. 29, No. 2 (2007) pp. 579-597
(pdf file),
see also Preprint 2005
P.Frolkovic,
K.Mikula,
Flux-based level set method: a finite volume method for evolving interfaces,
Applied Numerical Mathematics, Vol. 57, No. 4 (2007) pp. 436-454
(pdf file), see also Preprint 2003
O.Drblikova, M.Komornikova, M.Remesikova, P.Bourgine, K.Mikula, N.Peyrieras,
A.Sarti, Estimate of the cell number growth rate using PDE methods of image
processing and time series analysis,
Journal of Electrical Engineering, Vol. 58, No 7/s (2007) pp. 86-92
(pdf file)
P.Frolkovic, K.Mikula, N.Peyrieras, A.Sarti,
A counting number of cells and cell segmentation using advection-diffusion
equations, Kybernetika, Vol. 43, No. 6(2007) pp. 817-829
(pdf file)
Z.Faskova, R.Cunderlik, J.Janak, K.Mikula, M.Sprlak,
Gravimetric quasigeoid in Slovakia by the finite element method,
Kybernetika, Vol. 43, No. 6(2007) pp. 789-796
(pdf file)
B.Rizzi, M.Campana, C.Zanella, C.Melani, R.Cunderlík,
Z.Krivá, P.Bourgine, K.Mikula, N.Peyrieras, A.Sarti, 3D
zebrafish embryo image filtering by nonlinear partial differential
equations, Conf. Proc. IEEE Eng. Med. Biol. Soc. (2007) No.1, pp. 6251-4
(pdf file)
C.Zanella, B.Rizzi, C.Melani, M.Campana, P.Bourgine, K.Mikula,
N.Peyrieras, A.Sarti, Segmentation of
Cells from 3-D Confocal Images of Live Zebrafish Embryo, Conf. Proc. IEEE
Eng. Med. Biol. Soc. (2007) No.1, pp. 6027-30
(pdf file)
C.Melani, M.Campana, B.Lombardot, B.Rizzi, F.Veronesi,
C.Zanella, P.Bourgine, K.Mikula, N.Peyrieras,
A.Sarti, Cells tracking in a live zebrafish embryo, Conf. Proc.
IEEE Eng. Med. Biol. Soc. (2007) No.1, pp. 1631-4
(pdf file)
K.Mikula, Numerical solution, analysis and application of geometrical
nonlinear diffusion equations, Edition of Scientific Publications,
No. 34, Publishing House of the Slovak University of Technology, Bratislava,
2006, ISBN 80-227-2392-4
(pdf file)
S.Corsaro, K.Mikula, A.Sarti, F.Sgallari,
Semi-implicit co-volume method in 3D image
segmentation, SIAM Journal on Scientific Computing, Vol. 28, No. 6 (2006)
pp. 2248-2265
(pdf file)
K.Mikula, A.Sarti, F.Sgallari,
Co-volume method for Riemannian mean curvature flow in subjective surfaces
multiscale segmentation, Computing and Visualization in Science, Vol. 9,
No. 1 (2006) pp. 23-31
(pdf file)
K.Mikula,
D.Sevcovic, Evolution of curves on surface driven by the geodesic
curvature and external force, Applicable Analysis, Vol. 85, No. 4 (2006) pp.
345-362
(pdf file)
K.Mikula, A.Sarti, F.Sgallari,
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, 2005, pp. 583-626
(pdf file)
(poscript file)
R.Cunderlik, K.Mikula, Boundary element method for the gravity field
modelling in the Himalayas, Slovak Journal of Civil Engineering, Volume
XIII, 2005/4, pp. 13-18
J.Lovas, K.Mikula, Mathematical modeling of a combined hot-water heating
system by means of the finite element method,
Slovak Journal of Civil Engineering, Volume
XIII, 2005/2, pp. 15-19
K.Mikula, D.Sevcovic,
Tangentially stabilized Lagrangian algorithm for elastic curve evolution
driven by intrinsic Laplacian of curvature,
ALGORITMY 2005, Conference on Scientific Computing, Vysoke Tatry-Podbanske,
Slovakia, March 13-18, 2005,
Proceedings of contributed papers and
posters (2005) pp.
32-41
(pdf file)
V. Minarik, J. Kratochvil and K. Mikula,
Numerical simulation of dislocation dynamics by means of parametric
approach,
Proceedings of Czech-Japanese Seminar in Applied Mathematics 2004
, editors M. Benes, J. Mikyska, T. Oberhuber, Faculty of Nuclear
Sciences and Physical Engineering, Czech Technical University in Prague,
2005, ISBN 80-01-03181-0, pp. 128-138
K.Mikula, D.Sevcovic,
Qualitative analysis and computation of a flow of surface curves driven by
the geodesic curvature,
Proceedings of Czech-Japanese Seminar in Applied Mathematics 2004
, editors M. Benes, J. Mikyska, T. Oberhuber, Faculty of Nuclear
Sciences and Physical Engineering, Czech Technical University in Prague,
2005, ISBN 80-01-03181-0, pp. 176-183
P.Frolkovic,
K.Mikula,
High-resolution flux-based level set method,
Preprint 2005-12, Department of Mathematics and Descriptive Geometry,
Slovak University of Technology, Bratislava (2005)
( pdf file)
K.Mikula,
D.Sevcovic,
Computational and qualitative aspects of evolution of curves driven by
curvature and external force,
Computing and Visualization in
Science, Vol. 6, No. 4 (2004) pp. 211-225
(pdf file)
(poscript file)
K.Mikula, D.Sevcovic, A direct method for solving an anisotropic mean
curvature flow of planar curve with an external force,
Mathematical Methods
in Applied Sciences, Vol. 27, No. 13 (2004) pp. 1545-1565
(pdf file)
K.Mikula, T.Preusser, M.Rumpf, Morphological image sequence processing,
Computing and Visualization in
Science, Vol. 6, No. 4 (2004) pp. 197-209
(pdf file)
(poscript file)
M.Benes, V.Chalupecky, K.Mikula, Geometrical image segmentation by the
Allen-Cahn equation,
Applied Numerical Mathematics, Vol. 51 (2004) pp. 187-
205
(pdf file)
R.Cunderlik, M.Mojzes, K.Mikula, A comparison of the variational
solution of the Neumann geodetic boundary value problem with the
geopotential model EGM-96, Contributions to Geophysics and Geodesy, Vol.
34, No. 3 (2004) pp. 209-225 (pdf file)
V.Minarik, J.Kratochvil, K.Mikula, M.Benes, Numerical simulation of
dislocation dynamics, in Numerical Mathematics and Advanced Applications
ENUMATH 2003 (Eds. M.Feistauer et al.), Springer-Verlag, 2004, pp. 631-640
(pdf file)
S.Corsaro, K.Mikula, A.Sarti, F.Sgallari,
Semi-implicit co-volume method in 3D image
segmentation, Preprint 2004-12, Department of Mathematics and Descriptive
Geometry, Slovak University of
Technology, Bratislava (2004)
(pdf file)
(poscript file)
K.Mikula, Editorial: ALGORITMY 2002 conference - Part 1,
Computing and
Visualization in Science,
Vol. 6, No. 4 (2004) pp. 171-172
K.Mikula, Editorial: ALGORITMY 2002 conference - Part 2,
Computing and
Visualization in Science, Vol. 7, No. 1 (2004) pp. 1-2
K.Mikula, T.Preusser, M.Rumpf, F.Sgallari, On anisotropic geometric
diffusion in 3D image processing and image sequence analysis, in Trends in
Nonlinear Analysis (M.Kirkilionis et al. Eds.), Springer, Heidelberg, 2003,
pp. 307-322
(pdf file)
A.Handlovicova, K.Mikula, F.Sgallari,
Semi-implicit complementary volume scheme for solving level set like
equations in image processing and curve evolution,
Numerische Mathematik, Vol. 93, No. 4 (2003) pp. 675-695
(pdf file)
(poscript file)
K.Mikula, F.Sgallari, Semi-implicit finite volume scheme for image
processing in 3D cylindrical geometry,
Journal of Computational and Applied
Mathematics , Vol. 161, No. 1 (2003) pp. 119-132
(pdf file)
(poscript file)
C.Ungvarský, K.Mikula, Numerical solution to two factor model for option
pricing with stochastic volatility, Journal of Electrical Engineering, Vol.
54, No. 12/s (2003) pp. 24-28
(pdf file)
S.Corsaro, V. de Simone, A.Handlovicova, K.Mikula, F.Sgallari, Linear co-
volume scheme for solving anisotropic curvature driven motions, in
Numerical Mathematics and Advanced Applications, ENUMATH 2001 (Eds. F.
Brezzi et al.), Springer-Verlag Italia, Milano, 2003, pp. 483-494
(pdf file)
P.Frolkovic,
K.Mikula,
Flux-based level set method: a finite volume method for evolving interfaces,
Preprint IWR/SFB No. 2003-15 ,
Interdisciplinary Center for Scientific
Computing, University of Heidelberg (2003)
(pdf file - revised version)
K.Mikula,
Image processing with partial differential equations,
in Modern
Methods in Scientific Computing and Applications (A.Bourlioux and M.Gander,
Eds.), NATO Science Ser. II, Vol. 75, Kluwer Academic Publishers, Dodrecht,
2002, pp. 283-322
(pdf file)
(poscript file)
A.Sarti, K.Mikula, F.Sgallari, C.Lamberti,
Nonlinear multiscale analysis models for filtering of 3D+time biomedical
images, in Geometric methods in bio-medical image processing (Ed.
R.Malladi), Springer, 2002, 107-128
Z.Kriva, K.Mikula,
An adaptive finite volume scheme for solving nonlinear diffusion equations
in image processing,
Journal for Visual Communication and Image Representation, Vol. 13,
No.1/2 (2002) pp.22-35
( pdf file)
A.Handlovicova, K.Mikula, F.Sgallari,
Variational numerical methods for
solving nonlinear
diffusion equations
arising in image processing,
Journal for Visual Communication and Image Representation, Vol. 13,
No.1/2 (2002)
pp. 217-237
( pdf file)
A.Sarti, K.Mikula, F.Sgallari, C.Lamberti, Evolutionary PDEs for
biomedical image processing, Journal of Biomedical Informatics, Vol. 35,
No. 2 (2002) pp. 77-91
(pdf file)
A.Handlovicova, K.Mikula: Analysis of a semidiscrete scheme for solving
image smoothing equation of mean curvature flow type,
Acta Math. Univ.
Comenianae, Vol. 71, No. 1 (2002) pp. 93-112
(pdf file)
R.Cunderlik, K.Mikula, M.Mojzes,
3D BEM application to Neumann geodetic
BVP using the collocation with linear basis functions,
ALGORITMY 2002, Conference on Scientific Computing, Vysoke Tatry-Podbanske,
Slovakia, September 8-13, 2002,
Proceedings of contributed papers and
posters (2002) pp.
268-275
(poscript file)
(pdf file)
A.Balazova, D.Barokova, K.Mikula, D.Pfender, A.Soltesz, Numerical
modelling of the groundwater flow in the left floodplain area of the Danube
river,
ALGORITMY 2002, Conference on Scientific Computing, Vysoke
Tatry-Podbanske,
Slovakia, September 8-13, 2002,
Proceedings of contributed papers and
posters (2002) pp. 237-244
(poscript file)
(pdf file)
K.Mikula, Solution and application of anisotropic
curvature driven evolution of curves (and surfaces), in Numerical methods
for viscosity solutions and applications (M.Falcone and Ch. Makridakis,
Eds.),
Series on Advances in Mathematics for Applied Sciences - Vol. 59,
World Scientific, 2001, 173-196
(poscript file)
K.Mikula,
D.Sevcovic,
Evolution of plane curves driven by a nonlinear function of curvature and
anisotropy,
SIAM Journal on Applied Mathematics, Vol.61, No.5 (2001) 1473-1501
(poscript file)
(pdf file)
K.Mikula, N.Ramarosy,
Semi-implicit finite volume scheme for solving nonlinear diffusion equations
in image processing,
Numerische Mathematik 89, No.3 (2001) 561-590
(poscript file)
(pdf file)
E.Baensch, K.Mikula,
Adaptivity in 3D image processing,
Computing and Visualization in Science, Vol. 4, No. 1 (2001) 21-30
(pdf file)
(poscript file)
J.Kacur, K.Mikula,
Slow and fast diffusion effects in image processing,
Computing and Visualization in Science, Vol.3, No.4 (2001)
185-195
(poscript file)
(pdf file)
Z.Kriva, K.Mikula,
Adaptive finite volume schemes in processing of 3D data sets
Journal of Electrical Engineering, Vol 52, No. 10/s (2001) 53-58
K.Mikula, S.Morigi, F.Sgallari, Registration based on evolution models,
in Advanced Signal Processing Algorithms, Architectures and Implementations
XI, Proceedings of SPIE Int. conf. for optical engineering (F.T.Luk, Ed.),
San Diego (2001) pp. 346-356
K.Mikula,
Parallel filtering of three dimensional image sequences,
Daedalus, News from the MINOS
Project, No. 2 (2001) 6-7
(MSWord file)
K.Mikula, S.Morigi, A.Sarti, F.Sgallari: Parallel multiscale filtering
of 2D and 3D image sequences, in Science and Supercomputing at CINECA (Eds.
F.Garofalo, M.Moretti, M.Voli), 2001, pp. 433-441, podiel 25%
K.Mikula, Parallel filtering of three dimensional image sequences, in
Science and Supercomputing at CINECA (Eds. F.Garofalo, M.Moretti, M.Voli),
2001, pp. 674-677
Z.Kriva, K.Mikula,
A model and numerical scheme for processing of color images,
Journal of Electrical Engineering, Vol 51, No. 12/s (2000) 21-25
Z.Kriva, K.Mikula,
An Adaptive Finite Volume Method in Processing of Color Images,
ALGORITMY 2000, Conference on Scientific Computing, Vysoke Tatry-Podbanske,
Slovakia, September 10-15, 2000,
Proceedings of contributed papers and
posters (2000) 174-187
(pdf file)
(poscript file)
R.Cunderlik, K.Mikula, M.Mojzes,
The boundary element method applied to the determination of the global
quasigeoid,
ALGORITMY 2000, Conference on Scientific Computing, Vysoke Tatry-Podbanske,
Slovakia, September 10-15, 2000,
Proceedings of contributed papers and
posters (2000) 301-308
( MSWord file)
D.Sevcovic, K.Mikula: Evolution of plane curves driven by a nonlinear
function of curvature and anisotropy, Equadiff 99, Proceeding of the Int.
Conference on Differential Equations (Eds. B.Fiedler, K. Groger and J.
Spekels), World Scientific (2000) 283-285
A.Sarti, K.Mikula, F.Sgallari,
Nonlinear multiscale analysis of 3D echocardiographic sequences,
IEEE Transactions on Medical Imaging, Vol. 18, No.6 (1999) 453-467
(pdf file)
(poscript file)
K.Mikula, D.Sevcovic,
Solution of nonlinearly curvature driven evolution
of plane curves,
Applied Numerical Mathematics , Vol. 31, No.2 (1999) 191-207
(poscript file)
(pdf file)
M.Benes, K.Mikula, Simulation of anisotropic motion by mean curvature -
comparison of phase field and sharp interface approaches,
Acta Math. Univ. Comenianae, Vol. LXVII, 1 (1998) pp. 17- 42
(poscript file)
(pdf file)
A.Handlovicova, K.Mikula, A.Sarti,
Numerical solution of parabolic equations related to
level set formulation of mean curvature flow,
Computing and Visualization in Science , Vol.1, No. 3 (1998) pp. 179-182
(poscript file)
(pdf file)
J.Janak, M.Mojzes, K.Mikula, Lokalny kvazigeoid v oblasti Bratislavy,
Geodeticky a kartograficky obzor 4/98 (1998) pp. 73-79
K.Mikula, Parcialne diferencialne rovnice a numericke
metody vo financnej matematike,
Zbornik konferencie Matematicka statistika a numericka matematika na
vysokych skolach, Kalnica (1998) pp. 49-85
( MSWord file)
K.Mikula, Numerical experiments on geometry driven diffusion with
applications
in image processing, Science and Supercomputing at CINECA,
Report 1997 (Ed. M.Voli, CINECA
Supercomputing Group) (1998) pp. 689-692
K.Mikula, Solution of nonlinear curvature driven evolution of plane convex curves,
Applied Numerical Mathematics 23 (1997) 347-360
(poscript file)
(pdf file)
E.Baensch, K.Mikula, A coarsening finite
element strategy in image selective smoothing,
Computing and Visualization in Science ,
Vol. 1, No. 1 (1997) pp. 53-61
(poscript file)
(pdf file)
K.Mikula, A.Sarti, C.Lamberti, Geometrical diffusion in
3D-echocardiography,
Proceedings of contributed papers and posters,
ALGORITMY'97, Conference on Scientific Computing, West Tatra
Mountains (1997) pp. 167-181
(pdf file)
(poscript file)
J.Kacur, K.Mikula,
Slowed anisotropic diffusion,
B.t.H.Romeny, L.Florack, J.Koenderink,M. Viergevier (Eds.), Scale-space
theory in computer vision, Lecture Notes in Computer Science,
Vol. 1252,
Proceedings of
1-st International Conference on Scale Space Theory in Computer Vision,
Springer Berlin (1997) pp. 357-360
(pdf file)
(poscript file)
F.Brancaleoni, K.Mikula, A.Sarti, C.Lamberti,
3D echocardiography pre-processing for ventricular volume estimation,
Computers in Cardiology, IEEE Comp. Soc. Press,
Los Alamitos (Proceedings of the 1997 24th
Annual Meeting on Computers in Cardiology, Lund, Sweden) (1997) pp. 311-314
J.Janak, K.Mikula, M.Mojzes, Solution of Geodetic Free Boundary Problem,
Proceedings of contributed papers and posters,
ALGORITMY'97, Conference on Scientific Computing, West Tatra
Mountains (1997) pp. 59-70
K.Mikula, J.Kacur, Evolution of convex plane curves
describing anisotropic motions of phase interfaces,
SIAM J. Scientific Computing, vol.17 No.6 (1996), 1302-1327
J.Kacur, K.Mikula, Solution of nonlinear diffusion
appearing in image smoothing and edge detection,
Applied Numerical Mathematics 17 (1995), 47-59
(pdf file)
K.Mikula, Numerical solution of nonlinear diffusion
with finite extinction phenomenon,
Acta Math. Univ. Comenianae
64/2 (1995), 173-184
(pdf file)
K.Mikula, Spracovanie obrazu nelinearnou difuziou a systemom MATHEMATICA,
Zbornik prednasok 13. Sympozia o algoritmoch ALGORITMY'95, Krpacovo (1995)
pp. 165-171
J.Kacur, K.Mikula,
Numerical solution of the anisotropic curve shortening flow,
Proceedings of International Symposium on Numerical Analysis ISNA'92,
Prague, Part III. Contributed Papers (1992)
pp. 108-121