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An automated segmentation of NATURA 2000 habitats from Sentinel-2 optical data
Semi-automatic segmentation of NATURA 2000 habitats in Sentinel-2 satellite images by evolving open curves
1. | Department of Mathematics, Slovak University of Technology, Radlinského 11,810 05 Bratislava, Slovakia |
2. | Algoritmy:SK, s.r.o., Šulekova 6,811 06 Bratislava, Slovakia |
3. | Institute of Botany, Slovak Academy of Sciences, Dúbravská cesta 9,845 23 Bratislava, Slovakia |
In this paper we introduce mathematical model and real-time numerical method for segmentation of Natura 2000 habitats in satellite images by evolving open planar curves. These curves in the Lagrangian formulation are driven by a suitable velocity vector field, projected to the curve normal. Besides the vector field, the evolving curve is influenced also by the local curvature representing a smoothing term. The model is numerically solved using the flowing finite volume method discretizing the arising intrinsic partial differential equation with Dirichlet boundary conditions. The time discretization is chosen as an explicit due to the ability of real-time edge tracking. We present the results of semi-automatic segmentation of various areas across Slovakia, from the riparian forests to mountainous areas with scrub pine. The numerical results were compared to habitat boundaries tracked by GPS device in the field by using the mean and maximal Hausdorff distances as criterion.
References:
[1] |
M. Ambroz, M. Balažovjech, M. Medla and K. Mikula,
Numerical modeling of wildland surface fire propagation by evolving surface curves, Advances in Computational Mathematics, 45 (2019), 1067-1103.
doi: 10.1007/s10444-018-9650-4. |
[2] |
M. Balažovjech, K. Mikula, M. Petrášová and J. Urbán, Lagrangean method with topological changes for numerical modelling of forest fire propagation, Proceedings of ALGORITMY, (2012), 42-52. Google Scholar |
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[5] |
M. Kolář, M. Beneš and D. Ševčovič,
Computational analysis of the conserved curvature driven flow for open curves in the plane, Mathematics and Computers in Simulation, 126 (2016), 1-13.
doi: 10.1016/j.matcom.2016.02.004. |
[6] |
Z. Krivá, K. Mikula, M. Peyriéras, B. Rizzi, A. Sarti and O. Stašová, 3D early embryogenesis image filtering by nonlinear partial differential equations, Medical Image Analysis, 14 (2010), 510-526. Google Scholar |
[7] |
K. Mikula and D. Ševčovič,
Computational and qualitative aspects of evolution of curves driven by curvature and external force, Computing and Visualization in Science, 6 (2004), 211-225.
doi: 10.1007/s00791-004-0131-6. |
[8] |
K. Mikula and D. Ševčovič,
Evolution of curves on a surface driven by the geodesic curvature and external force, Applicable Analysis, 85 (2006), 345-362.
doi: 10.1080/00036810500333604. |
[9] |
K. Mikula, D. Ševčovič and M. Balažovjech,
A simple, fast and stabilized flowing finite volume method for solving general curve evolution equations, Communications in Computational Physics, 7 (2010), 195-211.
doi: 10.4208/cicp.2009.08.169. |
[10] |
P. Pauš, M. Beneš, M. Kolář and J. Kratochvíl, Dynamics of dislocations described as evolving curves interacting with obstacles, Modelling and Simulation in Materials Science and Engineering, 24 (2016), 34 pp. Google Scholar |
[11] |
P. Perona and J. Malik,
Scale space and edge detection using anisotropic diffusion, Proceedings of the IEEE Society Workshop on Computer Vision, 12 (1987), 629-639.
doi: 10.1109/34.56205. |
[12] |
Hausdorff distance, 20 12 2018, https://en.wikipedia.org/wiki/Hausdorff_distance. Google Scholar |
show all references
References:
[1] |
M. Ambroz, M. Balažovjech, M. Medla and K. Mikula,
Numerical modeling of wildland surface fire propagation by evolving surface curves, Advances in Computational Mathematics, 45 (2019), 1067-1103.
doi: 10.1007/s10444-018-9650-4. |
[2] |
M. Balažovjech, K. Mikula, M. Petrášová and J. Urbán, Lagrangean method with topological changes for numerical modelling of forest fire propagation, Proceedings of ALGORITMY, (2012), 42-52. Google Scholar |
[3] |
V. Caselles, R. Kimmel and G. Sapiro,
Geodesic active contours, International Journal of Computer Vision, 22 (1997), 61-79.
doi: 10.1109/ICCV.1995.466871. |
[4] |
S. Kichenassamy, A. Kumar, P. Olver, A. Tannenbaum, A. Yezzi, Jr. and ,
Conformal curvature flows: From phase transitions to active vision, Arch. Rational Mech. Anal., 134 (1996), 275-301.
doi: 10.1007/BF00379537. |
[5] |
M. Kolář, M. Beneš and D. Ševčovič,
Computational analysis of the conserved curvature driven flow for open curves in the plane, Mathematics and Computers in Simulation, 126 (2016), 1-13.
doi: 10.1016/j.matcom.2016.02.004. |
[6] |
Z. Krivá, K. Mikula, M. Peyriéras, B. Rizzi, A. Sarti and O. Stašová, 3D early embryogenesis image filtering by nonlinear partial differential equations, Medical Image Analysis, 14 (2010), 510-526. Google Scholar |
[7] |
K. Mikula and D. Ševčovič,
Computational and qualitative aspects of evolution of curves driven by curvature and external force, Computing and Visualization in Science, 6 (2004), 211-225.
doi: 10.1007/s00791-004-0131-6. |
[8] |
K. Mikula and D. Ševčovič,
Evolution of curves on a surface driven by the geodesic curvature and external force, Applicable Analysis, 85 (2006), 345-362.
doi: 10.1080/00036810500333604. |
[9] |
K. Mikula, D. Ševčovič and M. Balažovjech,
A simple, fast and stabilized flowing finite volume method for solving general curve evolution equations, Communications in Computational Physics, 7 (2010), 195-211.
doi: 10.4208/cicp.2009.08.169. |
[10] |
P. Pauš, M. Beneš, M. Kolář and J. Kratochvíl, Dynamics of dislocations described as evolving curves interacting with obstacles, Modelling and Simulation in Materials Science and Engineering, 24 (2016), 34 pp. Google Scholar |
[11] |
P. Perona and J. Malik,
Scale space and edge detection using anisotropic diffusion, Proceedings of the IEEE Society Workshop on Computer Vision, 12 (1987), 629-639.
doi: 10.1109/34.56205. |
[12] |
Hausdorff distance, 20 12 2018, https://en.wikipedia.org/wiki/Hausdorff_distance. Google Scholar |













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