# Semi-implicit scheme for semi-automatic segmentation in NaturaSat software

## Main Article Content

## Abstract

In this paper, we present new accurate and efficient semi-automatic segmentation method for Sentinel-2 satellite images which is used in NaturaSat software for exploration of Natura 2000 habitats. The method is based on the Lagrangian approach to evolving plane curves and the mathematical model incorporates the tangential redistribution of grid points. The Lagrangian curve evolution is solved by the semi-implicit scheme and new robust and efficient initial condition for curve evolution is proposed. The final semi-automatic segmentation is automatically adjusted to represent the desired boundaries accurately with a control of the smoothness of the final segmentation result. Together with comprehensive discussion on semi-automatic segmentation, the NaturaSat software design and its functionality is presented as well.

## Article Details

How to Cite

Ambroz, M., Kollár, M., & Mikula, K.
(2020).
Semi-implicit scheme for semi-automatic segmentation in NaturaSat software.

*Proceedings Of The Conference Algoritmy,*, 171 - 180. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/1579/831
Section

Articles

## References

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[9] M.Kimura, Numerical analysis for moving boundary problems using the boundary tracking method, Japan J. Indust. Appl. Math., 14 (1997), pp. 373-398.

[10] K.Mikula, M.Ohlberger, Inflow-Implicit/Outflow-Explicit Scheme for Solving Advection Equations, in Finite Volumes in Complex Applications VI, Problems and 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

[11] K.Mikula, M.Ohlberger, J.Urbán, Inflow-Implicit/Outflow-Explicit Finite Volume Methods for Solving Advection Equations, Applied Numerical Mathematics, Vol. 85 (2014) pp. 16-37

[12] K.Mikula, D.Ševčovič, Evolution of plane curves driven by a nonlinear function of curvature and anisotropy, SIAM J. Appl. Math., 61 (2001), pp. 1473–1501.

[13] K.Mikula, D.Ševčovič, 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

[14] K.Mikula, D.Ševčovič, M.Balažovjech, 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

[15] K.Mikula, J.Urbán, 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

[16] K.Mikula, J.Urbán, M.Kollár, M.Ambroz, I.Jarolimek, J.Šibik, M.Šibiková, Semi-automatic segmentation of NATURA 2000 habitats in Sentinel-2 satellite images by evolving open curves, Discrete and Continuous Dynamical Systems Series S, accepted

[17] K.Mikula, J.Urbán, M.Kollár, M.Ambroz, I.Jarolimek, J.Šibik, M.Šibiková, An automated segmentation of NATURA 2000 habitats from Sentinel-2 optical data, Discrete and Continuous Dynamical Systems Series S, accepted

[18] The Qt Company, Qt: Cross-platform software development for embedded & desktop, (2020). URL https://www.qt.io/

[2] EuropeanSpaceAgency,CopernicusOpenAccessHub,(2020).URL https://scihub.copernicus.eu/

[3] European Space Agency, OpenSearch API - Copernicus Open Access Hub, (2020). URL https://scihub.copernicus.eu/userguide/OpenSearchAPI

[4] Gailly, J., Adler, M, Zlib compression library, (2004). URL https://zlib.net/

[5] GDAL/OGR contributors, GDAL/OGR Geospatial Data Abstraction software Library Open Source Geospatial Foundation, (2020). URL https://gdal.org

[6] G. Guennebaud, B. Jacob,Eigen v3,(2020). URL http://eigen.tuxfamily.org

[7] T.Y.Hou, J.Lowengrub, M.Shelley, Removing the stiffness from interfacial flows and surface tension, J. Comput. Phys., 114 (1994) pp. 312-338.

[8] Ch. F. F. Karney, GeographicLib, (2019), URL https://geographiclib.sourceforge.io/

[9] M.Kimura, Numerical analysis for moving boundary problems using the boundary tracking method, Japan J. Indust. Appl. Math., 14 (1997), pp. 373-398.

[10] K.Mikula, M.Ohlberger, Inflow-Implicit/Outflow-Explicit Scheme for Solving Advection Equations, in Finite Volumes in Complex Applications VI, Problems and 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

[11] K.Mikula, M.Ohlberger, J.Urbán, Inflow-Implicit/Outflow-Explicit Finite Volume Methods for Solving Advection Equations, Applied Numerical Mathematics, Vol. 85 (2014) pp. 16-37

[12] K.Mikula, D.Ševčovič, Evolution of plane curves driven by a nonlinear function of curvature and anisotropy, SIAM J. Appl. Math., 61 (2001), pp. 1473–1501.

[13] K.Mikula, D.Ševčovič, 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

[14] K.Mikula, D.Ševčovič, M.Balažovjech, 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

[15] K.Mikula, J.Urbán, 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

[16] K.Mikula, J.Urbán, M.Kollár, M.Ambroz, I.Jarolimek, J.Šibik, M.Šibiková, Semi-automatic segmentation of NATURA 2000 habitats in Sentinel-2 satellite images by evolving open curves, Discrete and Continuous Dynamical Systems Series S, accepted

[17] K.Mikula, J.Urbán, M.Kollár, M.Ambroz, I.Jarolimek, J.Šibik, M.Šibiková, An automated segmentation of NATURA 2000 habitats from Sentinel-2 optical data, Discrete and Continuous Dynamical Systems Series S, accepted

[18] The Qt Company, Qt: Cross-platform software development for embedded & desktop, (2020). URL https://www.qt.io/