×

Semi-automatic segmentation of NATURA 2000 habitats in sentinel-2 satellite images by evolving open curves. (English) Zbl 1468.35215

Summary: 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.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
92F05 Other natural sciences (mathematical treatment)
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
68U10 Computing methodologies for image processing
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
35R37 Moving boundary problems for PDEs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] M. Ambroz; M. Balažovjech; M. Medla; K. Mikula, Numerical modeling of wildland surface fire propagation by evolving surface curves, Advances in Computational Mathematics, 45, 1067-1103 (2019) · Zbl 1415.65206
[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. · Zbl 1278.65131
[3] V. Caselles; R. Kimmel; G. Sapiro, Geodesic active contours, International Journal of Computer Vision, 22, 61-79 (1997) · Zbl 0894.68131
[4] S. Kichenassamy; A. Kumar; P. Olver; A. Tannenbaum; A. Yezzi; Jr.; , Conformal curvature flows: From phase transitions to active vision, Arch. Rational Mech. Anal., 134, 275-301 (1996) · Zbl 0937.53029
[5] M. Kolář; M. Beneš; D. Ševčovič, Computational analysis of the conserved curvature driven flow for open curves in the plane, Mathematics and Computers in Simulation, 126, 1-13 (2016)
[6] Z. Krivá; K. Mikula; M. Peyriéras; B. Rizzi; A. Sarti; O. Stašová, 3D early embryogenesis image filtering by nonlinear partial differential equations, Medical Image Analysis, 14, 510-526 (2010)
[7] K. Mikula; D. Ševčovič, Computational and qualitative aspects of evolution of curves driven by curvature and external force, Computing and Visualization in Science, 6, 211-225 (2004)
[8] K. Mikula; D. Ševčovič, Evolution of curves on a surface driven by the geodesic curvature and external force, Applicable Analysis, 85, 345-362 (2006) · Zbl 1097.35084
[9] 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, 7, 195-211 (2010) · Zbl 1364.65175
[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.
[11] P. Perona; J. Malik, Scale space and edge detection using anisotropic diffusion, Proceedings of the IEEE Society Workshop on Computer Vision, 12, 629-639 (1987)
[12] Hausdorff distance, 20 12 2018, https://en.wikipedia.org/wiki/Hausdorff_distance.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.