    March  2021, 14(3): 1033-1046. doi: 10.3934/dcdss.2020231

## 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

* Corresponding author

Received  January 2019 Revised  September 2019 Published  December 2019

Fund Project: This work was supported by projects APVV-16-0431, APVV-15-0522 and ESA Contract No. 4000122575/17/NL/SC

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.

Citation: Karol Mikula, Jozef Urbán, Michal Kollár, Martin Ambroz, Ivan Jarolímek, Jozef Šibík, Mária Šibíková. Semi-automatic segmentation of NATURA 2000 habitats in Sentinel-2 satellite images by evolving open curves. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1033-1046. doi: 10.3934/dcdss.2020231
##### References:
  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.  Google Scholar  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  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. Google Scholar  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.  Google Scholar  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.  Google Scholar  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  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.  Google Scholar  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.  Google Scholar  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.  Google Scholar  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  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. Google Scholar  Hausdorff distance, 20 12 2018, https://en.wikipedia.org/wiki/Hausdorff_distance. Google Scholar

show all references

##### References:
  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.  Google Scholar  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  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. Google Scholar  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.  Google Scholar  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.  Google Scholar  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  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.  Google Scholar  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.  Google Scholar  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.  Google Scholar  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  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. Google Scholar  Hausdorff distance, 20 12 2018, https://en.wikipedia.org/wiki/Hausdorff_distance. Google Scholar An example of artificial greyscale 2D image (left) and smoothed image (right) right">Figure 2.  3D graph of image intensity function $I^\sigma(\mathbf{x})$ (left) and graph of the image intensity gradient norm $\left|\nabla I^\sigma(\mathbf{x})\right|$ (right), for the smoothed image in Fig. 1 right right">Figure 3.  3D graph of the edge detector $g(\left|\nabla I^\sigma(\mathbf{x})\right|)$ for the smoothed image in Fig. 1 right right. We see that arrows points to the edge in the image from both sides">Figure 4.  A visualization of the vector field $\mathbf{v}\left(\mathbf{x}\right)$ for image in Fig. 1 right. We see that arrows points to the edge in the image from both sides A discrete segmentation curve evolving to habitat boundary in a real 3-band Sentinel-2 optical image. The green color shows trajectories of moving discrete curve points and blue points represents the result of segmentation of this particular section of the habitat border An open curve discretization (left) corresponding to the uniform discretization of parameter $u\in \left[0,1\right]$ (right) Trajectories of points of a discrete segmentation curve (red) evolved in the vector field $\mathbf{v}$ driven to the image edge. The final state of discrete segmentation curve is given by green points localized on the image edge Trajectories of points of a discrete segmentation curve (red) evolved in the vector field $\mathbf{v}$ and their final position (green) visualized over the original image. One can see a problem of non-uniform distribution of points on evolving discrete segmentation curve due to non-controlled tangential velocities in the vector field $\mathbf{v}$ Trajectories of points of a discrete segmentation curve (red) evolved in the vector field $\mathbf{v}$ and their final position (green) visualized over the original image. An improved distribution of the curve grid points after removing the tangential component of the velocity vector field $\mathbf{v}$ is obvious Trajectories of points of a discrete segmentation curve (red) evolved in the vector field $\mathbf{v}$ and their final position (green) visualized over the original image. Top: the curve evolution by (5) in a less smoothed image when problem of crossing, accumulating and not moving points may arise; bottom: such undesired behaviour is removed by employing the local curvature influence into the model (7) ] curve grid points (red), discrete curve segments (different colors) and the midpoints (black). Finite volumes $\mathbf{p}_{i-1},\mathbf{p}_i,$ and $\mathbf{p}_{i+1}$ are highlighted by green, brown and yellow color. Note that $\mathbf{p}_i$ is not a straight line given by $\mathbf{x}_{i-\frac{1}2}$ and $\mathbf{x}_{i+\frac{1}2}$, but a broken line given by $\mathbf{x}_{i-\frac{1}2}$, $\mathbf{x}_{i}$ and $\mathbf{x}_{i+\frac{1}2}$">Figure 10.  Visualization of the curve discretization  curve grid points (red), discrete curve segments (different colors) and the midpoints (black). Finite volumes $\mathbf{p}_{i-1},\mathbf{p}_i,$ and $\mathbf{p}_{i+1}$ are highlighted by green, brown and yellow color. Note that $\mathbf{p}_i$ is not a straight line given by $\mathbf{x}_{i-\frac{1}2}$ and $\mathbf{x}_{i+\frac{1}2}$, but a broken line given by $\mathbf{x}_{i-\frac{1}2}$, $\mathbf{x}_{i}$ and $\mathbf{x}_{i+\frac{1}2}$ An example of the semi-automatic segmentation showing consecutive building of the segmentation curve (yellow), the final result is on the bottom right Semi-automatic segmentation (yellow) and GPS track (light-blue) with almost exact overlap. The maximal Haussdorff distance is 62.1m and the mean Hausdorff distance is 14.0m in this case, which means that we obtained almost the pixel resolution (10m) accuracy An example of a complicated border of the riparian forest. We compare the semi-automatic segmentation (yellow) and GPS track (light-blue). The mean Haussdorff distance is 12.0m and the maximal Haussdorff distance, in this case, is 62.1m, indicating correctly discrepancy in habitat area estimate in the field and by employing the Sentinel-2 optical data The locality with the highest, 413.3m, maximal Hausdorff distance between semi-automatically segmented and GPS tracked curves among bushes with Pinus mugo tested areas, here also the mean Hausdorff distance was the highest, 44.8m. On the North-West habitat border, we can see the "ecotone zone" that was included during field tracking (light-blue) and excluded by using the semi-automatic segmentation (yellow) The locality dominated by Pinus mugo with the "ecotone zone" that was included during the field tracking (light-blue) and excluded by using the semi-automatic segmentation (yellow). The mean Hausdorff distance is 19.1m and the maximal Hausdorff distance is 171.0m
  Karol Mikula, Jozef Urbán, Michal Kollár, Martin Ambroz, Ivan Jarolímek, Jozef Šibík, Mária Šibíková. An automated segmentation of NATURA 2000 habitats from Sentinel-2 optical data. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1017-1032. doi: 10.3934/dcdss.2020348  Maika Goto, Kazunori Kuwana, Yasuhide Uegata, Shigetoshi Yazaki. A method how to determine parameters arising in a smoldering evolution equation by image segmentation for experiment's movies. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 881-891. doi: 10.3934/dcdss.2020233  Fan Jia, Xue-Cheng Tai, Jun Liu. Nonlocal regularized CNN for image segmentation. Inverse Problems & Imaging, 2020, 14 (5) : 891-911. doi: 10.3934/ipi.2020041  Yangang Chen, Justin W. L. Wan. Numerical method for image registration model based on optimal mass transport. Inverse Problems & Imaging, 2018, 12 (2) : 401-432. doi: 10.3934/ipi.2018018  Petr Pauš, Shigetoshi Yazaki. Segmentation of color images using mean curvature flow and parametric curves. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1123-1132. doi: 10.3934/dcdss.2020389  Ye Yuan, Yan Ren, Xiaodong Liu, Jing Wang. Approach to image segmentation based on interval neutrosophic set. Numerical Algebra, Control & Optimization, 2020, 10 (1) : 1-11. doi: 10.3934/naco.2019028  Dominique Zosso, Jing An, James Stevick, Nicholas Takaki, Morgan Weiss, Liane S. Slaughter, Huan H. Cao, Paul S. Weiss, Andrea L. Bertozzi. Image segmentation with dynamic artifacts detection and bias correction. Inverse Problems & Imaging, 2017, 11 (3) : 577-600. doi: 10.3934/ipi.2017027  Matthew S. Keegan, Berta Sandberg, Tony F. Chan. A multiphase logic framework for multichannel image segmentation. Inverse Problems & Imaging, 2012, 6 (1) : 95-110. doi: 10.3934/ipi.2012.6.95  Michael Hintermüller, Monserrat Rincon-Camacho. An adaptive finite element method in $L^2$-TV-based image denoising. Inverse Problems & Imaging, 2014, 8 (3) : 685-711. doi: 10.3934/ipi.2014.8.685  Jia Li, Zuowei Shen, Rujie Yin, Xiaoqun Zhang. A reweighted $l^2$ method for image restoration with Poisson and mixed Poisson-Gaussian noise. Inverse Problems & Imaging, 2015, 9 (3) : 875-894. doi: 10.3934/ipi.2015.9.875  Shi Yan, Jun Liu, Haiyang Huang, Xue-Cheng Tai. A dual EM algorithm for TV regularized Gaussian mixture model in image segmentation. Inverse Problems & Imaging, 2019, 13 (3) : 653-677. doi: 10.3934/ipi.2019030  Jianping Zhang, Ke Chen, Bo Yu, Derek A. Gould. A local information based variational model for selective image segmentation. Inverse Problems & Imaging, 2014, 8 (1) : 293-320. doi: 10.3934/ipi.2014.8.293  Lu Tan, Ling Li, Senjian An, Zhenkuan Pan. Nonlinear diffusion based image segmentation using two fast algorithms. Mathematical Foundations of Computing, 2019, 2 (2) : 149-168. doi: 10.3934/mfc.2019011  Ruiliang Zhang, Xavier Bresson, Tony F. Chan, Xue-Cheng Tai. Four color theorem and convex relaxation for image segmentation with any number of regions. Inverse Problems & Imaging, 2013, 7 (3) : 1099-1113. doi: 10.3934/ipi.2013.7.1099  Balázs Kósa, Karol Mikula, Markjoe Olunna Uba, Antonia Weberling, Neophytos Christodoulou, Magdalena Zernicka-Goetz. 3D image segmentation supported by a point cloud. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 971-985. doi: 10.3934/dcdss.2020351  Jie Huang, Xiaoping Yang, Yunmei Chen. A fast algorithm for global minimization of maximum likelihood based on ultrasound image segmentation. Inverse Problems & Imaging, 2011, 5 (3) : 645-657. doi: 10.3934/ipi.2011.5.645  Liam Burrows, Weihong Guo, Ke Chen, Francesco Torella. Reproducible kernel Hilbert space based global and local image segmentation. Inverse Problems & Imaging, 2021, 15 (1) : 1-25. doi: 10.3934/ipi.2020048  Macarena Boix, Begoña Cantó. Using wavelet denoising and mathematical morphology in the segmentation technique applied to blood cells images. Mathematical Biosciences & Engineering, 2013, 10 (2) : 279-294. doi: 10.3934/mbe.2013.10.279  Karol Mikula, Róbert Špir, Nadine Peyriéras. Numerical algorithm for tracking cell dynamics in 4D biomedical images. Discrete & Continuous Dynamical Systems - S, 2015, 8 (5) : 953-967. doi: 10.3934/dcdss.2015.8.953  Weihao Shen, Wenbo Xu, Hongyang Zhang, Zexin Sun, Jianxiong Ma, Xinlong Ma, Shoujun Zhou, Shijie Guo, Yuanquan Wang. Automatic segmentation of the femur and tibia bones from X-ray images based on pure dilated residual U-Net. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2020057

2019 Impact Factor: 1.233

## Metrics

• PDF downloads (149)
• HTML views (523)
• Cited by (0)

## Other articlesby authors

• on AIMS
• on Google Scholar

[Back to Top]