In this paper, we present a mathematical model and numerical method designed for the segmentation of satellite images, namely to obtain in an automated way borders of Natura 2000 habitats from Sentinel-2 optical data. The segmentation model is based on the evolving closed plane curve approach in the Lagrangian formulation including the efficient treatment of topological changes. The model contains the term expanding the curve in its outer normal direction up to the region of habitat boundary edges, the term attracting the curve accurately to the edges and the smoothing term given by the influence of local curvature. For the numerical solution, we use the flowing finite volume method discretizing the arising advection-diffusion intrinsic partial differential equation including the asymptotically uniform tangential redistribution of curve grid points. We present segmentation results for satellite data from a selected area of Western Slovakia (Záhorie) where the so-called riparian forests represent the important European Natura 2000 habitat. The automatic segmentation results are compared with the semi-automatic segmentation performed by the botany expert and with the GPS tracks obtained in the field. The comparisons show the ability of our numerical model to segment the habitat areas with the accuracy comparable to the pixel resolution of the Sentinel-2 optical data.

中文翻译：

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从Sentinel-2光学数据自动分割NATURA 2000生境

在本文中，我们提出了一种用于卫星图像分割的数学模型和数值方法，即以自动方式从Sentinel-2光学数据中获取Natura 2000生境的边界。分割模型基于拉格朗日公式中不断发展的闭合平面曲线方法，其中包括对拓扑变化的有效处理。该模型包含将曲线沿其外部法线方向扩展到栖息地边界边缘区域的术语，将曲线精确吸引到边缘的术语以及由局部曲率的影响给出的平滑术语。对于数值解，我们使用流动有限体积法离散化了产生的对流扩散本征偏微分方程，其中包括曲线网格点的渐近均匀切向重分布。我们提供了来自西部斯洛伐克（Záhorie）选定地区的卫星数据的分割结果，在该地区所谓的河岸森林代表了欧洲Natura 2000重要生境。将自动分割结果与植物学专家执行的半自动分割以及在现场获得的GPS轨迹进行比较。比较结果表明，我们的数值模型能够以与Sentinel-2光学数据的像素分辨率相当的精度对栖息地区域进行分割。我们提供了来自西部斯洛伐克（Záhorie）选定地区的卫星数据的分割结果，其中所谓的河岸森林代表了欧洲Natura 2000重要生境。将自动分割结果与植物学专家执行的半自动分割以及在现场获得的GPS轨迹进行比较。比较结果表明，我们的数值模型能够以与Sentinel-2光学数据的像素分辨率相当的精度对栖息地区域进行分割。我们提供了来自西部斯洛伐克（Záhorie）选定地区的卫星数据的分割结果，在该地区所谓的河岸森林代表了欧洲Natura 2000重要生境。将自动分割结果与植物学专家执行的半自动分割以及在现场获得的GPS轨迹进行比较。比较结果表明，我们的数值模型能够以与Sentinel-2光学数据的像素分辨率相当的精度对栖息地区域进行分割。