An automated segmentation of NATURA 2000 habitats from Sentinel-2 optical data

Figure 1.  First row: the original image $ I^0 $ and smoothed image $ I^{\sigma_0} $. Second row: the visualization of $ g(\mathbf{x}) $, smoothed edge detector $ g_1(\mathbf{x}) $ and a zoom of the vector field $ -\nabla g_1(\mathbf{x}) $ where we see arrows pointing towards the edges in $ I^0 $. Third row: the functions $ H(\mathbf{x}) $ using (5) and $ g_2(\mathbf{x} ) $ evaluated by using the initial circle plotted in the Fourth row, left. Fourth row: the initial segmentation curve placed in $ I^0 $ and its time evolution until the final segmentation state (bottom right). In the middle image we see that the evolving curve undergoes topological changes which are resolved efficiently

Figure 2.  Closed planar curve discretization (left) corresponding to the uniform discretization of the unit circle (right)

Figure 3.  Visualization of the curve discretization: curve grid points (red) and their midpoints. 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} $, see also [1]

Figure 4.  First row: the original image $ I^0 $ and smoothed image $ I^{\sigma_0} $. Second row: the visualization of the function $ g(\mathbf{x}) $ and smoothed edge detector $ g_1(\mathbf{x}) $. Third row: the function $ H(\mathbf{x}) $ and $ g_2(\mathbf{x}) $ evaluated by using the initial circle plotted in the Fourth row, left. Fourth row: the initial segmentation curve placed in $ I^0 $ (bottom left) and its time evolution (bottom middle) until the final segmentation state (bottom right) is reached

Figure 5.  First row: the original image $ I^0 $ and smoothed image $ I^{\sigma_0} $. Second row: the visualization of the function $ g(\mathbf{x}) $ and smoothed edge detector $ g_1(\mathbf{x}) $. Third row: the function $ H(\mathbf{x}) $ and $ g_2(\mathbf{x}) $ evaluated by using the initial circle plotted in the Fourth row, left. Fourth row: the initial segmentation curve placed in $ I^0 $ (bottom left) and its time evolution (bottom middle) until the final segmentation state (bottom right) is reached

Figure 6.  Left: the evolution of the segmentation curve from the initial circle to the final state. Right: the final automatic segmentation (red) together with the result of the semi-automatic segmentation (yellow) and the GPS track (light-blue)

Figure 7.  Left: the evolution of the segmentation curve from the initial circle to the final state. Right: the final automatic segmentation (red) together with the result of the semi-automatic segmentation (yellow) and the GPS track (light-blue)

Figure 8.  Left: the evolution of the segmentation curve from the initial circle to the final state. Right: the final automatic segmentation (red) together with the result of the semi-automatic segmentation (yellow) and the GPS track (light-blue)