Semi-automatic segmentation of NATURA 2000 habitats in Sentinel-2 satellite images by evolving open curves

Figure 1.  An example of artificial greyscale 2D image (left) and smoothed image (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

Figure 3.  3D graph of the edge detector $ g(\left|\nabla I^\sigma(\mathbf{x})\right|) $ for the smoothed image in Fig. 1 right

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

Figure 11.  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

Figure 5.  An open curve discretization (left) corresponding to the uniform discretization of parameter $ u\in \left[0,1\right] $ (right)

Figure 6.  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

Figure 7.  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} $

Figure 8.  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

Figure 9.  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)

Figure 10.  Visualization of the curve discretization [1] 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 12.  An example of the semi-automatic segmentation showing consecutive building of the segmentation curve (yellow), the final result is on the bottom right

Figure 13.  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

Figure 14.  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

Figure 15.  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)

Figure 16.  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