最陡峭的分水岭：从图表到图像
The steepest watershed: from graphs to images
摘要：
分水岭是一个强大的工具，用于分割轮廓在梯度图像上显示为脊线的对象。分水岭变换将地形表面与集水盆地的分区相关联，集水盆地定义为落在浮雕上的水滴的吸引区，并遵循最陡下降线。不幸的是，集水盆地可能重叠，不形成分区。此外，目前的流域算法，是短视的，不正确地估计向下的轨迹的陡度和高估的集水盆地的重叠区。任意划分相邻集水盆地之间的这些区域会导致等高线的局部化不佳。我们提出了一个算法没有近视，它认为总长度的轨迹估计其陡度。我们首先考虑拓扑表面上定义的节点加权图。图被修剪，以消除所有向下的轨迹，这不是最陡峭的。一个简单的邻域操作的迭代算法执行修剪和构造的集水盆地。然后，该算法适用于灰度图像。由于网格的固定邻域结构，图结构本身被编码为图像。一对自适应侵蚀和扩张修剪图和扩大集水盆地。因此，人们可以精确地检测集水盆地和最陡轨迹的图形。最后一个迭代算法允许遵循选定的向下轨迹，以便检测特定的结构，如河流或地形表面的深泓线。
英文摘要：
The watershed is a powerful tool for segmenting objects whose contours appear as crest lines on a gradient image. The watershed transform associates to a topographic surface a partition into catchment basins, defined as attraction zones of a drop of water falling on the relief and following a line of steepest descent. Unfortunately, catchment basins may overlap and do not form a partition. Moreover, current watershed algorithms, being shortsighted, do not correctly estimate the steepness of the downwards trajectories and overestimate the overlapping zones of catchment basins. An arbitrary division of these zones between adjacent catchment basin results in a poor localization of the contours. We propose an algorithm without myopia, which considers the total length of a trajectory for estimating its steepness. We first consider topographic surfaces defined on node weighted graphs. The graphs are pruned in order to eliminate all downwards trajectories which are not the steepest. An iterative algorithm with simple neighborhood operations performs the pruning and constructs the catchment basins. The algorithm is then adapted to gray tone images. The graph structure itself is encoded as an image thanks to the fixed neighborhood structure of grids. A pair of adaptative erosions and dilations prune the graph and extend the catchment basins. As a result one obtains a precise detection of the catchment basins and a graph of the steepest trajectories. A last iterative algorithm allows to follow selected downwards trajectories in order to detect particular structures such as rivers or thalweg lines of the topographic surface.
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