The watershed transformation treats the image it operates upon like a topographic map, with the brightness of each point representing its height, and finds the lines that run along the tops of ridges. There are different technical definitions of a watershed. In graphs, watershed lines may be defined on the nodes, on the edges, or image processing ieee papers pdf lines on both nodes and edges.
Watersheds may also be defined in the continuous domain. The idea was introduced in 1979 by S. The basic idea consisted of placing a water source in each regional minimum in the relief, to flood the entire relief from sources, and build barriers when different water sources meet. The resulting set of barriers constitutes a watershed by flooding.
A number of improvements, collectively called Priority-Flood, have since been made to this algorithm. Intuitively, a drop of water falling on a topographic relief flows towards the “nearest” minimum. The “nearest” minimum is that minimum which lies at the end of the path of steepest descent. In terms of topography, this occurs if the point lies in the catchment basin of that minimum. The previous definition does not verify this condition. Intuitively, the watershed is a separation of the regional minima from which a drop of water can flow down towards distinct minima. Label each minimum with a distinct label.
Initialize a set S with the labeled nodes. Previous notions focus on catchment basins, but not to the produced separating line. The topological watershed was introduced by M. Local minima of the gradient of the image may be chosen as markers, in this case an over-segmentation is produced and a second step involves region merging. Marker based watershed transformation make use of specific marker positions which have been either explicitly defined by the user or determined automatically with morphological operators or other ways. One of the most common watershed algorithms was introduced by F. The algorithm works on a gray scale image.
During the successive flooding of the grey value relief, watersheds with adjacent catchment basins are constructed. This flooding process is performed on the gradient image, i. Normally this will lead to an over-segmentation of the image, especially for noisy image material, e. Either the image must be pre-processed or the regions must be merged on the basis of a similarity criterion afterwards. A set of markers, pixels where the flooding shall start, are chosen. Each is given a different label. The neighboring pixels of each marked area are inserted into a priority queue with a priority level corresponding to the gradient magnitude of the pixel.
The pixel with the lowest priority level is extracted from the priority queue. If the neighbors of the extracted pixel that have already been labeled all have the same label, then the pixel is labeled with their label. All non-marked neighbors that are not yet in the priority queue are put into the priority queue. Redo step 3 until the priority queue is empty.
The non-labeled pixels are the watershed lines. Watersheds as optimal spanning forest have been introduced by Jean Cousty et al. Then they prove, through an equivalence theorem, their optimality in terms of minimum spanning forests. Afterward, they introduce a linear-time algorithm to compute them.