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Watersheds and Skeletons
The EDM is also important as the basis for a technique called watershed segmentation that can separate features which touch each other. As shown in the diagram, the EDM has values that rise to a maximum in the center of each feature. Plotting these values as a surface represents each separate feature as a mountain peak. If you imagine rain falling onto this terrain, the drops run down each mountain and the lines at which drops from two different mountains meet are the watershed lines. Removing those lines separates the features so that they can be measured individually, as shown in the Watershed Separation interactive tutorial.
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Skeletonization is produced by an erosion that iteratively removes pixels from the periphery of features with the restriction that no feature pixel can be removed if its neighboring feature pixels would then be separated from each other. The process continues until there are no further changes, and the result leaves pixels that mark the midlines of structures and capture the topological shape of objects as shown in the Skeletonization interactive tutorial. Counting the ends (pixels in the skeleton with a single neighbor) and nodes (pixels in the skeleton with more than two neighbors) provides shape information. Removing ends (pruning) cleans up tesselations of cells or grains, while removing nodes can separate the parts of complex mesh and fiber structures for measurement.
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Contributing Authors
John C. Russ - Materials Science and Engineering Dept., North Carolina State University, Raleigh, North Carolina, 27695.
Matthew Parry-Hill and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.
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