Watersheds for Semi-Supervised Classification

Watershed technique from mathematical morphology (MM) is one of the mast widely used operators for image segmentation. Recently watersheds are adapted to edge weighted graphs, allowing for wider applicability. However, a few questions remain to be answered - How do the boundaries of the watershed operator behave? Which loss function does the watershed operator optimize? How does watershed operator relate with existing ideas from machine learning. In this letter, a framework is developed, which allows one to answer these questions. This is achieved by generalizing the maximum margin principle to maximum margin partition and proposing a generic solution, MORPHMEDIAN, resulting in the maximum margin principle. It is then shown that watersheds form a particular class of MORPHMEDIAN classifiers. Using the ensemble technique, watersheds are also extended to ensemble watersheds. These techniques are compared with relevant methods from the literature and it is shown that watersheds perform better than support vector machines on some datasets, and ensemble watersheds usually outperform random forest classifiers.