Connected operators

Connected operators are filtering tools that act by merging elementary regions called flat zones. Connecting operators cannot create new contours nor modify their position. Therefore, they have very good contour-preservation properties and are capable of both low-level filtering and higher-level object recognition. This article gives an overview on connected operators and their application to image and video filtering. There are two popular techniques used to create connected operators. The first one relies on a reconstruction process. The operator involves first a simplification step based on a "classical" filter and then a reconstruction process. In fact, the reconstruction can be seen as a way to create a connected version of an arbitrary operator. The simplification effect is defined and limited by the first step. The examples we show include simplification in terms of size or contrast. The second strategy to define connected operators relies on a hierarchical region-based representation of the input image, i.e., a tree, computed in an initial step. Then, the simplification is obtained by pruning the tree, and, third, the output image is constructed from the pruned tree. This article presents the most important trees that have been used to create connected operators and also discusses important families of simplification or pruning criteria. We also give a brief overview on efficient implementations of the reconstruction process and of tree construction. Finally, the possibility to define and to use nonclassical notions of connectivity is discussed and illustrated.