Directed Connected Operators: Asymmetric Hierarchies for Image Filtering and Segmentation


Connected operators provide well-established solutions for Digital Image Processing, usually in conjunction with hierarchical schemes. In graph-based frameworks, such operators basically depend on symmetric adjacency relations between pixels. In this article, we tend to introduce a notion of directed connected operators for hierarchical Image Processing, by also considering non-symmetric adjacency relations. The induced image illustration models are now not partition hierarchies (i.e., trees), however directed acyclic graphs that generalize commonplace morphological tree structures like element trees, binary partition trees or hierarchical watersheds. We tend to describe the way to efficiently build and handle these richer data structures, and we tend to illustrate the versatility of the proposed framework in image filtering and image segmentation.

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