Connectivity in image processing and analysis: Theory, multiscale extensions and applications.

摘要

Connectivity plays an important role in image processing and analysis, and particularly in problems related to image segmentation, image filtering, image coding, motion analysis, multiscale signal decomposition, pattern recognition, and other application areas. In this dissertation, we study a general theory of connectivity in image processing and analysis. Connectivity is classically defined using either a topological or a graph-theoretic framework, and their fuzzy analogs. We provide a thorough review of several existing definitions of connectivity. Although these classical concepts have been extensively applied in image processing and analysis, they are unfortunately incompatible. The theory of connectivity classes, first proposed in the late eighties for binary images, and recently extended to arbitrary complete lattices, circumvents the shortcomings of classical definitions by providing a consistent unified theoretical framework that includes the majority of the existing concepts of connectivity. We review this theory, expand it with new results and examples, and demonstrate its usefulness in applications based on connected operators. We also propose the notion of multiscale connectivity. We provide a novel theoretical framework for multiscale connectivity, which includes the theory of connectivity classes in complete lattices as a special, single-scale case. Among the items we propose and study in connection with multiscale connectivities is the integration of connectivity with multiscale methods that are currently routinely employed in image processing and analysis applications. In particular, we define several multiscale tools based on multiscale connectivities, such as multiscale signal decompositions, hierarchical segmentation, hierarchical clustering and multiscale features. Several examples of application of these multiscale tools are provided using synthetic and real images.