Chapter

Mathematical Morphology and Its Applications to Image and Signal Processing

Volume 6671 of the series Lecture Notes in Computer Science pp 96-107

Preventing Chaining through Transitions While Favouring It within Homogeneous Regions

  • Pierre SoilleAffiliated withLancaster UniversityIPSC Global Security and Crisis Management Unit, Joint Research Centre, European Commission

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Abstract

By its very nature, alpha-connectivity is subject to the chaining property of single linkage clustering. Thanks to the selection of appropriate connectivity constraints, connected components that are affected by the chaining through transitions can be invalidated. However, it may happen that (i) a stream of small connected components at the transition between larger components are created and (ii) none of the connected components is matching a desired object whatever the threshold levels associated with the constraints. These two problems are caused by the presence of transitions. In this paper, we characterise transitions in view of their impact on constrained connected paths. We then show that both problems can be addressed simultaneously by either pre-filtering or by introducing a dissimilarity measurement preventing connections through transitions while keeping a definition based on absolute difference measurements.

Keywords

single-linkage clustering alpha-connectivity dissimilarity constrained connectivity increment operators smooth connection