Abstract
Classical hierarchical image representations and connected filters work on sets of connected components (CC). These approaches can be defective to describe the relations between disjoint objects or partitions of images. In practice, objects can be made of several connected components in images (due to occlusions for example), therefore it can be interesting to be able to take into account the relationship between these components to be able to detect the whole object. In Mathematical Morphology, second-generation connectivity (SGC) and tree-based shape-spaces study this relation between the connected components of an image. However, they have limitations. For this reason, we propose in this paper an extension of the usual shape-space paradigm into what we call a Generalized Shape-Space (GSS). This new paradigm allows us to analyze any graph of connected components hierarchically and to filter them thanks to connected operators.
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