Attribute-space connectivity and connected filters

In this paper connected operators from mathematical morphology are extended to a wider class of operators, which are based on connectivities in higher dimensional spaces, similar to scale spaces, which will be called attribute-spaces. Though some properties of connected filters are lost, granulometries can be defined under certain conditions, and pattern spectra in most cases. The advantage of this approach is that regions can be split into constituent parts before filtering more naturally than by using partitioning connectivities. Furthermore, the approach allows dealing with overlap, which is impossible in connectivity. A theoretical comparison to hyperconnectivity suggests the new concept is different. The theoretical results are illustrated by several examples. These show how attribute-space connected filters merge the ability of filtering based on local structure using classical, structuring-element-based filters to the object-attribute-based filtering of connected filters, and how this differs from similar attempts using second-generation connectivity.