Connected Morphological Operators and filters for Binary Images

Connected morphological operators act o n the level of the f la t zones of a n image, i.e., the connected regions where the grey-level i s constant. For binary i m ages, the f la t zones are the foreground and background grains (connected components) of the image. T h e f lat zones constitute a partition of the underlying space. A connected operator is a n operator that makes this part i t ion coarser. A grain operator i s a connected operator that is uniquely specified by two grain criteria, one for the foreground and one f o r the background components. This paper contains a brief discussion of connected operators and grain operators wi th a n emphasis o n connected filters, all in the context of binary images.