Mathematical morphology is the analysis of signals, particularly images, by shape and has been developed by Serra [ 7 , 8 , 9 ] from work by Matheron [ 10 ] but it also derives from work of others (Blum [ 11 ] for example). It is widely used in commercial image processing packages.
Of particular importance are Alternating Sequential Filters with greyscale structuring elements that match features [ 12 , 8 ]. They are said to be a powerful analogue of linear matched filters and there are strategies for designing optimal filters with rigid, two dimensional flat structuring elements [ 13 ]. More recently, alternating sequential filters, that do not impose a rigid geometry on objects, and connected sets have been described[ 14 , 15 , 16 , 17 , 18 ].
A separate stream of development has been that of rank filters, including median, root median, recursive median and, more generally, stack filters. Such filters have been developed primarily to remove random noise from signals and images, although there are suggestions for using them for tasks such as shape recognition [ 19 ]. There is a close relationship between rank filters and morphological filters [ 20 ]. Rank (median) filters are usually self-dual and robustly reject random noise. A recent development has been the sieve and its variants [ 21 , 22 , 23 , 24 , 25 , 26 ] which use the connected set operators found in Alternating Sequential Filters with ordering operators associated with rank filtering.
A. Bosson ESE PG