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-8- Properties Criteria Increasing extensive (or anti- Idempotent Preserve homotopy Complémentation. Hit or Miss, boundary 1 ! sic ustisivs / Ho No No No Erosion and dilation when 0 £ B, médian filtering Yes No No No Thinning and thickening No Yes No No Erosion and dilation when OGB Yes Yes No No Boundary of the boundary No No Yes No Projection, morphological filtering Sequential thinning, Skiz, skeleton, cond. bissector, watershed, ultimate érosion Yes No No Yes Yes Yes No No Opening, closing, convex hull, size distribution, thresholding, umb ra Yes Yes Yes No Bisplacement, similarity, affinity, symmetry Yes No No Yes Homotopic and sequential thinning and thickening No Yes Yes Yes Fig. 4 - Euclidean morphological criteria and their basic properties. 2—c - Morphological Filters. As an example of a type of morphological transforma¬ tion, we introduce the notioncfa morphological filter. In signal processing in one or several dimensions, one usually calls a filter any Euclidean opération which is linear, translation in¬ variant, and continuous. According to a well kriown resuit [£], every filter turns out to be the convolution product f * q> of a signal f by a (generalised) function cp. More in practice than theoretically, a fourth aspect also intervenes î the filters are often implicitly assimilated to band-pass filters* i.e. to