By Michael H.F. Wilkinson, Jos B.T.M. Roerdink
This publication constitutes the refereed court cases of the ninth overseas Symposium on Mathematical Morphology, ISMM 2009 held in Groningen, The Netherlands in August 2009. The 27 revised complete papers offered including one invited paper have been rigorously reviewed and chosen from various submissions. The papers are prepared in topical sections on conception, connectivity and attached filters, adaptive morphology, graphs and topology, segmentation, form, morphology of multi-valued photographs, and algorithms.
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McGraw-Hill, New York (2000) 17. : Fuzzy Spatial Relation Ontology for Image Interpretation. F. O. Box 407, 9700 AK Groningen, The Netherlands Abstract. In this paper the notion of hyperconnectivity, first put forward by Serra as an extension of the notion of connectivity is explored theoretically. Hyperconnectivity operators, which are the hyperconnected equivalents of connectivity openings are defined, which supports both hyperconnected reconstruction and attribute filters. The new axiomatics yield insight into the relationship between hyperconnectivity and structural morphology.
31) This is a hyperconnection under the the overlap criterion from (28). : ρHf (f |g) = δ¯f1 δB ρ( B B f | B g), (32) An Axiomatic Approach to Hyperconnectivity (a) (b) 45 (c) Fig. 5. Viscous hyperconnections: (a) reconstruction of Fig 4(a) by Fig 4(b) according to (29); (b) same according to (32); (c) difference (contrast stretched) as put forward in [10]. The difference between reconstruction according to (29) and (32) is quite small, as shown in Fig. 5. 4 Conclusion In this paper new axiomatics for hyperconnected filters have been introduced.
6) 2. Lukasiewicz operators, which are not t-representable: W ((a1 , b1 ), (a2 , b2 )) = (max(0, a1 + a2 − 1), min(1, b1 + 1 − a2 , b2 + 1 − a1)), (7) ⊥W ((a1 , b1 ), (a2 , b2 )) = (min(1, a1 + 1 − b2 , a2 + 1 − b1 ), max(0, b1 + b2 − 1)). e. the positive parts of the input bipolar values). The negative part of ⊥W is the usual Lukasiewicz t-norm of the negative parts (b1 and b2 ) of the input values. The two types of implication coincide for the Lukasiewicz operators [5]. Based on these concepts, we can now propose a definition for morphological erosion.