Mathematical Morphology and Its Applications to Signal and by Isabelle Bloch, Alain Bretto, Aurélie Leborgne (auth.), Cris PDF

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Additional resources for Mathematical Morphology and Its Applications to Signal and Image Processing: 11th International Symposium, ISMM 2013, Uppsala, Sweden, May 27-29, 2013. Proceedings

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0Gb memory. The M IG representing the Morse complexes is extracted using the algorithm described in [17]. We have developed a simplification algorithm for Morse complexes in arbitrary dimensions based on the removei,i+1 and removei,i−1 . A persistence value is associated with any remove operator by considering the function values of the two critical points p and q deleted by the operator. Intuitively, the persistence of a pair of critical points measures the importance of the pair and is equal to the absolute difference in function values between the two points [8].

Jeulin Subsets RG , where G are open parts of E, generate a σ algebra on Πg (E), σ(RG ), on which a probability can be constructed. A random tessellation Θ is characterized by P (RG ) = P {G ⊂ Ci }. In the present paper, we study some models of random tessellations in the Euclidean space Rn . In addition, we will consider locally finite random tessellations, for which the random number of classes in every bounded domain D is a finite random number N (D). With this σ algebra, we can define events (and their probability) like “x belongs to a single class”, “x1 and x2 ” belong to a single class, “x1 , x2 , ...

Introduction ` a la th´eorie des ensembles al´eatoires. Cahiers du Centre de Morphologie Math´ematique, Fascicule 4 (1969) 12. : Random sets and Integral Geometry. Wiley (1975) 13. : Random Points, Sets and Tessellations on the Surface of a Sphere, Sankhy¯ a. The Indian Journal of Statistics, Series A, 145–174 (1971) 14. : Random Johnson-Mehl tessellations. Advances in Applied Probability 24, 814–844 (1992) 15. : Anisotropic growth of Voronoi Cells. Advances in Applied Probability 26, 43–53 (1994) 16.

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