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Additional info for Combinatorial Image Analysis: 17th International Workshop, IWCIA 2015, Kolkata, India, November 24-27, 2015. Proceedings

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Herm`es Science Publications, Paris (2007) 2. : New 2D parallel thinning algorithms based on critical kernels. , Polthier, K. ) IWCIA 2006. LNCS, vol. 4040, pp. 45–59. Springer, Heidelberg (2006) 3. : A simple parallel 3D thinning algorithm. In: Proceedings of the 10th IEEE International Conference Pattern Recognition, ICPR 1990, pp. 188–190 (1990) 4. : Parallel connectivity-preserving thinning algorithms. , Rosenfeld, A. ) Topological Algorithms for Digital Image Processing, pp. 145–179. , Amsterdam (1996) 5.

Vl , denoted by ψ(p), is defined by ψ(p) = min1≤k≤l ψ(vk−1 , vk ) if l > 0 and ψ(p) = 1 if l = 0; the ψ-strength of connectedness of A = ∅ to B = ∅ via W is defined as ψ W (A, B) = max {ψ(p) | p is a (W ∪ A ∪ B) - path from A to B}. (1) For a, b ∈ V , a W -path from {a} to {b} will also be called a W -path from a to b. Similarly, we write ψ X (a, B), ψ X (A, b), and ψ X (a, b) for ψ X ({a}, B), ψ X (A, {b}), and ψ X ({a}, {b}), respectively. Note that ψ(a, b) = ψ ∅ (a, b) ≤ ψ X (a, b) ≤ ψ V (a, b), that ψ X (A, B) = 1 if A ∩ B = ∅, and that ψ ∅ (A, B) = max ψ(a, b).

In the cases of RFC and IRFC segmentation, such results are given in [18, Sect. 4]. In this section we state one such result for MOFS, which shows that it is possible to introduce a large number of additional seed points without changing the resulting MOFS. Let Ψ = ψ1 , . . , ψM be any sequence of affinities on V and S = S1 , . . , SM any sequence of M pairwise disjoint nonempty subsets of V that are consistent with the affinities. Then, for 1 ≤ i ≤ M , we define Pi (Ψ, S) to be the collection of all subsets P of V that satisfy both of the following conditions: 1.

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