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. Author manuscript; available in PMC: 2013 Jun 15.
Published in final edited form as: Med Image Comput Comput Assist Interv. 2008;11(0 1):833–841. doi: 10.1007/978-3-540-85988-8_99

Alg. 1.

The algorithm to separate touching cells using concave vertex graph

Input: Given the region of interest (ROI) containing touching cells.

  • Extract the boundary contour C, detect the concave points V, the inner edges E in R(C), construct the concave vertex graph G.

  • for each vertex v(i) ∈ V

    • Find the path pij and calculate the length ||pij || using (2).

  • Initialize mincost = +∞ and Q = Ø.

  • while (V is not empty)

    • for each vertex v(i) ∈ V

      • * for each vertex v(j ≠ i) ∈ V

        • Apply the path pij to separate the graph G in to L and R.

        • Calculate the cost c using (6) and save in Q.

    • Sort Q and pick up the path pij with the lowest cost c.

    • if (c < 1.5 * mincost)

      • Record path pij and the region R(C, pij) with cost c in the result.

      • The edges and zero degree vertices in the R(C, pij) are removed from G.

      • Set mincost = c and Q = Ø

    • else return result.