. Author manuscript; available in PMC: 2015 Jan 13.

Published in final edited form as: Mach Learn Med Imaging. 2014;8679:306–313. doi: 10.1007/978-3-319-10581-9_38

Table 1. Persistent Reeb Graph Match Algorithm.

Set

D_{min}^{n} = \infty

. Repeat the following steps until the minimal edge weight of

R_{n}^{1}

and

R_{n}^{2}

are above the persistence threshold δ.

Calculate the cost matrix D⁺.
Calculate the cost matrix D^–.
Compute the distance D at the current pruning level. If $D < D_{min}^{n}$ , set $D_{min}^{n} = D$ and record the correspondence.
Prune the minimal edge in both Reeb graphs, and update the pruning cost $P_{n}^{1}$ and $P_{n}^{2}$ . Go back to step 1.