Efficient Globally Optimal Matching of Anatomical Trees of the Liver

Abstract

Many inexact automatic tree matching algorithms are nowadays available. However, they provide matches that are not completely error free. Another option is to use manually matched node-pairs, but this enormously slows down the process. Our contribution to the state of the art is to combine the advantages of both solutions. We enhance the automatic tree matching algorithm designed by Graham et al., so that it is possible to interact with it by previously selecting important matches or by subsequently fixing the provided wrong matches. Thanks to this enhancement the speed of the algorithm is greatly increased. It takes 7.45 seconds for trees up to 192 nodes and less than 1 second if three input matches are provided. In addition to this an in-depth evaluation of the robustness of the algorithm is presented. The results are remarkable. The average of wrong matches varies between 1.17 and 1.4 node-pairs in the worst cases. The rate of correct matches is high.