Matching of 3D tree structures using association graphs

Abstract

AbstractMatching of tree structures is equivalent to the problem of searching for maximum cliques in tree association graphs. Pelillo and colleagues have recently proposed a method for searching for maximum weight cliques that gives weight to association graphs on the basis of similarities of the attributes of tree nodes. Here, the obtained maximum weight clique corresponds to the maximum similarity subtree isomorphism. This paper proposes a tree structure‐matching scheme using tree association graphs, as a general scheme for performing nonrigid body registration of tree structures in three‐dimensional medical images. Matching of tree structures of three‐dimensional medical images of bronchi, blood vessels, and the like must be capable of handling changes in body positions accompanying their changes as well as physiological changes due to breathing exercises etc. In addition, it needs to recognize topology errors of pseudo or false branches occurring during image processing. This study, as attributes of tree nodes, constructs similarities using body volume change rates extending over the parents, children and siblings, focusing on the positional relations of the nodes of the parents, children, and siblings. The similarities proposed are those having high general properties that can be applied to changes in positions and shapes that occur inside a body since they focus on their general properties. In addition, as a method for avoiding mismatches due to topology errors, changing the weights of neighboring edges on the basis of similarities is added. The proposed scheme has been confirmed to show a high correct solution rate or true positive fraction regardless of high degree changes in positions and shapes when applied to a bronchial model generated inside a computer. It has also been confirmed that mismatches due to topology errors occur at a very low rate with the proposed scheme. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 87(2): 59–72, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.10216