Abstract
In this paper we propose a novel algorithm for the efficient search of the most similar brains from a large collection of MR imaging data. The key idea is to compactly represent and quantify the differences of cortical surfaces in terms of their intrinsic geometry by comparing the Reeb graphs constructed from their Laplace-Beltrami eigenfunctions. To overcome the topological noise in the Reeb graphs, we develop a progressive pruning and matching algorithm based on the persistence of critical points. Given the Reeb graphs of two cortical surfaces, our method can calculate their distance in less than 10 milliseconds on a PC. In experimental results, we apply our method on a large collection of 1326 brains for searching, clustering, and automated labeling to demonstrate its value for the “Big Data” science in human neuroimaging.
This work was supported by NIH grants K01EB013633 and P41EB015922.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Mueller, S., Weiner, M., Thal, L., Petersen, R.C., Jack, C., Jagust, W., Trojanowski, J.Q., Toga, A.W., Beckett, L.: The Alzheimer’s disease neuroimaging initiative. Clin. North Am. 15, 869–877, xi–xii (2005)
Essen, D.V., Ugurbil, K., et al.: The human connectome project: A data acquisition perspective. NeuroImage 62(4), 2222–2231 (2012)
Toga, A., Clark, K., Thompson, P., Shattuck, D., Van Horn, J.: Mapping the human connectome. Neurosurgery 71(1), 1–5 (2012)
Van Horn, J.D., Toga, A.: Human neuroimaging as a “Big Data” science. Brain Imaging and Behavior, 1–9 (2013)
Reuter, M., Wolter, F.E., Shenton, M., Niethammer, M.: Laplace-beltrami eigenvalues and topological features of eigenfunctions for statistical shape analysis. Computer-Aided Design 41(10), 739–755 (2009)
Shi, Y., Lai, R., Toga, A.: Cortical surface reconstruction via unified Reeb analysis of geometric and topological outliers in magnetic resonance images. IEEE Trans. Med. Imag. (3), 511–530 (2013)
Edelsbrunner, Letscher, Zomorodian: Topological persistence and simplification. Discrete Comput. Geom. 28(4), 511–533 (2002)
Lee, H., Kang, H., Chung, M., Kim, B.N., Lee, D.S.: Persistent brain network homology from the perspective of dendrogram. IEEE Trans. Med. Imag. 31(12), 2267–2277 (2012)
Rustamov, R.M.: Laplace-beltrami eigenfunctions for deformation invariant shape representation. In: Proc. Eurograph. Symp. on Geo. Process., pp. 225–233 (2007)
Shi, Y., Lai, R., Toga, A.W.: Conformal mapping via metric optimization with application for cortical label fusion. In: Gee, J.C., Joshi, S., Pohl, K.M., Wells, W.M., Zöllei, L. (eds.) IPMI 2013. LNCS, vol. 7917, pp. 244–255. Springer, Heidelberg (2013)
Reeb, G.: Sur les points singuliers d’une forme de Pfaff completement integrable ou d’une fonction nemérique. Comptes Rendus Acad. Sciences 222, 847–849 (1946)
Klein, A., Tourville, J.: 101 labeled brain images and a consistent human cortical labeling protocol. Frontiers in Neuroscience 6(171) (2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Shi, Y., Li, J., Toga, A.W. (2014). Persistent Reeb Graph Matching for Fast Brain Search. In: Wu, G., Zhang, D., Zhou, L. (eds) Machine Learning in Medical Imaging. MLMI 2014. Lecture Notes in Computer Science, vol 8679. Springer, Cham. https://doi.org/10.1007/978-3-319-10581-9_38
Download citation
DOI: https://doi.org/10.1007/978-3-319-10581-9_38
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-10580-2
Online ISBN: 978-3-319-10581-9
eBook Packages: Computer ScienceComputer Science (R0)