Abstract
Automatic feature tracking is widely used for the analysis of time-dependent data. If the features exhibit splitting behavior, it is best characterized by tree-like tracks. For a large number of time steps, each with numerous features, these data become increasingly difficult to analyze. In this paper, we focus on the problem of comparing and contrasting hundreds to thousands of trees to support developmental biologists in their study of cell division patterns in embryos. To this end, we propose a new visual analytics method called structure map. This two-dimensional, color-coded map arranges trees into tiles along a Hilbert curve, preserving a tree similarity measure, which we define via graph Laplacians. The structure map supports both global and local analysis based on user-selected tree descriptors. It helps analysts identify similar trees, observe clustering and sizes of clusters within the forest, and detect outliers in a compact and uniform representation. We apply the structure map for analyzing 3D cell tracking from two periods of zebrafish embryogenesis: blastulation to early epiboly and tailbud extension. In both cases, we show how the structure map supported biologists to find systematic differences in the data set as well as detect erroneous cell behaviors.
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
References
Arsić, B., Cvetković, D., Simić, S.K., Škarić, M.: Graph spectral techniques in computer sciences. Appl. Anal. Discrete Math. 6, 1–30 (2012)
Bille, P.: A survey on tree edit distance and related problems. Theor. Comput. Sci. 337(1), 217–239 (2005)
Bremm, S., von Landesberger, T., Hess, M., Schreck, T., Weil, P., Hamacherk, K.: Interactive visual comparison of multiple trees. In: IEEE VAST, pp. 31–40 (2011)
Bruls, M., Huizing, K., van Wijk, J.: Squarified treemaps. In: Proceedings of Joint Eurograph and IEEE TCVG Symposium on Visualization, pp. 33–42 (1999)
Buss, S.: Alogtime algorithms for tree isomorphism, comparison, and canonization. In: Computational Logic and Proof Theory, pp. 18–33. Springer, Heidelberg (1997)
Fangerau, J., Höckendorf, B., Rieck, B., Heine, C., Wittbrodt, J., Leitte, H.: Supplemental video. https://vimeo.com/86031849 (2014). Accessed 06 Feb 2014
Graham, M., Kennedy, J.: A survey of multiple tree visualisation. Inf. Vis. 9, 235–252 (2010)
Herman, I., Melançon, G., Marshall, M.S.: Graph visualization and navigation in information visualization: a survey. IEEE Trans. Vis. Comput. Graph. 6, 24–43 (2000)
Huisken, J., Stainier, D.Y.: Selective plane illumination microscopy techniques in developmental biology. Development 136(12), 1963–1975 (2009)
Jolliffe, I.: Principal Component Analysis, 2nd edn. Springer, New York (2002)
Keller, P.J., Schmidt, A.D., Wittbrodt, J., Stelzer, E.H.: Reconstruction of zebrafish early embryonic development by scanned light sheet microscopy. Science 322(5904), 1065–1069 (2008)
Kohonen, T.: Self-Organizing Maps. Springer, New York (2001)
Kubicka, E., Kubicki, G., McMorris, F.: An algorithm to find agreement subtrees. J. Classif. 12, 91–99 (1995)
Lou, X., Kaster, F.O., Lindner, M.S., Kausler, B.X., Köthe, U., Hockendorf, B., Wittbrodt, J., Jänicke, H., Hamprecht, F.A.: Deltr: digital embryo lineage tree reconstructor. In: Biomedical Imaging: From Nano to Macro, pp. 1557–1560. IEEE, Chicago (2011)
Moreland, K.: Diverging color maps for scientific visualization. In: Proceedings of 5th International Symposium. Advances in Visual Computing: Part II, pp. 92–103. Springer, Heidelberg (2009)
Munzner, T., Guimbretière, F., Tasiran, S., Zhang, L., Zhou, Y.: TreeJuxtaposer: scalable tree comparison using focus+context with guaranteed visibility. ACM Trans. Graph. 22(3), 453–462 (2003)
Navigli, R., Lapata, M.: Graph connectivity measures for unsupervised word sense disambiguation. In: Proceedings of 20th International Joint Conference on Artifical Intelligence, pp. 1683–1688 (2007)
Reingold, E.M., Tilford, J.S.: Tidier drawings of trees. IEEE Trans. Softw. Eng. 7(2), 223–228 (1981)
Schulz, H.: Treevis.net: a tree visualization reference. IEEE Comput. Graph. 31, 11–15 (2011)
Shneiderman, B.: Tree visualization with tree-maps: 2-D space-filling approach. ACM Trans. Graph. 11, 92–99 (1992)
van Ham, F., van Wijk, J.J.: Beamtrees: compact visualization of large hierarchies. Inf. Vis. 2, 31–39 (2003)
von Landesberger, T., Gorner, M., Schreck, T.: Visual analysis of graphs with multiple connected components. In: IEEE VAST, pp. 155–162. IEEE, Atlantic City (2009)
von Landesberger, T., Kuijper, A., Schreck, T., Kohlhammer, J., Wijk, J.V., Fekete, J.-D., Dieter, W. F.: Visual analysis of large graphs: state-of-the-art and future research challenges. Comput. Graph. Forum 30, 1719–1749 (2011)
Ware, C.: Information Visualization: Perception for Design, 3rd edn. Morgan Kaufmann, San Francisco (2012)
Wilson, R.C., Zhu, P.: A study of graph spectra for comparing graphs and trees. Pattern Recogn. 41(9), 2833–2841 (2008)
Wong, P.C., Foote, H., Mackey, P., Chin, G., Huang, Z., Thomas, J.: A space-filling visualization technique for multivariate small-world graphs. IEEE Trans. Vis. Comput. Graph. 18, 797–809 (2012)
Zhao, S., McGuffin, M.J., Chignell, M.H.: Elastic hierarchies: combining treemaps and node-link diagrams. In: Proceedings of IEEE Symposium on Information Visualization (2005)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Fangerau, J., Höckendorf, B., Rieck, B., Heine, C., Wittbrodt, J., Leitte, H. (2016). Interactive Similarity Analysis and Error Detection in Large Tree Collections. In: Linsen, L., Hamann, B., Hege, HC. (eds) Visualization in Medicine and Life Sciences III. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-319-24523-2_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-24523-2_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-24521-8
Online ISBN: 978-3-319-24523-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)