Abstract
Developments in image acquisition technology make high volumes of neuron images available to neuroscientists for analysis. However, manual processing of these images is not practical and is infeasible for larger and larger scale studies. Reliable interpretation and analysis of high volume data requires accurate quantitative measures. This requires analysis algorithms to use mathematical models that inherit the underlying geometry of biological structures in order to extract topological information. In this paper, we first introduce principal curves as a model for the underlying skeleton of axons and branches, then describe a recursive principal curve tracing (RPCT) method to extract this topology information from 3D microscopy imagery. RPCT first finds samples on the one dimensional principal set of the intensity function in space. Then, given an initial direction and location, the algorithm iteratively traces the principal curve in space using our principal curve tracing (PCT) method. Recursive implementation of PCT provides a compact solution for extracting complex tubular structures that exhibit bifurcations.
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Notes
KDE is used as an example since it encompasses parametric mixture models as a special case; the method is general for any pdf model.
Assuming Gaussian kernels here for illustration.
References
Al-Kofahi, K., Can, A., et al. (2004). Median-based robust algorithms for tracing neurons from noisy confocal microscope images. IEEE Transactions on Information Technology in Biomedicine, 7(4), 302–317.
Aykac, D., Hoffman, E., et al. (2003). Segmentation and analysis of the human airway tree from three-dimensional X-ray CT images. IEEE Transactions on Medical Imaging, 22(8), 940–950.
Bas, E., & Erdogmus, D. (2010a). Piecewise linear cylinder models for 3-dimensional axon segmentation. In 4th IEEE international symposium on biomedical imaging: From nano to macro.
Bas, E., & Erdogmus, D. (2010b). Principal curve tracing. In European symposium on artificial neural networks.
Bear, M., Connors, B., & Paradiso, M. (2007). Neuroscience: Exploring the brain. Philadelphia: Lippincott Williams Wilkins.
Brown, K., Barrionuevo, G., Canty, A., De Paola, V., Hirsch, J., Jefferis, G., et al. (2011). The diadem data sets: Representative light microscopy images of neuronal morphology to advance automation of digital reconstructions. Neuroinformatics, 1–15. doi:10.1007/s12021-010-9095-5.
Cai, H., Xu, X., et al. (2006). Repulsive force based snake model to segment and track neuronal axons in 3d microscopy image stacks. Neuroimage, 32, 1608–1620.
Cai, H., Xu, X., et al. (2008). Using nonlinear diffusion and mean shift to detect and connect cross-sections of axons in 3d optical microscopy images. Medical Image Analysis, 12, 666–675.
Carreira-Perpinán, M., & Zemel, R. (2005). Proximity graphs for clustering and manifold learning. Advances in Neural Information Processing Systems, 17, 225–232.
Cetingul, H., Plank, G., et al. (2009). Stochastic tractography in 3-D images via nonlinear filtering and spherical clustering. In MICCAI workshop on probabilistic models for medical, PMMIA (pp. 268–279).
Chang, K., & Ghosh, J. (2002). A unified model for probabilistic principal surfaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(1), 22–41.
Chen, J., Sato, Y., et al. (2002). Orientation space filtering for multiple orientation line segmentation. IEEE Transactions in Pattern Analysis and Machine Intelligence, 22(5), 417–429.
Cormen, T., Leiserson, C., et al. (2001). Introduction to algorithms. The algorithms of Kruskal and Prim. MIT Press and McGraw-Hill.
Deschamps, T., & Cohen, L. (2001). Fast extraction of minimal paths in 3D images and applications to virtual endoscopy. Medical Image Analysis, 5(4), 281–299.
Einbeck, J., Tutz, G., et al. (2005). Local principal curves. Statistics and Computing, 15(4), 301–313.
Erdogmus, D., & Ozertem, U. (2007). Self-consistent locally defined principal surfaces. In Proceedings of the IEEE international conference on acoustics, speech and signal processing (Vol. 2, pp. 549–552).
Frangi, A., Niessen, W., et al. (1999). Model-based quantitation of 3-D magnetic resonance angiographic images. IEEE Transactions on Medical Imaging, 18(10), 946–956.
Hastie, T., & Stuetzle, W. (2003). Principal curves. Journal of the American Statistical Association, 84(406), 502–516.
Huang, S., Li, J., et al. (2009). Learning brain connectivity of Alzheimer’s disease from neuroimaging data. Advances in Neural Information Processing Systems, 22, 808–816.
Jurrus, E., Hardy, M., et al. (2009). Axon tracking in serial block-face scanning electron microscopy. Medical Image Analysis, 13(1), 180–188.
Kegl, B., Krzyzak, A., et al. (2000). Learning and design of principal curves. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(3), 281–297.
Krishnan, A., Asher, I., Davis, D., Okunieff, P., & O’Dell, W. (2008). Evidence that MR diffusion tensor imaging (tractography) predicts the natural history of regional progression in patients irradiated conformally for primary brain tumors. International Journal of Radiation Oncology, Biology, Physics, 71(5), 1553–1562.
Livet, J., Weissman, T., Kang, H., Lu, J., Bennis, R., Sanes, J., et al. (2007). Transgenic strategies for combinatorial expression of fluorescent proteins in the nervous system. Nature, 450(7166), 56–62.
Meinicke, P., Klanke, S., et al. (2005). Principal surfaces from unsupervised kernel regression. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(9), 1379–1391.
Palágyi, K., & Kuba, A. (1998). A 3d 6-subiteration thinning algorithm for extracting medial lines. Pattern Recognition Letters, 19(7), 613–627.
Rodriguez, A., Ehlenberger, D., et al. (2009). Three-dimensional neuron tracing by voxel scooping. Journal of Neuroscience Methods, 184(1), 169–175.
Schmitt, S., Scholz, M., et al. (2004). New methods for the computer-assisted 3d reconstruction of neurons. NeuroImage, 23(4), 1283–1298.
Sheikh, Y., Khan, E., et al. (2007). Mode-seeking by medoidshifts. In Proceedings of the IEEE international conference on computer vision (Vol. 141, pp. 1–8). Citeseer.
Sugihara, I. (2011). Bright field neuronal preparation optimized for automatic computerized reconstruction, a case with cerebellar climbing fibers. Neuroinformatics. doi:10.1007/s12021-011-9098-x.
Vasilkoski, Z., & Stepanyants, A. (2009). Detection of the optimal neuron traces in confocal microscopy images. Journal of Neuroscience Methods, 178(1), 197–204.
Wang, J., Zhou, X., et al. (2007). Dynamic local tracing for 3d axon curvilinear structure detection from microscopic image stack. In 4th IEEE international symposium on biomedical imaging: From nano to macro (pp. 81–84).
Wink, O., Niessen, W., et al. (2004). Multiscale vessel tracking. IEEE Transactions on Medical Imaging, 23(1), 130–133.
Zhou, W., Li, H., et al. (2008). 3d dendrite reconstruction and spine identification. In Proceedings of MICCAI’08, part II (pp. 18–26).
Acknowledgements
The authors would like to thank the organizers and data providers of the Diadem Challenge for putting together this challenge.
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This work was partially supported by NSF grants ECCS0929576, ECCS0934506, IIS0934509, and IIS0914808.
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Bas, E., Erdogmus, D. Principal Curves as Skeletons of Tubular Objects. Neuroinform 9, 181–191 (2011). https://doi.org/10.1007/s12021-011-9105-2
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DOI: https://doi.org/10.1007/s12021-011-9105-2