# Automated Reconstruction of Dendritic and Axonal Trees by Global Optimization with Geometric Priors

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## Abstract

We present a novel probabilistic approach to fully automated delineation of tree structures in noisy 2D images and 3D image stacks. Unlike earlier methods that rely mostly on local evidence, ours builds a set of candidate trees over many different subsets of points likely to belong to the optimal tree and then chooses the best one according to a global objective function that combines image evidence with geometric priors. Since the best tree does not necessarily span all the points, the algorithm is able to eliminate false detections while retaining the correct tree topology. Manually annotated brightfield micrographs, retinal scans and the DIADEM challenge datasets are used to evaluate the performance of our method. We used the DIADEM metric to quantitatively evaluate the topological accuracy of the reconstructions and showed that the use of the geometric regularization yields a substantial improvement.

## Keywords

DIADEM Tree reconstruction Global optimization Minimum arborescence*k*-MST Ant colony optimization

## Notes

### Acknowledgements

This work was supported in part by the Swiss National Science Foundation and in part by the MicroNano ERC project. Christian Blum also acknowledges support from the *Ramón y Cajal* program of the Spanish Government.

We would like to thank Felix Schürmann for his advice and for giving us access to the brightfield dataset and corresponding ground-truth.

## References

- Al-Kofahi, K.A., Lasek, S., Szarowski, D. H., Pace, C. J., Nagy, G., Turner, J. N., et al. (2002). Rapid automated three-dimensional tracing of neurons from confocal image stacks.
*Transactions on Information Technology in Biomedicine, 6*(2), 171–187.PubMedCrossRefGoogle Scholar - Ascoli, G. A., Svoboda, K., & Liu Y. (2010). Digital reconstruction of axonal and dendritic morphology DIADEM challenge. http://diademchallenge.org/.
- Blum, C. (2007). Revisiting dynamic programming for finding optimal subtrees in trees.
*European Journal of Operational Research, 177*(1), 102–115.CrossRefGoogle Scholar - Blum, C., & Blesa M. (2005). Combining ant colony optimization with dynamic programming for solving the K-cardinality tree problem. In
*Computational intelligence and bioinspired systems. Lecture notes in computer science*(Vol. 3512, pp. 25–33).Google Scholar - Cai, H., Xu, X., Lu, J., Lichtman, J., Yung, S., & Wong, S. (2006). Repulsive force based snake model to segment and track neuronal axons in 3D microscopy image stacks.
*NeuroImage, 32*(4), 1608–1620.PubMedCrossRefGoogle Scholar - Can, A., Shen, H., Turner, J., Tanenbaum, H., & Roysam, B. (1999). Rapid automated tracing and feature extraction from retinal fundus images using direct exploratory algorithms.
*Transactions on Information Technology in Biomedicine, 3*(2), 125–138.PubMedCrossRefGoogle Scholar - Dorigo, M., & Stütale, T. (2004).
*Ant colony optimization*. Cambridge, MA: MIT Press.CrossRefGoogle Scholar - Duhamel, C., Gouveia, L., Moura, P., & Souza, M. (2008). Models and heuristics for a minimum arborescence problem.
*Networks, 51*(1), 34–47.CrossRefGoogle Scholar - Fan, D. (2006).
*Bayesian inference of vascular structure from retinal images*. Ph.D. thesis, Dept. of Computer Science, U. of Warwick, Coventry, UK.Google Scholar - Felzenszwalb, P., & Huttenlocher, D. (2005). Pictorial structures for object recognition.
*International Journal of Computer Vision, 16*(1), 55–79.CrossRefGoogle Scholar - Felzenszwalb, P., & McAllester, D. (2006). A min-cover approach for finding salient curves. In
*Conference on computer vision and pattern recognition*(pp. 61–74).Google Scholar - Fischler, M., & Heller, A. (1998). Automated techniques for road network modeling. In
*DARPA image understanding workshop*(pp. 501–516).Google Scholar - Frangi, A. F., Niessen, W. J., Vincken, K. L., & Viergever, M. A. (1998). Multiscale vessel enhancement filtering.
*Lecture Notes in Computer Science, 1496*, 130–137.Google Scholar - Garg, N. (1996). A 3-approximation for the minimum tree spanning K vertices. In
*IEEE symposium on foundations of computer science*(Vol. 27, pp. 302–309). Washington, DC, USA: IEEE Computer Society.Google Scholar - Gonzalez, G., Aguet, F., Fleuret, F., Unser, M., & Fua, P. (2009). Steerable features for statistical 3D dendrite detection. In
*Conference on medical image computing and computer assisted intervention*(Vol. 12, pp. 625–32).Google Scholar - Gonzalez, G., Fleuret, F., & Fua, P. (2008). Automated delineation of dendritic networks in noisy image stacks. In
*European conference on computer vision. Lecture notes in computer science*(Vol. 5305, pp. 214–227). Berlin/Heidelberg: Springer.Google Scholar - Huang, K., & Yan, M. (2006). Robust optic disk detection in retinal images using vessel structure and radon transform. In
*SPIE*(Vol. 6144).Google Scholar - Jacob, M., & Unser, M. (2004). Design of steerable filters for feature detection using canny-like criteria.
*IEEE Transactions on Pattern Analysis and Machine Intelligence, 26*(8), 1007–1019.PubMedCrossRefGoogle Scholar - Law, M., & Chung, A. (2008). Three dimensional curvilinear structure detection using optimally oriented flux. In
*European conference on computer vision*(pp. 368–382).Google Scholar - Lee, T., Kashyap, R., & Chu, C. (1994). Building skeleton models via 3-D medial surface axis thinning algorithms.
*CVGIP: Graphical Models and Image Processing, 56*(6), 462–478.CrossRefGoogle Scholar - Leordeanu, M., Hebert, M., & Sukthankar, R. (2007). Beyond local appearance: Category recognition from pairwise interactions of simple features. In
*Conference on computer vision and pattern recognition*(pp. 1 –8).Google Scholar - Meijering, E., Jacob, M., Sarria, J. C. F., Steiner, P., Hirling, H., & Unser, M. (2004). Design and validation of a tool for neurite tracing and analysis in fluorescence microscopy images.
*Cytometry Part A, 58A*(2), 167–176.CrossRefGoogle Scholar - Platt, J. (2000). Advances in large margin classifiers. Chap probabilistic outputs for SVMs and comparisons to regularized likelihood methods. Cambridge, MA: MIT Press.Google Scholar
- Santamaría-Pang, A., Colbert, C. M., Saggau, P., & Kakadiaris, I. (2007). Automatic centerline extraction of irregular tubular structures using probability volumes from multiphoton imaging. In
*Conference on medical image computing and computer assisted intervention*(pp. 486–494).Google Scholar - Schoelkopf, B., Burges, C., & Smola, A. (1999). Advances in Kernel methods. In
*Support vector learning*. Cambridge, MA: MIT Press.Google Scholar - Staal, J., Abramoff, M., Niemeijer, M., Viergever, M., & van Ginneken, B. (2004). Ridge based vessel segmentation in color images of the retina.
*IEEE Transactions on Medical Imaging, 23*, 501–509.PubMedCrossRefGoogle Scholar - Sun, K., Sang, N., & Zhang, T. (2007). Marked point process for vascular tree extraction on angiogram. In
*Conference on computer vision and pattern recognition*(pp. 467–478).Google Scholar - Vasilkoski, Z., & Stepanyants, A. (2009). Detection of the optimal neuron traces in confocal microscopy images.
*Journal of Neuroscience Methods, 178*(1), 197–204.PubMedCrossRefGoogle Scholar - Weaver, C., Hof, P., Wearne, S., & Brent, L. (2004). Automated algorithms for multiscale morphometry of neuronal dendrites.
*Neural Computation, 16*(7), 1353–1383.PubMedCrossRefGoogle Scholar - Xie, J., Zhao, T., Lee, T., Myers, G., & Peng, H. (2010). Automatic neuron tracing in volumetric microscopy images with anisotropic path searching. In
*Conference on medical image computing and computer assisted intervention*.Google Scholar - Xu, J., Wu, J., Feng, D., & Cui, Z. (2009). DSA image blood vessel skeleton extraction based on anti-concentration diffusion and level set method.
*Computational intelligence and intelligent systems, 51*, 188–198.CrossRefGoogle Scholar - Yedidya, T., & Hartley, R. (2008). Tracking of blood vessels in retinal images using Kalman filter. In
*Digital image computing: Techniques and applications*(pp. 52–58).Google Scholar