Abstract
In this paper, we investigate the problem of approximating a neuron (which is a disconnected polyhedron P reconstructed from points sampled from the surface of a neuron) with minimal cylindrical segments. The problem is strongly NP-hard when we take sample points as input. We present a general algorithm which combines a method to identify critical vertices of P and useful user feedback to decompose P into desired components. For each decomposed component Q, we present an algorithm which tries to minimize the radius of the approximate enclosing cylindrical segment. Previously, this process can only be done manually by researchers in computational biology. Empirical results show that the algorithm is very efficient in practice.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This research is supported by NSF CARGO grant DMS-0138065.
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
Agarwal, P., Aronov, B., Sharir, M.: Line transversals of balls and smallest enclosing cylinders in three dimensions. In: Proc. 8th ACM-SIAM Symp on Discrete Algorithms (SODA 1997), New Orleans, LA, January 1997, pp. 483–492 (1997)
Chan, T.: Approximating the diameter, width, smallest enclosing cylinder, and minimum-width annulus. In: Proc. 16th ACM Symp on Computational Geometry (SCG 2000), Hong Kong, June 2000, pp. 300–309 (2000)
Matoušek, J., Sharir, M., Welzl, E.: A subexponential bound for linear programming. Algorithmica 16, 498–516 (1992)
Gärtner, B.: http://www.inf.ethz.ch/personal/gaertner/miniball.html
Jacobs, G., Theunissen, F.: Functional organization of a neural map in the cricket cercal sensory system. J. of Neuroscience 16(2), 769–784 (1996)
Jacobs, G., Theunissen, F.: Extraction of sensory parameters from a neural map by primary sensory interneurons. J. of Neuroscience 20(8), 2934–2943 (2000)
Lau, R., Green, M., To, D., Wong, J.: Real-time Continuous Multi-Resolution Method for Models of Arbitrary Topology. Presence: Teleoperators and Virtual Environments 7, 22–35 (1998)
Paydar, S., Doan, C., Jacobs, G.: Neural mapping of direction and frequency in the cricket cercal sensory system. J. of Neuroscience 19(5), 1771–1781 (1999)
Preparata, F.P., Shamos, M.I.: Computational Geometry: An Introduction. Springer, Heidelberg (1985)
Schömer, E., Sellen, J., Teichmann, M., Yap, C.K.: Smallest enclosing cylinders. Algorithmica 27, 170–186 (2000)
Welzl, E.: Smallest enclosing disks (balls and ellipsoids). In: Maurer, H.A. (ed.) New Results and New Trends in Computer Science. LNCS, vol. 555, pp. 359–370. Springer, Heidelberg (1991)
Zhu, B.: Approximating convex polyhedra with axis-parallel boxes. Intl. J. of Computational Geometry and Applications 7(3), 253–267 (1997)
Zhu, B.: Approximating 3D points with cylindrical segments. In: Ibarra, O.H., Zhang, L. (eds.) COCOON 2002. LNCS, vol. 2387, pp. 400–409. Springer, Heidelberg (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lin, W., Zhu, B., Jacobs, G., Orser, G. (2004). Cylindrical Approximation of a Neuron from Reconstructed Polyhedron. In: Laganá, A., Gavrilova, M.L., Kumar, V., Mun, Y., Tan, C.J.K., Gervasi, O. (eds) Computational Science and Its Applications – ICCSA 2004. ICCSA 2004. Lecture Notes in Computer Science, vol 3045. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24767-8_27
Download citation
DOI: https://doi.org/10.1007/978-3-540-24767-8_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22057-2
Online ISBN: 978-3-540-24767-8
eBook Packages: Springer Book Archive