Abstract
We present a variational approach to simultaneously trace the axis and determine the thickness of 3-D (or 2-D) tubular structures defined by sparsely and unevenly sampled noisy surface points. Many existing approaches try to solve the axis-tracing and the precise fitting in two subsequent steps. In contrast to this our model is initialized with a small cylinder segment and converges to the final tubular structure in a single energy minimization using a gradient descent scheme. The energy is based on the error of fit and simultaneously penalizes strong curvature and thickness variations. We demonstrate the performance of this closed formulation on volumetric microscopic data sets of the Arabidopsis root tip, where only the nuclei of the cells are visible.
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References
Bauer, U., Polthier, K.: Generating parametric models of tubes from laser scans. Computer-Aided Design 41(10), 719–729 (2009)
de Boor, C.: A practical guide to splines, 3rd edn. Applied Mathematical Sciences, vol. 27. Springer (1978)
Friman, O., Hindennach, M., Kühnel, C., Peitgen, H.O.: Multiple hypothesis template tracking of small 3d vessel structures. Med. Image Anal. 14, 160–171 (2010)
Kirbas, C., Quek, F.: A review of vessel extraction techniques and algorithms. ACM Comput. Surv. 36(2), 81–121 (2004)
Laptev, I., Mayer, H., Lindeberg, T., Eckstein, W., Steger, C., Baumgartner, A.: Automatic extraction of roads from aerial images based on scale space and snakes. In: Machine Vision and Applications, vol. 12, pp. 23–31 (2000)
Lee, I.K.: Curve reconstruction from unorganized points. Computer Aided Geometric Design 17(2), 161–177 (2000)
Meijering, E., Jacob, M., Sarria, J.C., Steiner, P., Hirling, H., Unser, M.: Design and validation of a tool for neurite tracing and analysis in fluorescence microscopy images. Cytometry Part A 58A(2), 167–176 (2004)
Pock, T., Beichel, R., Bischof, H.: A Novel Robust Tube Detection Filter for 3D Centerline Extraction. In: Kalviainen, H., Parkkinen, J., Kaarna, A. (eds.) SCIA 2005. LNCS, vol. 3540, pp. 481–490. Springer, Heidelberg (2005)
Schnabel, R., Wahl, R., Klein, R.: Efficient ransac for point-cloud shape detection. Computer Graphics Forum 26(2), 214–226 (2007)
Skibbe, H., Reisert, M., Ronneberger, O., Burkhardt, H.: Increasing the Dimension of Creativity in Rotation Invariant Feature Design Using 3D Tensorial Harmonics. In: Denzler, J., Notni, G., Süße, H. (eds.) DAGM 2009. LNCS, vol. 5748, pp. 141–150. Springer, Heidelberg (2009)
Wang, Q., Ronneberger, O., Schulze, E., Baumeister, R., Burkhardt, H.: Using Lateral Coupled Snakes for Modeling the Contours of Worms. In: Denzler, J., Notni, G., Süße, H. (eds.) DAGM 2009. LNCS, vol. 5748, pp. 542–551. Springer, Heidelberg (2009)
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Schmidt, T., Keuper, M., Pasternak, T., Palme, K., Ronneberger, O. (2012). Modeling of Sparsely Sampled Tubular Surfaces Using Coupled Curves. In: Pinz, A., Pock, T., Bischof, H., Leberl, F. (eds) Pattern Recognition. DAGM/OAGM 2012. Lecture Notes in Computer Science, vol 7476. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32717-9_9
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DOI: https://doi.org/10.1007/978-3-642-32717-9_9
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