Abstract
Shape modeling is an important constituent of both computer graphics and computer vision research. This paper proposes an efficient shape modeling scheme using the active geometric deformable models, for implementing solid modeling techniques on free form shapes. A fast and computationally efficient narrow band level set algorithm is proposed for reducing the overall computational cost. When compared to traditional geometric modeling, the proposed level set model can easily handle topology changes, is free of edge connectivity and mesh quality problems and provides the advantages of implicit models, supporting straightforward solid modeling operations on complex structures of unknown topology. Using this model boolean operations have been implemented on arbitrary shapes extracted from both synthetic and real image data including some low contrast medical images, with promising results.
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References
Adalsteinsson, D., Sethian, J.A.: A fast level set method for propagating interfaces. J. Comput. Phys. 118, 269–277 (1995)
Agoston, M.K.: Computer Graphics and Geometric Modeling. Springer, London (2005)
Caselles, V., Catte, F., Coll, T., Dibos, F.: A geometric model for active contours in image processing. Numer. Math. 66, 1–31 (1993)
Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. Int. J. Comput. Vis 22, 61–79 (1997)
Chan, T., Vese, L.: Active contours without edges. IEEE Trans. Image Process. 10, 266–277 (2001)
Chopp, D.L.: Computing minimal surfaces via level set curvature flow. J. Comput. Phys. 106, 77–91 (1993)
Gomes, J., Faugeras, O.: Reconciling distance functions and level sets. J. Vis. Commun. Image Represent. 11, 209–223 (2000)
Han, X., Xu, C., Prince, J.: A topology preserving level set method for geometric deformable models. IEEE Trans. Pattern Anal. Mach. Intell. 25, 755–768 (2003)
Jain, M.K.: Numerical Solutions of Differential Equations. Wiley, New York (1979)
Kachouie, N.N., Fieguth, P.: A narrow band level set method with dynamic velocity for neural stem cell cluster segmentation, image analysis and recognition. Lect. Notes. Comput. Sci. 3656, 1006–1013 (2005)
Kass, M., Witkin, A.: Terzopoulos, D.: Snakes: active contour models. Int. J. Comput. Vis. 1, 321–331 (1987)
Kimia, B.B., Tannenbaum, A.R., Zucker, S.W.: Shapes, shocks, and deformations I: the components of two dimensional shape and the reaction-diffusion space. Int. J. Comput. Vis. 15, 189–224 (1995)
Li, C., Chenyang, X., Gui, C., Fox, M.D.: Level set evolution without re-initialization: A New Variational Formulation. IEEE Conf. Proc. Comput. Vis. Pattern Recognit.1063-6919/05 (2005)
Malladi, R., Sethian, J.A., Vemuri, B.C.: Shape modeling with front propagation: A level set approach. IEEE Trans. Pattern Anal. Mach. Intell. 17, 158–175 (1995)
Museth, K.: An efficient level set toolkit for visual effects. In: SIGGRAPH’09: SIGGRAPH Talks, pp. 1–1. ACM, New York (2009)
Museth, K., Breen, D.E., Whitaker, R.T., Mauch, S., Johnson, D.: Algorithms for interactive editing of level set models. Int. J. Eurographics Assoc. Comput. Graph. Forum. 24(4), 821–841 (2005)
Nielsen, M.B., Museth, K.: Dynamic tubular grid: an efficient data structure and algorithms for high resolution level sets. J. Sci. Comput. 26(3), 261–299 (2006)
Osher, S., Fedkiw, R.: Level Set Methods and Dynamic Implicit Surfaces. Springer, New York (2002)
Osher, S., Paragios, N.: Geometric Level Set Methods in Imaging. Vision and Graphics. Springer, New York (2003)
Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79, 12–49 (1988)
Rosenthal, P., Molchanov, V., Linsen, L.: A narrow band level set method for surface extraction from unstructured point-based volume data. In: Proceedings of WSCG, The 18th international conference on computer graphics, Visualization and Computer Vision. pp. 73–80. UNION Agency—Science Press, Plzen, Czech Republic (2010)
Rosenthal, P., Linsen, L.: Smooth surface extraction from unstructured point-based volume data using PDEs. IEEE Trans. Vis. Comput. Graph. 14(6), 1531–1546 (2008)
Rossignac, T.R., Requicha, A.A.G.: Solid modeling. In: Webster, J. (ed.) Encyclopedia of Electrical and Electronics Engineering. Wiley, New York (1999)
Sethian, J.A.: Level Set Methods and Fast Marching Methods. Cambridge University Press, Cambridge (1999)
Vemuri B., Chen Y.: Joint image registration and segmentation. Geometric Level Set Methods in Imaging, Vision, and Graphics pp. 251–269. Springer, New York (2003)
Whitaker, R.T.: A level-set approach to 3D reconstruction from range data. Int. J. Comput. Vis. 3, 203–231 (1998)
Whitaker, R.T., Breen, D., Museth, K., Soni, N.: Segmentation of biological volume datasets using a level-set framework. In: Chen, M., Kaufman, A. (eds.) Volume Graphics. pp. 249–263. Springer, Vienna (2001)
Zhao, H., Chan, T., Merriman, B., Osher, S.: A variational level set approach to multiphase motion. J. Comput. Phys. 127, 179–195 (1996)
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Bindu, V.R., Ramachandran Nair, K.N. (2015). Boolean Operations on Free Form Shapes in a Level Set Framework. In: Jain, L., Behera, H., Mandal, J., Mohapatra, D. (eds) Computational Intelligence in Data Mining - Volume 3. Smart Innovation, Systems and Technologies, vol 33. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2202-6_41
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DOI: https://doi.org/10.1007/978-81-322-2202-6_41
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