CSDL Home IEEE Transactions on Visualization & Computer Graphics 2010 vol.16 Issue No.05 - September/October

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Issue No.05 - September/October (2010 vol.16)

pp: 854-869

Herng-Hua Chang , National Taiwan University of Science and Technology, Taipei

Woei-Chyn Chu , National Yang-Ming University, Taipei

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2009.212

ABSTRACT

Physics-based particle systems are an effective tool for shape modeling. Also, there has been much interest in the study of shape modeling using deformable contour approaches. In this paper, we describe a new deformable model with electric flows based upon computer simulations of a number of charged particles embedded in an electrostatic system. Making use of optimized numerical techniques, the electric potential associated with the electric field in the simulated system is rapidly calculated using the finite-size particle (FSP) method. The simulation of deformation evolves based upon the vector sum of two interacting forces: one from the electric fields and the other from the image gradients. Inspired by the concept of the signed distance function associated with the entropy condition in the level set framework, we efficiently handle topological changes at the interface. In addition to automatic splitting and merging, the evolving contours enable simultaneous detection of various objects with varying intensity gradients at both interior and exterior boundaries. This electric flows approach for shape modeling allows one to connect electric properties in electrostatic equilibrium and classical active contours based upon the theory of curve evolution. Our active contours can be applied to model arbitrarily complicated objects including shapes with sharp corners and cusps, and to situations where no a priori knowledge about the object's topology and geometry is made. We demonstrate the capabilities of this new algorithm in recovering a wide variety of structures on simulated and real images in both 2D and 3D.

INDEX TERMS

Shape modeling, shape recovery, deformable models, particle systems, finite-size particle (FSP), Poisson's equation, electrostatic equilibrium.

CITATION

Herng-Hua Chang, Woei-Chyn Chu, "Active Shape Modeling with Electric Flows",

*IEEE Transactions on Visualization & Computer Graphics*, vol.16, no. 5, pp. 854-869, September/October 2010, doi:10.1109/TVCG.2009.212REFERENCES

- [1] W.T. Reeves, "Particle Systems—A Technique for Modeling a Class of Fuzzy Objects,"
ACM Trans. Graphics, vol. 2, no. 2, pp. 91-108, 1983.- [2] R. Szeliski and D. Tonnesen, "Surface Modeling with Oriented Particle Systems,"
Computer Graphics, vol. 26, no. 2, pp. 185-194, 1992.- [3] R. Szeliski, D. Tonnesen, and D. Terzopoulos, "Modeling Surfaces of Arbitrary Topology with Dynamic Particles"
Proc. IEEE Computer Vision and Pattern Recognition (CVPR), pp. 82-87, June 1993.- [4] D. Stahl, N. Ezquerra, and G. Turk, "Bag-of-Particles as a Deformable Model"
Proc. IEEE Technical Committee on Visualization and Graphics (TCVG), pp. 141-150, May 2002.- [5] A. Habibi and A. Luciani, "Dynamic Particle Coating,"
IEEE Trans. Visualization and Computer Graphics, vol. 8, no. 4, pp. 383-394, Oct.-Dec. 2002.- [6] O. Etzmuss, J. Gross, and W. Strasser, "Deriving a Particle System from Continuum Mechanics for the Animation of Deformable Objects,"
IEEE Trans. Visualization and Computer Graphics, vol. 9, no. 4, pp. 538-550, Oct.-Dec. 2003.- [7] A.P. Witkin and P.S. Heckbert, "Using Particles to Sample and Control Implicit Surfaces,"
Proc. ACM SIGGRAPH Computer Graphics, pp. 269-278, 1994.- [8] J.C. Hart, E. Bachta, W. Jarosz, and T. Fleury, "Using Particles to Sample and Control More Complex Implicit Surfaces,"
Proc. IEEE Int'l. Conf. Shape Modeling and Applications (SMI), pp. 129-136, 2002.- [9] M.D. Meyer, P. Georgel, and R.T. Whitaker, "Robust Particle Systems for Curvature Dependent Sampling of Implicit Surfaces,"
Proc. IEEE Int'l. Conf. Shape Modeling and Applications (SMI), pp. 124-133, 2005.- [10] E.J. Hastings, R.K. Guha, and K.O. Stanley, "NEAT Particles: Design, Representation, and Animation of Particle System Effects,"
Proc. IEEE Symp. Computational Intelligence and Games (CIG), pp. 154-160, 2007.- [11] S. Osher and R. Fedkiw,
Level Set Methods and Dynamic Implicit Surfaces. Springer-Verlag, 2003.- [12] M. Kass, A. Witkin, and D. Terzopoulos, "Snakes: Active Contour Models,"
Int'l J. Computer Vision, vol. 1, no. 4, pp. 321-331, 1988.- [13] L.D. Cohen, "On Active Contour Models and Balloons,"
CVGIP: Image Understanding, vol. 53, no. 2, pp. 211-218, Mar. 1991.- [14] S. Osher and J.A. Sethian, "Fronts Propagating with Curvature Dependent Speed: Algorithms Based on Hamiltons-Jacobi Formulations,"
J. Computer Physics, vol. 79, pp. 12-49, 1988.- [15] V. Caselles, F. Catte, T. Coll, and F. Dibos, "A Geometric Model for Active Contours in Image Processing,"
Numerische Mathematik, vol. 66, pp. 1-31, 1993.- [16] R. Malladi, J.A. Sethian, and B.C. Vemuri, "Shape Modeling with Front Propagation: A Level Set Approach,"
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 2, pp. 158-175, Feb. 1995.- [17] A.E. Lefohn, J.M. Kniss, C.D. Hansen, and R.T. Whitaker, "A Streaming Narrow-Band Algorithm: Interactive Computation and Visualization of Level Sets,"
IEEE Trans. Visualization and Computer Graphics, vol. 10, no. 4, pp. 422-433, July-Aug. 2004.- [18] S. Osher and N. Paragios,
Geometric Level Set Methods in Imaging, Vision, and Graphics. Springer-Verlag, 2003.- [19] V. Caselles, R. Kimmel, and G. Sapiro, "Geodesic Active Contours,"
Int'l J. Computer Vision, vol. 22, no. 1, pp. 61-79, 1997.- [20] S. Kichenassamy, A. Kumar, P. Olver, A. Tannenbaum, and A. Yezzi, "Gradient Flows and Geometric Active Contour Models,"
Proc. IEEE Int'l Conf. Computer Vision, pp. 810-815, 1995.- [21] A. Yezzi, S. Kichenassamy, A. Kumar, P. Olver, and A. Tannenbaum, "A Geometric Snake Model for Segmentation of Medical Imagery,"
IEEE Trans. Medical Imaging, vol. 16, no. 2, pp. 199-209, Apr. 1997.- [22] Y. Bai, X. Han, and J.L. Prince, "Topology-Preserving Geometric Deformable Model on Adaptive Quadtree Grid,"
Proc. IEEE Conf. Computer Vision and Pattern Recognition (CVPR), pp. 1-8, 2007.- [23] D.A. Lorenz, P. Maass, H. Preckel, and D. Trede, "Topology-Preserving Geodesic Active Contours for Segmentation of High Content Fluorescent Cellular Images,"
Proc. Applied Math. and Mechanics, vol. 8, no. 1, pp. 10941-10942, 2008.- [24] H.-H. Chang and D.J. Valentino, "Image Segmentation Using a Charged Fluid Method,"
J. Electron Imaging, vol. 15, no. 2, p. 023011, 2006.- [25] J.A. Sethian,
Level Set Methods and Fast Marching Methods, 2nd ed. Cambridge Univ. Press, 1999.- [26] H.-H. Chang, "Computer Simulations of Isolated Conductors in Electrostatic Equilibrium,"
Physical Rev. E, vol. 78, no. 5, p. 056704, 2008.- [27] A.B. Langdon and C.K. Birdsall, "Theory of Plasma Simulation Using Finite-Size Particles,"
Physics of Fluids, vol. 13, no. 8, pp. 2115-2122, 1970.- [28] J.M. Dawson, "Particle Simulation of Plasmas,"
Rev. of Modern Physics, vol. 55, no. 2, pp. 403-447, 1983.- [29] W.L. Kruer, J.M. Dawson, and B. Rosen, "The Dipole Expansion Method for Plasma Simulation,"
J. Computational Physics, vol. 13, pp. 114-129, 1973.- [30] T. Tajima,
Computational Plasma Physics: With Applications to Fusion and Astrophysics. Addison-Wesley, 1989.- [31] V.K. Decyk and J.M. Dawson, "Computer Model for Bounded Plasma,"
J. Computational Physics, vol. 30, pp. 407-427, 1979.- [32] MGH,
Internet Brain Segmentation Repository (IBSR), http://www.cma.mgh.harvard.eduibsr/, 2007.- [33] J.E. Cates, A.E. Lefohn, and R.T. Whitaker, "GIST: An Interactive, GPU-Based Level Set Segmentation Tool for 3D Medical Images,"
Medical Image Analysis, vol. 8, no. 3, pp. 217-231, 2004. |