Kluwer - Handbook of Biomedical Image Analysis Vol

[11]Biben, T., Misbah, C., Leyrat, A., and Verdier, C., An advected-field approach to the dynamics of fluid interfaces, Europhys. Lett., Vol. 63, pp. 623–629, 2003.

[12]Bottigli, U., and Golosio, B., Feature extraction from mammographic images using fast marching methods, Nucl. Instrum. Methods Phys. Res. A, Vol. 487, pp. 209–215, 2002.

[13]Breen, D. E., and Whitaker, R. T., A level-set approach for the metamorphosis of solid models, IEEE Trans. Visualization Comput. Graphics, Vol. 7, pp. 173–192, 2001.

[14]Burchard, P., Cheng, L.-T., Merriman, B., and Osher, S., Motion of curves in three spatial dimensions using a level set approach, J. Comput. Phys., Vol. 170, pp. 720–741, 2001.

[15]Burger, M., A level set method for inverse problems, Inverse Problems, Vol. 17, pp. 1327–1355, 2001.

[16]Caiden, R., Fedkiw, R. P., and Anderson, C., A numerical method for two-phase flow consisting of separate compressible and incompressible regions, J. Comput. Phys., Vol. 166, pp. 1–27, 2001.

[17]Chan, T., and Vese, L., A level set algorithm for minimizing the Mumford–Shah functional in image processing. In: IEEE Computing Society Proceedings of the 1st IEEE Workshop on “Variational and Level Set Methods in Computer Vision”, pp. 161–168, 2001.

[18]Chen, S., Merriman, B., Kang, M., Caflisch, R. E., Ratsch, C., Cheng, L. T., Gyure, M., Fedkiw, R. P., Anderson, C., and Osher, S., A level set method for thin film epitaxial growth, J. Comput. Phys., Vol. 167, pp. 475–500, 2001.

[19]Chopp, D. L., Computing minimal surfaces via level set curvature flow, J. Comput. Phys., Vol. 106, No. 1, pp. 77–91, 1993.

[20]Chopp, D. L., Numerical computation of self-similar solutions for mean curvature flow, J. Exp. Math., Vol. 3, No. 1, pp. 1–15, 1994.

[21]Chopp, D. L., A level-set method for simulating island coarsening, J. Comput. Phys., Vol. 162, pp. 104–122, 2000.

[22]Chopp, D. L., Some improvements of the fast marching method, SIAM

J.Sci. Comput., Vol. 23, No. 1, pp. 230–244, 2001.

[23]Chopp, D. L., The bidirectional fast marching method, Preprint, 2003.

[24]Chopp, D. L., and Sukumar, N., Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method, Int. J. Eng. Sci., Vol. 41, No. 8, pp. 845–869, 2003.

[25]Chopp, D. L., and Velling, J. A., Foliations of hyperbolic space by constant mean curvature surfaces sharing ideal boundary, J. Exp. Math., Vol. 12, No. 3, pp. 339–350, 2003.

[26]Chung, M. H., A level set approach for computing solutions to inviscid compressible flow with moving solid boundary using fixed cartesian grids, Int. J. Numer. Methods Fluids, Vol. 36, 373–389, 2001.

[27]Combettes, P. L. and Luo, J., An adaptive level set method for nondifferentiable constrained image recovery, IEEE Trans. Image Processing, Vol. 11, pp. 1295–1304, 2002.

[28]Danielsson P. E., and Lin, Q. F., A modified fast marching method, Image Anal., Proc., Vol. 2749, pp. 1154–1161, 2003.

[29]Daux, C., Moes,¨ N., Dolbow, J., Sukumar, N., and Belytschko, T., Arbitrary cracks and holes with the extended finite element method, Int.

J.Numer. Methods Eng., Vol. 48, No. 12, pp. 1741–1760, 2000.

[30]Deng, J. W. and Tsui, H. T., A fast level set method for segmentation of low contrast noisy biomedical images, Pattern Recognit. Lett., Vol. 23, pp. 161–169, 2002.

[31]Deng, S. Z., Ito, K., and Li, Z. L., Three-dimensional elliptic solvers for interface problems and applications, J. Comput. Phys., Vol. 184, pp. 215–243, 2003.

[32]Deschamps, T. and Cohen, L. D., Fast extraction of minimal paths in 3d images and applications to virtual endoscopy, Med. Image Anal., Vol. 5, pp. 281–299, 2001.

[33]Dockery, J. and Klapper, I., Finger formation in biofilm layers, SIAM J. Appl. Math., Vol. 62, pp. 853–869, 2002.

[34]Du, Q., Li, D. Z., Li, Y. Y., Li, R., and Zhang, P. W., Simulating a double casting technique using level set method, Comput. Mater. Sci., Vol. 22,

pp.200–212, 2001.

[35]Elad, A. and Kimmel, R., On bending invariant signatures for surfaces, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 25, pp. 1285–1295, 2003.

[36]Elperin, T. and Vikhansky, A., Variational model of granular flow in a three-dimensional rotating container, Physica A, Vol. 303, pp. 48–56, 2002.

[37]Emmerich, H., Modeling elastic effects in epitaxial growth—stress induced instabilities of epitaxially grown surfaces, Contin. Mech. Thermodyn., Vol. 15, pp. 197–215, 2003.

[38]Enright, D., Fedkiw, R., Ferziger, J., and Mitchell, I., A hybrid particle level set method for improved interface capturing, J. Comput. Phys., Vol. 183, No. 1, pp. 83–116, 2002.

[39]Evans, L.C. and Spruck, J., Motion of level sets by mean curvature i, J. Differ. Geom., Vol. 33, p. 635, 1991.

[40]Evans, L. C. and Spruck, J., Motion of level sets by mean curvature ii, Trans. Am. Math. Soc., Vol. 330, No. 1, pp. 321–332, 1992.

[41]Evans, L. C. and Spruck, J., Motion of level sets by mean curvature iii, J. Geom. Anal., Vol. 2, pp. 121–150, 1992.

[42]Evans, L. C. and Spruck, J., Motion of level sets by mean curvature iv, J. Geom. Anal., Vol. 5, No. 1, pp. 77–114, 1995.

[43]Ferraye, R., Dauvignac, J. Y., and Pichot, C., A boundary-oriented inverse scattering method based on contour deformations by means of level sets for radar imaging, Int. J. Appl. Electromag. Mech., Vol. 15,

pp.213–218, 2001.

[44]Ferraye, R., Dauvignac, J. Y., and Pichot, C., An inverse scattering method based on contour deformations by means of a level set method

using frequency hopping technique, IEEE Trans. Antennas Propag.,

Vol. 51, pp. 1100–1113, 2003.

[45]Ferraye, R., Dauvignac, J. Y., and Pichot, C., Reconstruction of complex and multiple shape object contours using a level set method, J. Electromagn. Waves Appl., Vol. 17, pp. 153–181, 2003.

[46]Fomel, S. and Sethian, J. A., Fast-phase space computation of multiple arrivals, Proc. Nat. Acad. Sci., Vol. 99, No. 11, pp. 7329–7334, 2002.

[47]Frenkel, M. and Basri, R., Curve matching using the fast marching method, Energy Minimization Methods Comput. Vision Pattern Recognition, Proc., Vol. 2683, pp. 35–51, 2003.

[48]Fukano, T. and Inatomi, T., Analysis of liquid film formation in a horizontal annular flow by dns, Int. J. Multiphase Flow, Vol. 29, pp. 1413– 1430, 2003.

[49]Geurts, B. J., Mixing efficiency in turbulent shear layers, J. Turbulence, Vol. 2, pp. 1–24, 2001.

[50]Gibou, F., Fedkiw, R., Cheng, L.-T., and Kang, M., A second order accurate symmetric discretization of the Poisson equation on irregular domains, J. Comput. Phys., Vol. 176, pp. 1–23, 2002.

[51]Gibou, F., Ratsch, C., and Caflisch, R., Capture numbers in rate equations and scaling laws for epitaxial growth, Phys. Rev. B, Vol. 67, pp. 155403–155406, 2003.

[52]Goldenberg, R., Kimmel, R., Rivlin, E., and Rudzsky, M., Fast geodesic active contours, IEEE Trans. Image Process., Vol. 10, pp. 1467–1475, 2001.

[53]Gravouil, A., Moes, N., and Belytschko, T., Non-planar 3d crack growth by the extended finite element and level sets. Part ii Level set update, Int. J. Numer. Methods Eng., Vol. 53, No. 11, pp. 2569–2586, 2002.

[54]Han, X., Xu, C. Y., and Prince, J. L., A topology preserving level set method for geometric deformable models, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 25, pp. 755–768, 2003.

[55]Harten, A., Engquist, B., Osher, S., and Chakravarthy, S., Uniformly high order accurate essentially non-oscillatory schemes. iii, J. Comput. Phys., Vol. 71, No. 2, pp. 231–303, 1987.

[56]Hindmarsh, M., Level set method for the evolution of defect and brane networks, Phys. Rev. D, Vol. 68, pp. 043510–043529, 2003.

[57]Hoch, P. and Rascle, M., Hamilton-Jacobi equations on a manifold and applications to grid generation or refinement, SIAM J. Sci. Comput., Vol. 23, pp. 2055–2073, 2002.

[58]Hunter, J. K., Li, Z. L., and Zhao, H. K., Reactive autophobic spreading of drops, J. Comput. Phys., Vol. 183, pp. 335–366, 2002.

[59]Hwang, H. H., Meyyappan, M., Mathad, G. S., and Ranade, R., Simulations and experiments of etching of silicon in hbr plasmas for high aspect ratio features, J. Vacuum Sci. Technol. B, Vol. 20, pp. 2199–2205, 2002.

[60]Ito, K., Kunisch, K., and Li, Z. L., Level-set function approach to an inverse interface problem, Inverse Problems, Vol. 17, pp. 1225–1242, 2001.

[61]Ji, H., Chopp, D., and Dolbow, J. E., A hybrid extended finite element/level set method for modeling phase transformations, Int. J. Numer. Methods Eng., Vol. 54, No. 8, pp. 1209–1233, 2002.

[62]Khenner, M., Averbuch, A., Israeli, M., and Nathan, M., Numerical simulation of grain-boundary grooving by level set method, J. Comput. Phys., Vol. 170, pp. 764–784, 2001.

[63]Khenner, M., Averbuch, A., Israeli, M., Nathan, M., and Glickman, E., Level set modeling of transient electromigration grooving, Comput. Mater. Sci., Vol. 20, pp. 235–250, 2001.

[64]Ki, H., Mohanty, P. S., and Mazumder, J., Modelling of high-density laser-material interaction using fast level set method, J. Phys. D: Appl. Phys., Vol. 34, pp. 364–372, 2001.

[65]Ki, H., Mohanty, P. S., and Mazumder, J., Modeling of laser keyhole welding: Part ii Simulation of keyhole evolution, velocity, temperature

profile, and experimental verification, Metall. Mater. Trans., A, Vol. 33,

pp. 1831–1842, 2002.

[66]Ki, H., Mohanty, P. S., and Mazumder, J., Multiple reflection and its influence on keyhole evolution, J. Laser Appl., Vol. 14, pp. 39–45, 2002.

[67]Kimmel, R., and Sethian, J. A., Optimal algorithm for shape from shading and path planning, J. Math. Imaging Vision, Vol. 14, pp. 237–244, 2001.

[68]Kobayashi, K., and Sugihara, K., Approximation of multiplicatively weighted crystal growth Voronoi diagram and its application, Electron. Commun. Japan 3, Vol. 85, pp. 21–31, 2002.

[69]Kobayashi, K., and Sugihara, K., Crystal voronoi diagram and its applications, Future Gener. Comput. Syst., Vol. 18, pp. 681–692, 2002.

[70]Kohno, H., and Tanahashi, T., Finite element simulation of single crystal growth process using gsmac method, J. Comput. Appl. Math., Vol. 149, pp. 359–371, 2002.

[71]Kohno, H. and Tanahashi, T., Three-dimensional gsmac-fem simulations of the deformation process and the flow structure in the floating zone method, J. Cryst. Growth, Vol. 237, pp. 1870–1875, 2002.

[72]Koren, B., Lewis, M. R., van Brummelen, E. H., and van Leer, B., Riemann-problem and level-set approaches for homentropic two-fluid flow computations, J. Comput. Phys., Vol. 181, pp. 654–674, 2002.

[73]La Magna, A., D’Arrigo, G., Garozzo, G., and Spinella, C., Computational analysis of etched profile evolution for the derivation of 2d dopant density maps in silicon, Mater. Sci. Eng. B, Vol. 102, pp. 43–48, 2003.

[74]LeVeque, R., and Li, Z., The immersed interface method for elliptic equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal., Vol. 31, pp. 1019–1044, 1994.

[75]LeVeque, R. J., Numerical Methods for Conservation Laws, Birkhauser¨ Verlag, Basel, 1990.

[76]Li, Z. L., An overview of the immersed interface method and its applications, Taiwanese J. Math., Vol. 7, No. 1, pp. 1–49, 2003.

[77]Li, Z. L. and Cai, W., A level set-boundary element method for simulation of dynamic powder consolidation of metals, Numer. Anal. Appl., Vol. 1988, pp. 527–534, 2001.

[78]Li, Z. L., Zhao, H. K., and Gao, H. J., A numerical study of electromigration voiding by evolving level set functions on a fixed Cartesian grid, J. Comput. Phys., Vol. 152, No. 1, pp. 281–304, 1999.

[79]Liu, F., Luo, Y. P., and Hu, D. C., Adaptive level set image segmentation using the Mumford and Shah functional, Opt. Eng., Vol. 41, pp. 3002–3003, 2002.

[80]Melenk, J. M., and Babuska,ˇ I., The partition of unity finite element method: Basic theory and applications, Comput. Meth. Appl. Mech. Eng., Vol. 139, pp. 289–314, 1996.

[81]Moes,¨ N., Dolbow, J., and Belytschko, T., A finite element method for crack growth without remeshing, Int. J. Numer. Methods Eng., Vol. 46, No. 1, pp. 131–150, 1999.

[82]Moes,¨ N., Gravouil, A., and Belytschko, T., Non-planar 3d crack growth by the extended finite element and the level sets. Part I: Mechanical model, Int. J. Numer. Methods Eng., Vol. 53, No. 11, pp. 2549–2568, 2002.

[83]Nishimura, I., Garrell, R. L., Hedrick, M., Iida, K., Osher, S., and Wu, B., Precursor tissue analogs as a tissue-engineering strategy, Tissue Eng., Vol. 9, pp. S77–S89, 2003.

[84]Osher S. and Fedkiw, R., Level Set Methods and Dynamic Implicit Surfaces, Springer Verlag, Heidelberg, 2002.

[85]Osher S. and Sethian, J. A., Fronts propagating with curvaturedependent speed: Algorithms based on Hamilton–Jacobi formulations, J. Comput. Phys., Vol. 79, No. 1, pp. 12–49, 1988.

[86]Osher, S. J. and Santosa, F., Level set methods for optimization problems involving geometry and constraints. i: Frequencies of a

two-density inhomogeneous drum, J. Comput. Phys., Vol. 171, pp.

272–288, 2001.

[87]Paragios, N., A variational approach for the segmentation of the left ventricle in cardiac image analysis, Int. J. Comput. Vision, Vol. 50,

pp.345–362, 2002.

[88]Peskin, C. S., Numerical analysis of blood flow in the heart, J. Comput. Phys., Vol. 25, pp. 220–252, 1977.

[89]Petersen, M., Zangwill, A., and Ratsch, C., Homoepitaxial Ostwald ripening, Surf. Sci., Vol. 536, pp. 55–60, 2003.

[90]Phan, A. V., Kaplan, T., Gray, L. J., Adalsteinsson, D., Sethian, J. A., Barvosa-Carter, W., and Aziz, M. J., Modelling a growth instability in a stressed solid, Modelling Simul. Mater. Sci. Eng., Vol. 9, pp. 309–325, 2001.

[91]Picaud, V., Hiebel, P., and Kauffmann, J. M., Superconducting coils quench simulation, the Wilson’s method revisited, IEEE Trans. Magnetics, Vol. 38, pp. 1253–1256, 2002.

[92]Pillapakkam, S. B. and Singh, P., A level-set method for computing solutions to viscoelastic two-phase flow, J. Comput. Phys., Vol. 174,

pp.552–578, 2001.

[93]Preusser, T., and Rumpf, M., A level set method for anisotropic geometric diffusion in 3d image processing, SIAM J. Appl. Math., Vol. 62, pp. 1772–1793, 2002.

[94]Quecedo, M., and Pastor, M., Application of the level set method to the finite element solution of two-phase flows, Int. J. Numer. Methods Eng., Vol. 50, pp. 645–663, 2001.

[95]Ratsch, C., Gyure, M. F., Caflisch, R. E., Gibou, F., Petersen, M., Kang, M., Garcia, J., and Vvedensky, D. D., Level-set method for island dynamics in epitaxial growth, Phys. Rev. B, Vol. 65, pp. 195403–195415, 2002.

[96]Ratsch, C., Kang, M., and Caflisch, R. E., Atomic size effects in continuum modeling, Phys. Rev. E, Vol. 6402, pp. 020601–020604, 2001.

[97]Richards, D. F., Bloomfield, M. O., Sen, S., and Cale, T. S., Extension velocities for level set based surface profile evolution, J. Vac. Sci. Technol. A, Vol. 19, pp. 1630–1635, 2001.

[98]Schmidt, H. and Klein, R., A generalized level-set/in-cell-reconstruction approach for accelerating turbulent premixed flames, Combust. Theory Modelling, Vol. 7, pp. 243–267, 2003.

[99]Schupp, S., Elmoataz, A., Fadili, M. J., and Bloyet, D., Fast statistical level sets image segmentation for biomedical applications, ScaleSpace Morphology Computer Vision, Proc., Vol. 2106, pp. 380–388, 2001.

[100]Sethian, J. A., Personal communication, 2002,

[101]Sethian, J. A. and Vladimirsky, A., Ordered upwind methods for static Hamilton–Jacobi equations, Proc. Nat. Acad. Sci., Vol. 98, No. 20,

pp.11069–11074, 2001.

[102]Sethian, J.A., Curvature and the evolution of fronts, Commun. Math. Phy., Vol. 101, pp. 487–499, 1985.

[103]Sethian, J. A., Numerical algorithms for propagating interfaces: Hamilton–Jacobi equations and conservation laws, J. Differ. Geom., Vol. 31, pp. 131–161, 1990.

[104]Sethian, J.A., Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision and Material Science, Cambridge University Press, Cambridge, 1996.

[105]Sethian, J.A., A marching level set method for monotonically advancing fronts, Proc. Nat. Acad. Sci., Vol., 93, No. 4, pp. 1591–1595, 1996.

[106]Sethian, J.A., Fast marching methods, SIAM Rev., Vol. 41, No. 2,

pp.199–235, 1999.

[107]Smereka, P., Spiral crystal growth, Physica D, Vol. 138, pp. 282–301, 2000.

[108]Smith, K. A., Solis, F. J., and Chopp, D. L., A projection method for motion of triple junctions by level sets, Interfaces Free Bounda., Vol. 4, No. 3, pp. 263–276, 2002.

[109]Son, G., Efficient implementation of a coupled level-set and volume- of-fluid method for three-dimensional incompressible two-phase flows, Numer. Heat Transfer, Vol. 43, pp. 549–565, 2003.

[110]Son, G. and Hur, N., A coupled level set and volume-of-fluid method for the buoyancy-driven motion of fluid particles, Numer. Heat Transfer B, Vol., 42, pp. 523–542, 2002.

[111]Son, G., Ramanujapu, N., and Dhir, V. K., Numerical simulation of bubble merger process on a single nucleation site during pool nucleate boiling, Trans. ASME, J. Heat Transfer, Vol. 124 pp. 51–62, 2002.

[112]Son, G. H., A numerical method for bubble motion with phase change, Numer. Heat Transfer, B, Vol. 39, pp. 509–523, 2001.

[113]Son, G. H., Numerical study on a sliding bubble during nucleate boiling, Ksme Int. J., Vol. 15, pp. 931–940, 2001.

[114]Spira, A., Kimmel, R., and Sochen, N., Efficient Beltrami flow using a short time kernel, Scale Space Methods Comput. Vision, Proc., Vol. 2695, pp. 511–522, 2003.

[115]Stolarska, M., and Chopp, D. L., Modeling spiral cracking due to thermal cycling in integrated circuits, Int. J. of Eng. Sci., Vol. 41, No. 20, pp. 2381–2410, 2003.

[116]Stolarska, M., and Chopp, D. L., Modeling thermal fatigue cracking in integrated circuits by level sets and the extended finite element method, Int. J. Eng. Sci., Vol. 41, pp. 2381–2410, 2003.

[117]Stolarska, M., Chopp, D. L., Moes¨ N., and Belytschko, T., Modelling crack growth by level sets in the extended finite element method, Int. J. Numer. Methods Eng., Vol. 51, No. 8, pp. 943–960, 2001.

[118]Sukumar, N., Chopp, D. L., Moes¨ N., and Belytschko, T., Modeling holes and inclusions by level sets in the extended finite element method, Comput. Methods Appl. Mech. and Eng., Vol. 190, No. 46–47, pp. 6183–6200, 2001.

[119]Sukumar, N., Chopp, D. L., Moes, N., and Belytschko, T., Modeling holes and inclusions by level sets in the extended finite-element