A computation of a crystalline flow starting from non-admissible polygon using expanding selfsimilar solutions

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2886, Issue , 2003, Pages 465-474

  Hontani, Hidekata ^a   Giga, Mi Ho ^b   Giga, Yoshikazu ^b   Deguchi, Koichiro ^c  

^a YAMAGATA UNIVERSITY   (Japan)

^b HOKKAIDO UNIVERSITY   (Japan)

^c TOHOKU UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; GEOMETRY; NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS;

CRYSTALLINE FLOW; CURVATURE FLOW; NORMAL DIRECTION; SELF-SIMILAR SOLUTION; SINGULAR ORDINARY DIFFERENTIAL EQUATION; SYSTEM OF ODES;

CRYSTALLINE MATERIALS;

EID: 0242460241     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-39966-7_44     Document Type: Article

References (18)

1. Koenderink, J. J.: The Structure of Images, Biological Cybernetics, 50 (1984) 363-370
2. Alvarez, L. and Guichard, F.: Axioms and Fundamental Equations of Image Processing, Arch. Rational Mech. Anal., 123 (1993) 199-257
3. Mokhtarian, F. and Mackworth, A.: A Theory of Multiscale, Curvature-Based Shape Representation for Planner Curves, IEEE Transactions on Pattern Analysis and Machine Intelligence, 14, No.8 (1992) 789-805
4. Rattarangsi, A. and Chin, R. T.: Scale-Based Detection of Corners of Planar Curves, IEEE Transactions on Pattern Analysis and Machine Intelligence, 14, No.4 (1992) 430-449
5. Kimia, B. B., and Tannenbaum, A. R. and Zucker S. W.: Shapes, Shocks, and Deformations I: The Components of Two-Dimensional Shape and the Reaction-Diffusion Space, International Journal of Computer Vision, 15 (1995) 189-224
6. Hontani, H. and Deguchi, K.: Multi-Scale Image Analysis for Detection of Characteristic Component Figure Shapes and Sizes, Proceedings of 14th International Conference on Pattern Recognition (1998) 1470-1472
7. Osher, S. and Sethian, J. A.: Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys. 79 (1988) 12-49
8. Evans, L. C. and Spruck, J.: Motion of level-sets by mean curvature, I, J. Differential Geometry, 33 (1991) 635-681
9. Chen, Y.-G., Giga, Y. and Goto, S.: Remarks on viscosity solutions for evolution equations, J. Differential Geometry, 33 (1991) 749-786
10. Angenent, S. B. and Gurtin, M. E.: Multiphase thermomechanics with interfacial structure 2. Evolution of an isothermal interface, Arch. Rational Mech. Anal., 108 (1989) 323-391
11. Taylor, J.: Constructions and conjectures in crystalline nondifferential geometry, Proceedings of the Conference on Differential Geometry, 52, Pitman, London (1991) 321-336
12. Giga, M. -H. and Giga, Y.: Crystalline and level-set flow - Convergence of a crystalline algorithm for a general anisotropic curvature flow in the plane, Free boundary problems: theory and applications I (ed. N. Kenmochi) Gakuto International Ser. Math. Sci. Appl., 13 (2000) 64-79
13. Giga, M.-H. and Giga, Y.: Generalized Motion by Nonlocal Curvature in the Plane, Arch. Rational Mech. Anal., 159 (2001) 295-333
14. Giga, M. -H., Giga, Y. and Hontani, H.: Selfsimilar solutions in motion of curves by crystalline energy, Minisymposium lecture of 5th International Congress on Industrial and Applied Mathematics, Sydney, (2003), July
15. Gurtin, M. E.: Thermomechanics of Evolving Phase Boundaries in the Plane, Oxford, Clarendon Press (1993)
16. Giga, Y.: A level set method for surface evolution equations, Sugaku 47 (1993) 321-340:
17. Eng. translation, Sugaku Exposition 10 (1995), 217-241
18. Giga, Y. and Goto, S.: Motion of hypersurfaces and geometric equations, J. Mathematical Society Japan, 44 (1992) 99-111