Conformal self-organizing map for a genus-zero manifold

Visual Computer

Volumn 21, Issue 5, 2005, Pages 340-353

  Liou, Cheng Yuan ^a   Kuo, Yen Ting ^a  

^a NATIONAL TAIWAN UNIVERSITY   (Taiwan)

Author keywords

Conformal mapping; Conformality; Deformation measure; Self organizing map; Surface reconstruction

Indexed keywords

ALGORITHMS; CODES (SYMBOLS); COMPUTER SIMULATION; CONTEXT FREE GRAMMARS; HIERARCHICAL SYSTEMS; LASERS; OPTIMIZATION; PROBLEM SOLVING; REAL TIME SYSTEMS; SCANNING;

CONFORMALITY; DEFORMATION MEASURES; SELF-ORGANIZING MAP; SURFACE RECONSTRUCTION;

CONFORMAL MAPPING;

EID: 21544462894     PISSN: 01782789     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00371-005-0290-6     Document Type: Review

References (29)

1. Amenta N, Bern M, Kamvysselis M (1999) A new Voronoi-bascd surface reconstruction algorithm. In: Proceedings of SIGGRAPH, pp 415-421
2. Barhak J, Fischer A (2001) Parameterization and reconstruction from 3D scattered points based on neural network and PDE techniques. IEEE Trans Visual Comput Graph 7(1):1-16
3. Barrett O (1996) Elementary differential geometry. Academic Press, New York
4. Bauer HU, Pawelzik KR (1992) Quantifying the neighborhood preservation of self-organizing feature maps. IEEE Trans Neural Netw 3:570-578
5. Chen SW, Stockman GC, Chang KE (1996) SO dynamic deformation for building of 3-D models. IEEE Trans Neural Netw 7(2):374-387
6. Choi DI, Park SH (1994) Self-creating and organizing neural networks. IEEE Trans Neural Netw 5:561-575
7. Churchill RV, Brown JW (1984) Complex variables and applications, 4th edn. McGraw-Hill, New York
8. Curless B, Levoy M (1996) A volumetric method for building complex models from range images. In: Proceedings of SIGGRAPH, pp 303-312
9. Driscoll TA (1996) A MATLAB toolbox for Schwarz-Christoffel mapping. ACM Trans Math Soft 22:168-186
10. Edelsbrunner H, Mucke DP (1994) Three-dimensional alpha shapes. ACM Trans Graph 13:43-72
11. Gotsman C, Gu X, Sheffer A (2003) Fundamentals of spherical parameterization for 3D meshes. ACM Trans Graphics 22:358-363
12. Gu X, Yau ST (2002) Computing conformal structures of surfaces. Commun Inf Syst 2(2): 121-146
13. Gu X, Wang Y, Chan TF, Thompson PM, Yau ST (2004) Genus zero surface conformal mapping and its application to brain surface mapping. IEEE Trans Med Imag 23(7): 1-8
14. Hoppe H, DeRose T, Duchamp T, McDonald J, Stuetzle W (1992) Surface reconstruction from unorganized points. In: Proceedings of SIGGRAPH, pp 71-78
15. Hoppe H (2002) Irregular to completely regular meshing in computer graphics. Invited Talk, 11th International Meshing Roundtable, Sandia National Laboratories, September 15-18, p 141
16. Ivrissimtzis IP, Jeong WK, Seidel HP (2003) Using growing cell structures for surface reconstruction. In: Proceedings of the International Conference on Shape Modeling and Applications, Seoul, Korea, pp 78-88
17. Kenner H (1976) Geodesic math and how to use it. University of California Press, Berkeley
18. Kohonen T (1982) Self-organized formation of topologically correct feature maps. Biol Cybern 43:59-69
19. Levy B, Petitjean S, Ray N, Maillot J (2002) Least squares conformal maps for automatic texture atlas generation. In: Computer Graphics, Proceedings of SIGGRAPH 21(3):362-371
20. Liou CY, Tai WP (1999) Conformal self-organization for continuity on a feature map. Neural Netw 12:893-905
21. Liou CY, Tai WP (2000) Conformality in the self-organization network. Artif Intell 116:265-286
22. Ohmori K, Kunii TL (2001) Shape modeling using homotopy. In: Proceedings of the International Conference on Shape Modeling and Applications. (SMI), 7-11 May, Genoa, Italy, pp 126-133
23. Ritter H (1999) Self-organizing maps in non-Euclidean spaces. In: Oja E, Kaski S (eds) Kohonen maps. Elsevier, Amsterdam, pp 97-110
24. Surazhsky V, Gotsman C (2003) Explicit surface remeshing. In: Proceedings of the Eurographics Symposium on Geometry Processing, pp 17-2
25. Tai WP (1997) Conformal self-organization. Dissertation, National Taiwan University
26. Tai WP, Liou CY (2000) Image representation by self-organizing conformal network. Vis Comput 16(2):91-105
27. Varady T, Martin RR, Cox J (1997) Reverse engineering of geometric models-an introduction. Comput Aided Des 29(4):255-268
28. Yu Y (1999) Surface reconstruction from unorganized points using self-organizing neural networks. In: Proceedings of IEEE Visualization, San Francisco, California, pp 61-64
29. Cyberware designs, manufactures, and sells standard and custom 3D scanning systems and software. "http://www.cyberware.com/samples/index. html"