Strongly normal sets of contractible tiles in N dimensions

Pattern Recognition

Volumn 40, Issue 2, 2007, Pages 530-543

  Kong, T Yung ^a   Saha, Punam Kumar ^b   Rosenfeld, Azriel ^c  

^a CITY UNIVERSITY OF NEW YORK   (United States)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

^c UNIVERSITY OF MARYLAND   (United States)

Author keywords

Attachment; Contractible; Helly; n Dimensional; Nerve; Shared subset; Simple; Strongly normal

Indexed keywords

NUMERICAL METHODS; PATTERN RECOGNITION;

ATTACHMENT; CONTRACTIBLE; HELLY; N-DIMENSIONAL; NERVES; SHARED SUBSETS; STRONGLY NORMAL;

SET THEORY;

EID: 33750330520     PISSN: 00313203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.patcog.2005.11.013     Document Type: Article

References (68)

1. Kong T.Y., and Rosenfeld A. Digital topology: Introduction and survey. Comput. Vision Graphics Image Process. 48 (1989) 357-393
2. T.Y. Kong, A. Rosenfeld (Eds.), Topological Algorithms for Digital Image Processing, Elsevier/North-Holland, Amsterdam, 1996.
3. Klette R., and Rosenfeld A. Digital Geometry: Geometric Methods for Digital Picture Analysis (2004), Morgan Kaufmann, Amsterdam
4. Pavlidis T. Discrete geometry and Azriel Rosenfeld. Pattern Recognition Lett. 26 (2005) 235-238
5. Rosenfeld A. Digital geometry: Introduction and bibliography. In: Klette R., Rosenfeld A., and Sloboda F. (Eds). Advances in Digital and Computational Geometry (1998), Springer, Singapore 1-54
6. Abrams L., Fishkind D.E., and Priebe C.E. A proof of the spherical homeomorphism conjecture for surfaces. IEEE Trans. Med. Imaging 21 (2002) 1564-1566
7. Abrams L., Fishkind D.E., and Priebe C.E. The generalized spherical homeomorphism theorem for digital images. IEEE Trans. Med. Imaging 23 (2004) 655-657
8. Nyström I., and Smedby O. Skeletonization of volumetric vascular images-distance information utilized for visualization. J. Combinatorial Optim. 5 (2001) 27-41
9. Saha P.K., Gomberg B.R., and Wehrli F.W. Three-dimensional digital topological characterization of cancellous bone architecture. Int. J. Imaging Syst. Technol. 11 (2000) 81-90
10. Shattuck D.W., and Leahy R.M. Automated graph-based analysis and correction of cortical volume topology. IEEE Trans. Med. Imaging 18 (1999) 1167-1177
11. Xu C., Pham D.L., Rettmann M.E., Yu D.N., and Prince J.L. Reconstruction of the human cerebral cortex from magnetic resonance images. IEEE Trans. Med. Imaging 18 (1999) 467-480
12. Herman G.T. Geometry of Digital Spaces (1998), Birkhäuser, Boston
13. Ayala R., Domínguez E., Francés A.R., and Quintero A. Weak lighting functions and strong 26-surfaces. Theor. Comput. Sci. 283 (2002) 29-66
14. Ayala R., Domínguez E., Francés A.R., and Quintero A. Homotopy in digital spaces. Discrete Appl. Math. 125 (2003) 3-24
15. Ayala R., Domínguez E., Francés A.R., and Quintero A. Digital homotopy with obstacles. Discrete Appl. Math. 139 (2004) 5-30
16. Chen L. Discrete surfaces and manifolds: a theory of digital-discrete geometry and topology (2004), Scientific & Practical Computing, Rockville, MD
17. Evako A.V., Kopperman R., and Mukhin Y.V. Dimensional properties of graphs and digital spaces. J. Math. Imaging Vision 6 (1996) 109-119
18. Fourey S., Kong T.Y., and Herman G.T. Generic axiomatized digital surface-structures. Discrete Appl. Math. 139 (2004) 65-93
19. Fourey S., and Malgouyres R. Intersection number and topology preservation within digital surfaces. Theor. Comput. Sci. 283 (2002) 109-150
20. Khalimsky E.D., Kopperman R.D., and Meyer P.R. Computer graphics and connected topologies on finite ordered sets. Topology Appl. 36 (1990) 1-17
21. Kopperman R.D., Meyer P.R., and Wilson R.G. A Jordan surface theorem for three-dimensional digital spaces. Discrete Comput. Geometry 6 (1991) 155-161
22. Kovalevsky V.A. Finite topology as applied to image analysis. Comput. Vision Graphics Image Process. 46 (1989) 141-161
23. Malgouyres R., and Lenoir A. Topology preservation within digital surfaces. Graphical Models 62 (2000) 71-84
24. n. Int. J. Pattern Recognition Artif. Intell. 5 (1991) 797-808
25. n (1993), Springer, Berlin
26. Sklansky J., and Kibler D.F. A theory of nonuniformly digitized binary pictures. IEEE Trans. Syst. Man Cybernetics 6 (1976) 637-647
27. Cook R.D., Malkus D.S., Plesha M.E., and Witt R.J. Concepts and Applications of Finite Element Analysis. fourth ed. (2002), Wiley, New York
28. Frey P.J., and George P.L. Mesh Generation: Application to Finite Elements (2000), Hermes Science Publications, Paris
29. Li T.S., Armstrong C.G., and McKeag R.M. Quad mesh generation for k-sided faces and hex mesh generation for trivalent polyhedra. Finite Elements Anal. Design 26 (1997) 279-301
30. Giertsen C. Volume visualization of sparse irregular meshes. IEEE Comput. Graphics Appl. 12 2 (1992) 40-48
31. Saha P.K. Tensor scale: A local morphometric parameter with applications to computer vision and image processing. Comput. Vision Image Understanding 99 (2005) 384-413
32. A. Madabhushi, J.K. Udupa, A. Souza, Generalized scale: Theory, algorithms, and application to image inhomogeneity correction, Comput. Vision and Image Understanding 101 (2006) 100-121.
33. Saha P.K., Majumder D.D., and Rosenfeld A. Local topological parameters in a tetrahedral representation. Graphical Models Image Process. 60 (1998) 423-436
34. Saha P.K., and Rosenfeld A. Strongly normal sets of convex polygons or polyhedra. Pattern Recognition Lett. 19 (1998) 1119-1124
35. Brass P. On strongly normal tessellations. Pattern Recognition Lett. 20 (1999) 957-960
36. 3. Pattern Recognition 33 (2000) 105-118
37. Saha P.K., and Rosenfeld A. The digital topology of sets of convex voxels. Graphical Models 62 (2000) 343-352
38. Saha P.K., and Rosenfeld A. Local and global topology preservation in locally finite sets of tiles. Inf. Sci. 137 (2001) 303-311
39. Borgefors G. Distance transformations in arbitrary dimensions. Computer Vision Graphics Image Process. 27 (1984) 321-345
40. Eggers H. Parallel Euclidean distance transformations in imaging. Pattern Recognition Lett. 17 (1996) 751-757
41. Herman G.T. Discrete multidimensional Jordan surfaces. CVGIP: Graphical Models Image Process. 54 (1992) 507-515
42. Jonker P.P. Morphological operations on 3D and 4D images: from shape primitive detection to skeletonization. In: Borgefors G., Nyström I., and Sanniti di Baja G. (Eds). Discrete Geometry for Computer Imagery: Nineth International Conference (DGCI 2000, Uppsala, Sweden, December 2000), Proceedings (2000), Springer, Berlin 371-391
43. Jonker P.P. Skeletons in N dimensions using shape primitives. Pattern Recognition Lett. 23 (2002) 677-686
44. n. Theor. Comput. Sci. 283 (2002) 3-28
45. n - 1)-disconnected sets. Theor. Comput. Sci. 305 (2003) 221-235
46. Gau C.J., and Kong T.Y. Minimal nonsimple sets in 4D binary images. Graphical Models 65 (2003) 112-130
47. Kong T.Y., and Gau C.J. Minimal non-simple sets in 4-dimensional binary images with (8, 80)-adjacency. In: Klette R., and Žunić J. (Eds). Combinatorial Image Analysis: 10th International Workshop (IWCIA 2004, Auckland, New Zealand, December 2004), Proceedings (2004), Springer, Berlin 318-333
48. J.-O. Lachaud, Coding cells of digital spaces: A framework to write generic digital topology algorithms, in: A. Del Lungo, V. Di Gesù, A. Kuba (Eds.), Electronic Notes in Discrete Mathematics, vol. 12 (Proceedings of IWCIA 2003), Palermo, Italy, March 2003, Elsevier, 2003.
49. Ragnemalm I. The Euclidean distance transform in arbitrary dimensions. Pattern Recognition Lett. 14 (1993) 883-888
50. Saito T., and Toriwaki J.I. New algorithms for Euclidean distance transformation of an n-dimensional digitized picture with applications. Pattern Recognition 27 (1994) 1551-1565
51. Samet H., and Tamminen M. Efficient component labeling of images of arbitrary dimension represented by linear bintrees. IEEE Trans. Pattern Anal. Mach. Intell. 10 (1988) 579-586
52. Udupa J.K. Multidimensional digital boundaries. CVGIP: Graphical Models Image Process. 56 (1994) 311-323
53. Klein G.J., and Huesman R. Four-dimensional processing of deformable cardiac PET data. Med. Image Anal. 6 (2002) 29-46
54. A.A. Amini, J.L. Prince (Eds.), Measurement of Cardiac Deformations from MRI: Physical and Mathematical Models, Kluwer, Dordrecht, 2001.
55. Osman N.S., McVeigh E.R., and Prince J.L. Imaging heart motion using harmonic phase MRI. IEEE Trans. Med. Imaging 19 (2000) 186-202
56. Gau C.J., and Kong T.Y. Minimal nonsimple sets of voxels in binary images on a face-centered cubic grid. Int. J. Pattern Recognition Artif. Intell. 13 (1999) 485-502
57. Kong T.Y. On topology preservation in 2D and 3D thinning. Int. J. Pattern Recognition Artif. Intell. 9 (1995) 813-844
58. P.K. Saha, T.Y. Kong, A. Rosenfeld, Strongly normal sets of tiles in N dimensions, in: S. Fourey, G.T. Herman, T.Y. Kong (Eds.), Electronic Notes in Theoretical Computer Science, vol. 46 (Proceedings of IWCIA 2001, Philadelphia, USA, August 2001), Elsevier, 2001.
59. Kulpa W. Intersection properties of Helly families. Topology Appl. 116 (2001) 227-233
60. Armstrong M.A. Basic Topology (1983), Springer, New York
61. Maunder C.R.F. Algebraic Topology (1996), Dover, Mineola, NY
62. Webster R. Convexity (1994), Oxford University Press, Oxford
63. Björner A. Topological methods. In: Graham R.L., Grötschel M., and Lovász L. (Eds). Handbook of Combinatorics vol. II (1995), MIT Press, Cambridge, MA 1819-1872
64. Saha P.K., and Chaudhuri B.B. Detection of 3D simple points for topology preserving transformation with applications to thinning. IEEE Trans. Pattern Anal. Mach. Intell. 16 (1994) 1028-1032
65. Spanier E.H. Algebraic Topology (1989), Springer, New York
66. Hatcher A. Algebraic Topology (2002), Cambridge University Press, Cambridge
67. Björner A., Lovász L., Vrećica S.T., and Živaljević R.T. Chessboard complexes and matching complexes. J. London Math. Soc. (Series II) 49 (1994) 25-39
68. Kong T.Y., and Roscoe A.W. Characterizations of simply-connected finite polyhedra in 3-space. Bull. London Math. Soc. 17 (1985) 575-578