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Volumn 35, Issue 1, 2009, Pages 23-35

On parallel thinning algorithms: Minimal non-simple sets, P-simple points and critical kernels

Author keywords

4D space; Collapse; Critical kernel; Cubical complex; Minimal non simple set; P simple point; Parallel thinning; Simple point; Topology preservation

Indexed keywords

4D SPACE; COLLAPSE; CRITICAL KERNEL; CUBICAL COMPLEX; MINIMAL NON-SIMPLE SET; P-SIMPLE POINT; PARALLEL THINNING; SIMPLE POINT; TOPOLOGY PRESERVATION;

EID: 67651046230     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10851-009-0152-3     Document Type: Article
Times cited : (26)

References (34)
  • 1
    • 0001206843 scopus 로고
    • Diskrete Räume
    • P.S. Alexandroff 1937 Diskrete Räume Math. Sb. 2 3 501 518
    • (1937) Math. Sb. , vol.2 , Issue.3 , pp. 501-518
    • Alexandroff, P.S.1
  • 3
    • 0039874700 scopus 로고
    • Sufficient conditions for 3D parallel thinning algorithms
    • Bertrand, G.: Sufficient conditions for 3D parallel thinning algorithms. In: SPIE Vision Geometry IV, vol. 2573, pp. 52-60 (1995)
    • (1995) SPIE Vision Geometry IV , vol.2573 , pp. 52-60
    • Bertrand, G.1
  • 6
    • 43449104235 scopus 로고    scopus 로고
    • Two-dimensional parallel thinning algorithms based on critical kernels
    • G. Bertrand M. Couprie 2008 Two-dimensional parallel thinning algorithms based on critical kernels J. Math. Imaging Vis. 31 1 35 56
    • (2008) J. Math. Imaging Vis. , vol.31 , Issue.1 , pp. 35-56
    • Bertrand, G.1    Couprie, M.2
  • 7
    • 0003193239 scopus 로고
    • Some aspects of the topology of 3-manifolds related to the Poincaré conjecture
    • R.H. Bing 1964 Some aspects of the topology of 3-manifolds related to the Poincaré conjecture Lect. Mod. Math. II 93 128
    • (1964) Lect. Mod. Math. , vol.2 , pp. 93-128
    • Bing, R.H.1
  • 8
    • 84867924920 scopus 로고    scopus 로고
    • Strong thinning and polyhedric approximation of the surface of a voxel object
    • J. Burguet R. Malgouyres 2003 Strong thinning and polyhedric approximation of the surface of a voxel object Discrete Appl. Math. 125 93 114
    • (2003) Discrete Appl. Math. , vol.125 , pp. 93-114
    • Burguet, J.1    Malgouyres, R.2
  • 11
    • 62249139463 scopus 로고    scopus 로고
    • New characterizations of simple points in 2D, 3D and 4D discrete spaces
    • M. Couprie G. Bertrand 2009 New characterizations of simple points in 2D, 3D and 4D discrete spaces IEEE Trans. Pattern Anal. Mach. Intell. 31 4 637 648
    • (2009) IEEE Trans. Pattern Anal. Mach. Intell. , vol.31 , Issue.4 , pp. 637-648
    • Couprie, M.1    Bertrand, G.2
  • 12
    • 0037810951 scopus 로고    scopus 로고
    • Minimal non-simple sets in 4D binary images
    • DOI 10.1016/S1524-0703(03)00010-9
    • C.-J. Gau T.Y. Kong 2003 Minimal non-simple sets in 4D binary images Graph. Models 65 112 130 (Pubitemid 36863823)
    • (2003) Graphical Models , vol.65 , Issue.1-3 , pp. 112-130
    • Gau, C.J.1    Kong, T.Y.2
  • 14
    • 38249010670 scopus 로고
    • Tests for connectivity preservation for parallel reduction operators
    • R.W. Hall 1992 Tests for connectivity preservation for parallel reduction operators Topol. Appl. 46 3 199 217
    • (1992) Topol. Appl. , vol.46 , Issue.3 , pp. 199-217
    • Hall, R.W.1
  • 16
    • 38249019149 scopus 로고
    • Computer graphics and connected topologies on finite ordered sets
    • E. Khalimsky R. Kopperman P.R. Meyer 1990 Computer graphics and connected topologies on finite ordered sets Topol. Appl. 36 1 17
    • (1990) Topol. Appl. , vol.36 , pp. 1-17
    • Khalimsky, E.1    Kopperman, R.2    Meyer, P.R.3
  • 17
  • 18
    • 84957710644 scopus 로고    scopus 로고
    • Topology-preserving deletion of 1's from 2-, 3- and 4-dimensional binary images
    • Discrete Geometry for Computer Imagery, Springer Berlin
    • Kong, T.Y.: Topology-preserving deletion of 1's from 2-, 3- and 4-dimensional binary images. In: Discrete Geometry for Computer Imagery. Lecture Notes in Computer Science, vol. 1347, pp. 3-18. Springer, Berlin (1997)
    • (1997) Lecture Notes in Computer Science , vol.1347 , pp. 3-18
    • Kong, T.Y.1
  • 20
    • 51549103885 scopus 로고    scopus 로고
    • Minimal non-deletable and minimal non-codeletable sets in binary images
    • T.Y. Kong 2008 Minimal non-deletable and minimal non-codeletable sets in binary images Theor. Comput. Sci. 406 1-2 97 118
    • (2008) Theor. Comput. Sci. , vol.406 , Issue.12 , pp. 97-118
    • Kong, T.Y.1
  • 23
    • 85075951361 scopus 로고
    • On the problem of determining whether a parallel reduction operator for N-dimensional binary images always preserves topology
    • Kong, T.Y.: On the problem of determining whether a parallel reduction operator for N-dimensional binary images always preserves topology. In: Proc. SPIE Vision Geometry II, vol. 2060, pp. 69-77 (1993)
    • (1993) Proc. SPIE Vision Geometry II , vol.2060 , pp. 69-77
    • Kong, T.Y.1
  • 24
    • 0343555175 scopus 로고
    • Problems in the topology of binary digital images
    • Elsevier Amsterdam
    • Kong, T.Y., Litherland, R., Rosenfeld, A.: Problems in the topology of binary digital images. In: Open Problems in Topology, pp. 376-385. Elsevier, Amsterdam (1990)
    • (1990) Open Problems in Topology , pp. 376-385
    • Kong, T.Y.1    Litherland, R.2    Rosenfeld, A.3
  • 26
    • 1842636145 scopus 로고    scopus 로고
    • A 3D 12-subiteration thinning algorithm based on P-simple points
    • C. Lohou G. Bertrand 2004 A 3D 12-subiteration thinning algorithm based on P-simple points Discrete Appl. Math. 139 171 195
    • (2004) Discrete Appl. Math. , vol.139 , pp. 171-195
    • Lohou, C.1    Bertrand, G.2
  • 27
    • 25144522750 scopus 로고    scopus 로고
    • A 3D 6-subiteration curve thinning algorithm based on P-simple points
    • DOI 10.1016/j.dam.2005.02.030, PII S0166218X05001319, IWCIA 2003-Ninth International Workshop on Combinatorial Image Analysis
    • C. Lohou G. Bertrand 2005 A 3D 6-subiteration curve thinning algorithm based on P-simple points Discrete Appl. Math. 151 198 228 (Pubitemid 41334766)
    • (2005) Discrete Applied Mathematics , vol.151 , Issue.1-3 , pp. 198-228
    • Lohou, C.1    Bertrand, G.2
  • 28
    • 0028425191 scopus 로고
    • On topology preservation in 3d thinning
    • C.M. Ma 1994 On topology preservation in 3d thinning Comput. Vis. Graph. Image Process. 59 3 328 339
    • (1994) Comput. Vis. Graph. Image Process. , vol.59 , Issue.3 , pp. 328-339
    • Ma, C.M.1
  • 29
    • 0036203023 scopus 로고    scopus 로고
    • n-dimensional skeletonization: A unified mathematical framework
    • DOI 10.1117/1.1426080, Reportnr 20024
    • A. Manzanera T.M. Bernard F. Prêteux B. Longuet 2002 N-dimensional skeletonization: a unified mathematical framework J. Electron. Imaging 11 1 25 37 (Pubitemid 34278370)
    • (2002) Journal of Electronic Imaging , vol.11 , Issue.1 , pp. 25-37
    • Manzanera, A.1    Bernard, T.M.2    Preteux, F.3    Longuet, B.4
  • 31
    • 0024072430 scopus 로고
    • Minimal test patterns for connectivity preservation in parallel thinning algorithms for binary digital images
    • C. Ronse 1988 Minimal test patterns for connectivity preservation in parallel thinning algorithms for binary digital images Discrete Appl. Math. 21 1 67 79
    • (1988) Discrete Appl. Math. , vol.21 , Issue.1 , pp. 67-79
    • Ronse, C.1
  • 32
    • 0016577724 scopus 로고
    • A characterization of parallel thinning algorithms
    • A. Rosenfeld 1975 A characterization of parallel thinning algorithms Inf. Control 29 286 291
    • (1975) Inf. Control , vol.29 , pp. 286-291
    • Rosenfeld, A.1
  • 33
    • 84963025705 scopus 로고
    • Simplicial spaces, nuclei and m-groups
    • J.H.C. Whitehead 1939 Simplicial spaces, nuclei and m-groups Proc. Lond. Math. Soc. 45 2 243 327
    • (1939) Proc. Lond. Math. Soc. , vol.45 , Issue.2 , pp. 243-327
    • Whitehead, J.H.C.1
  • 34
    • 0000745408 scopus 로고
    • On the dunce hat
    • E.C. Zeeman 1964 On the dunce hat Topology 2 341 358
    • (1964) Topology , vol.2 , pp. 341-358
    • Zeeman, E.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.