메뉴 건너뛰기




Volumn 30, Issue 5, 2008, Pages 823-836

Theoretical foundations of spatially-variant mathematical morphology part I: Binary images

Author keywords

Adaptive morphology; Affine morphology; Basis representation; Circular morphology; Hit or miss transform; Kernel representation; Mathematical morphology; Median filter; Spatially variant morphology; Upper semicontinuity

Indexed keywords

IMAGE PROCESSING; MATHEMATICAL MORPHOLOGY; MATHEMATICAL TRANSFORMATIONS; TOPOLOGY;

EID: 41749110019     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.2007.70754     Document Type: Article
Times cited : (87)

References (61)
  • 1
    • 0037461024 scopus 로고    scopus 로고
    • Automatic Analysis of DNA Microarray Images Using Mathematical Morphology
    • J. Angulo and J. Serra, "Automatic Analysis of DNA Microarray Images Using Mathematical Morphology," Bioinformatics, vol. 19, no. 5, pp. 553-562, 2003.
    • (2003) Bioinformatics , vol.19 , Issue.5 , pp. 553-562
    • Angulo, J.1    Serra, J.2
  • 2
    • 0026392293 scopus 로고
    • Minimal Representation for Translation-Invariant Set Mappings by Mathematical Morphology
    • Dec
    • G.J.F. Banon and J. Barrera, "Minimal Representation for Translation-Invariant Set Mappings by Mathematical Morphology," SIAM J. Applied Math., vol. 51, pp. 1782-1798, Dec. 1991.
    • (1991) SIAM J. Applied Math , vol.51 , pp. 1782-1798
    • Banon, G.J.F.1    Barrera, J.2
  • 3
    • 0027543317 scopus 로고
    • Decomposition of Mappings between Complete Lattices by Mathematical Morphology - Part I: General Lattices
    • Feb
    • G.J.F. Banon and J. Barrera, "Decomposition of Mappings between Complete Lattices by Mathematical Morphology - Part I: General Lattices," Signal Processing, vol. 30, no. 3, pp. 299-327, Feb. 1993.
    • (1993) Signal Processing , vol.30 , Issue.3 , pp. 299-327
    • Banon, G.J.F.1    Barrera, J.2
  • 7
    • 33750349048 scopus 로고    scopus 로고
    • Spatially-Variant Morphological Restoration and Skeleton Representation
    • Nov
    • N. Bouaynaya, M. Charif-Chefchaouni, and D. Schonfeld, "Spatially-Variant Morphological Restoration and Skeleton Representation," IEEE Trans. Image Processing, vol. 15, no. 11, pp. 3579-3591, Nov. 2006.
    • (2006) IEEE Trans. Image Processing , vol.15 , Issue.11 , pp. 3579-3591
    • Bouaynaya, N.1    Charif-Chefchaouni, M.2    Schonfeld, D.3
  • 8
    • 33645995232 scopus 로고
    • Morphological Representation of Non-Linear Operators: Theory and Applications,
    • PhD dissertation, Univ. of Illinois at Chicago
    • M. Charif-Chefchaouni, "Morphological Representation of Non-Linear Operators: Theory and Applications," PhD dissertation, Univ. of Illinois at Chicago, 1993.
    • (1993)
    • Charif-Chefchaouni, M.1
  • 10
    • 0030129411 scopus 로고    scopus 로고
    • Statistical Analysis of Space-Varying Morphological Openings with Flat Structuring Elements
    • Apr
    • C.-S. Chen, J.-L. Wu, and Y.-P. Hung, "Statistical Analysis of Space-Varying Morphological Openings with Flat Structuring Elements," IEEE Trans. Signal Processing, vol. 44, no. 4, pp. 1010-1014, Apr. 1996.
    • (1996) IEEE Trans. Signal Processing , vol.44 , Issue.4 , pp. 1010-1014
    • Chen, C.-S.1    Wu, J.-L.2    Hung, Y.-P.3
  • 11
    • 0033114998 scopus 로고    scopus 로고
    • Theoretical Aspects of Vertically Invariant Gray-Level Morphological Operators and Their Application on Adaptive Signal and Image Filtering
    • Apr
    • C.-S. Chen, J.-L. Wu, and Y.-P. Hung, "Theoretical Aspects of Vertically Invariant Gray-Level Morphological Operators and Their Application on Adaptive Signal and Image Filtering," IEEE Trans. Signal Processing, vol. 47, no. 4, pp. 1049-1060, Apr. 1999.
    • (1999) IEEE Trans. Signal Processing , vol.47 , Issue.4 , pp. 1049-1060
    • Chen, C.-S.1    Wu, J.-L.2    Hung, Y.-P.3
  • 12
    • 33747779552 scopus 로고
    • An Adaptive Morphological Filter for Image Processing
    • Oct
    • F. Cheng and A.N. Venetsanopoulos, "An Adaptive Morphological Filter for Image Processing," IEEE Trans. Image Processing, vol. 1, no. 4, pp. 533-539, Oct. 1992.
    • (1992) IEEE Trans. Image Processing , vol.1 , Issue.4 , pp. 533-539
    • Cheng, F.1    Venetsanopoulos, A.N.2
  • 13
    • 0029404248 scopus 로고
    • Theoretical Aspects of Morphological Filters by Reconstruction
    • Nov
    • J. Crespo, J. Serra, and R.W. Schafer, "Theoretical Aspects of Morphological Filters by Reconstruction," Signal Processing, vol. 47, no. 2, pp. 201-225, Nov. 1995.
    • (1995) Signal Processing , vol.47 , Issue.2 , pp. 201-225
    • Crespo, J.1    Serra, J.2    Schafer, R.W.3
  • 14
    • 33749613836 scopus 로고    scopus 로고
    • Locally Adaptable Mathematical Morphology
    • Sept
    • O. Cuisenaire, "Locally Adaptable Mathematical Morphology," Proc. IEEE Int'l Conf. Image Processing, vol. 2, pp. 125-128, Sept. 2005.
    • (2005) Proc. IEEE Int'l Conf. Image Processing , vol.2 , pp. 125-128
    • Cuisenaire, O.1
  • 15
    • 33749550887 scopus 로고    scopus 로고
    • General Adaptive Neighborhood Image Processing - Part I: Introduction and Theoretical Aspects
    • Sept
    • J. Debayle and J.C. Pinoli, "General Adaptive Neighborhood Image Processing - Part I: Introduction and Theoretical Aspects," J. Math. Imaging and Vision, vol. 25, no. 2, pp. 245-266, Sept. 2006.
    • (2006) J. Math. Imaging and Vision , vol.25 , Issue.2 , pp. 245-266
    • Debayle, J.1    Pinoli, J.C.2
  • 16
    • 33749542261 scopus 로고    scopus 로고
    • General Adaptive Neighborhood Image Processing - Part II: Practical Application Examples
    • Sept
    • J. Debayle and J.C. Pinoli, "General Adaptive Neighborhood Image Processing - Part II: Practical Application Examples," J. Math. Imaging and Vision, vol. 25, no. 2, pp. 267-284, Sept. 2006.
    • (2006) J. Math. Imaging and Vision , vol.25 , Issue.2 , pp. 267-284
    • Debayle, J.1    Pinoli, J.C.2
  • 17
    • 0022566246 scopus 로고
    • A Digital Version of the Matheron Representation Theorem for Increasing τ-Mappings in Terms of a Basis for the Kernel
    • June
    • E.R. Dougherty and C.R. Giardina, "A Digital Version of the Matheron Representation Theorem for Increasing τ-Mappings in Terms of a Basis for the Kernel," Proc. IEEE Computer Vision and Pattern Recognition pp. 534-536, June 1986.
    • (1986) Proc. IEEE Computer Vision and Pattern Recognition , pp. 534-536
    • Dougherty, E.R.1    Giardina, C.R.2
  • 19
    • 21144445430 scopus 로고    scopus 로고
    • Signature Analysis and Defect Detection in Layered Manufacturing of Ceramic Sensors and Actuators
    • Dec
    • T. Fang, M.A. Jafari, S.C. Danforth, and A. Safari, "Signature Analysis and Defect Detection in Layered Manufacturing of Ceramic Sensors and Actuators," Machine Vision and Applications, vol. 15, no. 2, pp. 63-75, Dec. 2003.
    • (2003) Machine Vision and Applications , vol.15 , Issue.2 , pp. 63-75
    • Fang, T.1    Jafari, M.A.2    Danforth, S.C.3    Safari, A.4
  • 20
    • 0021373850 scopus 로고
    • Feature Enhancement of Mammograms Using Fixed and Adaptive Neighborhoods
    • Feb
    • R. Gordon and R.M. Rangayyan, "Feature Enhancement of Mammograms Using Fixed and Adaptive Neighborhoods," Applied Optics, vol. 23, no. 4, pp. 560-564, Feb. 1984.
    • (1984) Applied Optics , vol.23 , Issue.4 , pp. 560-564
    • Gordon, R.1    Rangayyan, R.M.2
  • 21
    • 0000537985 scopus 로고    scopus 로고
    • Morphological Methods for Biomedical Image Analysis
    • M. Sonka and J.M. Fitzpatrick, eds, pp, SPIE Optical Eng. Press
    • J. Goutsias and S. Batman, "Morphological Methods for Biomedical Image Analysis," Handbook of Medical Imaging, Progress in Medical Image Processing and Analysis, vol. 3, M. Sonka and J.M. Fitzpatrick, eds., pp. 175-272. SPIE Optical Eng. Press, 2000.
    • (2000) Handbook of Medical Imaging, Progress in Medical Image Processing and Analysis , vol.3 , pp. 175-272
    • Goutsias, J.1    Batman, S.2
  • 23
    • 24144486285 scopus 로고    scopus 로고
    • Minimal-Memory Bit-Vector Architecture for Computational Mathematical Morphology Using Subspace Projections
    • Aug
    • J.C. Handley, "Minimal-Memory Bit-Vector Architecture for Computational Mathematical Morphology Using Subspace Projections," IEEE Trans. Image Processing, vol. 14, no. 8, pp. 1088-1095, Aug. 2005.
    • (2005) IEEE Trans. Image Processing , vol.14 , Issue.8 , pp. 1088-1095
    • Handley, J.C.1
  • 24
    • 0039222943 scopus 로고
    • Mathematical Morphology: An Algebraic Approach
    • H.J.A.M. Heijmans, "Mathematical Morphology: An Algebraic Approach," CWI Newsletter, vol. 14, pp. 7-27, 1987.
    • (1987) CWI Newsletter , vol.14 , pp. 7-27
    • Heijmans, H.J.A.M.1
  • 26
    • 0034314944 scopus 로고    scopus 로고
    • Nonlinear Multiresolution Signal Decomposition Schemes - I: Morphological Pyramids
    • Nov
    • H.J.A.M. Heijmans and J. Goutsias, "Nonlinear Multiresolution Signal Decomposition Schemes - I: Morphological Pyramids," IEEE Trans. Image Processing, vol. 9, no. 11, pp. 1862-1876, Nov. 2000.
    • (2000) IEEE Trans. Image Processing , vol.9 , Issue.11 , pp. 1862-1876
    • Heijmans, H.J.A.M.1    Goutsias, J.2
  • 27
    • 0034316249 scopus 로고    scopus 로고
    • Nonlinear Multiresolution Signal Decomposition Schemes - II: Morphological Wavelets
    • Nov
    • H.J.A.M. Heijmans and J. Goutsias, "Nonlinear Multiresolution Signal Decomposition Schemes - II: Morphological Wavelets," IEEE Trans. Image Processing, vol. 9, no. 11, pp. 1897-1913, Nov. 2000.
    • (2000) IEEE Trans. Image Processing , vol.9 , Issue.11 , pp. 1897-1913
    • Heijmans, H.J.A.M.1    Goutsias, J.2
  • 30
    • 7644239523 scopus 로고    scopus 로고
    • Doppler Frequency Extraction of Radar Echo Signal Based on Time-Frequency Analysis and Morphological Operation
    • S. Hou, S. Wu, and S. Ma, "Doppler Frequency Extraction of Radar Echo Signal Based on Time-Frequency Analysis and Morphological Operation," Proc. Int'l Conf. Signal Processing, vol. 3, pp. 2017-2020, 2004.
    • (2004) Proc. Int'l Conf. Signal Processing , vol.3 , pp. 2017-2020
    • Hou, S.1    Wu, S.2    Ma, S.3
  • 31
    • 31144435146 scopus 로고    scopus 로고
    • Shape Representation and Recognition through Morphological Curvature Scale Spaces
    • Feb
    • A.C. Jalba, M.H.F. Wilkinson, and J.B.T.M. Roerdink, "Shape Representation and Recognition through Morphological Curvature Scale Spaces," IEEE Trans. Image Processing, vol. 15, no. 2, pp. 331-341, Feb. 2006.
    • (2006) IEEE Trans. Image Processing , vol.15 , Issue.2 , pp. 331-341
    • Jalba, A.C.1    Wilkinson, M.H.F.2    Roerdink, J.B.T.M.3
  • 33
    • 0028468504 scopus 로고
    • Morphological Reduction of Skeleton Redundancy
    • July
    • R. Kresch and D. Malah, "Morphological Reduction of Skeleton Redundancy," Signal Processing, vol. 38, no. 1, pp. 143-151, July 1994.
    • (1994) Signal Processing , vol.38 , Issue.1 , pp. 143-151
    • Kresch, R.1    Malah, D.2
  • 34
    • 0032186820 scopus 로고    scopus 로고
    • Skeleton-Based Morphological Coding of Binary Images
    • Oct
    • R. Kresch and D. Malah, "Skeleton-Based Morphological Coding of Binary Images," IEEE Trans. Image Processing, vol. 7, no. 10, pp. 1387-1399, Oct. 1998.
    • (1998) IEEE Trans. Image Processing , vol.7 , Issue.10 , pp. 1387-1399
    • Kresch, R.1    Malah, D.2
  • 35
    • 0003637706 scopus 로고
    • La Squelettization et son Application aux Mesures Topologuiques des Mosaiques Polycristallines,
    • PhD dissertation, School of Mines
    • C. Lantuejoul, "La Squelettization et son Application aux Mesures Topologuiques des Mosaiques Polycristallines," PhD dissertation, School of Mines, 1978.
    • (1978)
    • Lantuejoul, C.1
  • 38
    • 0024700098 scopus 로고
    • Pattern Spectrum and Multiscale Shape Representation
    • July
    • P.A. Maragos, "Pattern Spectrum and Multiscale Shape Representation," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 7, pp. 701-716, July 1989.
    • (1989) IEEE Trans. Pattern Analysis and Machine Intelligence , vol.11 , Issue.7 , pp. 701-716
    • Maragos, P.A.1
  • 39
    • 34250872297 scopus 로고
    • A Representation Theory for Morphological Image and Signal Processing
    • June
    • P.A. Maragos, "A Representation Theory for Morphological Image and Signal Processing," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 6, pp. 586-599, June 1989.
    • (1989) IEEE Trans. Pattern Analysis and Machine Intelligence , vol.11 , Issue.6 , pp. 586-599
    • Maragos, P.A.1
  • 42
    • 0022790410 scopus 로고
    • Morphological Skeleton Representation and Coding of Binary Images
    • Oct
    • P.A. Maragos and R.W. Schafer, "Morphological Skeleton Representation and Coding of Binary Images," IEEE Trans. Acoustics, Speech, and Signal Processing, vol. 34, no. 5, pp. 1228-1244, Oct. 1986.
    • (1986) IEEE Trans. Acoustics, Speech, and Signal Processing , vol.34 , Issue.5 , pp. 1228-1244
    • Maragos, P.A.1    Schafer, R.W.2
  • 43
    • 0023400884 scopus 로고
    • Morphological Filters - Part I: Their Set-Theoric Analysis and Relations to Linear Shift-Invariant Filters
    • Aug
    • P.A. Maragos and R.W. Schafer, "Morphological Filters - Part I: Their Set-Theoric Analysis and Relations to Linear Shift-Invariant Filters," IEEE Trans. Acoustics, Speech, and Signal Processing, vol. 35, no. 8, pp. 1153-1169, Aug. 1987.
    • (1987) IEEE Trans. Acoustics, Speech, and Signal Processing , vol.35 , Issue.8 , pp. 1153-1169
    • Maragos, P.A.1    Schafer, R.W.2
  • 44
    • 0023400430 scopus 로고
    • Morphological Filters - Part II: Their Relation to Median, Order-Statistics and Stack Filters
    • P.A. Maragos and R.W. Schafer, "Morphological Filters - Part II: Their Relation to Median, Order-Statistics and Stack Filters," IEEE Trans. Acoustics, Speech, and Signal Processing, vol. 35, 1987.
    • (1987) IEEE Trans. Acoustics, Speech, and Signal Processing , vol.35
    • Maragos, P.A.1    Schafer, R.W.2
  • 45
    • 0037334277 scopus 로고    scopus 로고
    • Morphological Operations by Locally Variable Structuring Elements and Their Applications to Region Extraction in Ultrasound Images
    • Feb
    • I. Masayasu, T. Masayoshi, and N. Akira, "Morphological Operations by Locally Variable Structuring Elements and Their Applications to Region Extraction in Ultrasound Images," Systems and Computers in Japan, vol. 34, no. 3, pp. 33-43, Feb. 2003.
    • (2003) Systems and Computers in Japan , vol.34 , Issue.3 , pp. 33-43
    • Masayasu, I.1    Masayoshi, T.2    Akira, N.3
  • 48
    • 0033880427 scopus 로고    scopus 로고
    • Group Morphology
    • J.B.T.M. Roerdink, "Group Morphology," Pattern Recognition, vol. 33, no. 6, pp. 877-895, 2000.
    • (2000) Pattern Recognition , vol.33 , Issue.6 , pp. 877-895
    • Roerdink, J.B.T.M.1
  • 49
    • 0037481174 scopus 로고    scopus 로고
    • Multiresolution Maximum Intensity Volume Rendering by Morphological Adjunction Pyramids
    • June
    • J.B.T.M. Roerdink, "Multiresolution Maximum Intensity Volume Rendering by Morphological Adjunction Pyramids," IEEE Trans. Image Processing vol. 12, no. 6, pp. 653-660, June 2003.
    • (2003) IEEE Trans. Image Processing , vol.12 , Issue.6 , pp. 653-660
    • Roerdink, J.B.T.M.1
  • 50
    • 0024092664 scopus 로고
    • Mathematical Morphology for Structuring Elements without Translation Symmetry
    • J.B.T.M. Roerdink and H.J.A.M. Heijmans, "Mathematical Morphology for Structuring Elements without Translation Symmetry," Signal Processing, vol. 15, no. 3, pp. 271-277, 1988.
    • (1988) Signal Processing , vol.15 , Issue.3 , pp. 271-277
    • Roerdink, J.B.T.M.1    Heijmans, H.J.A.M.2
  • 51
    • 0026171306 scopus 로고
    • Morphological Representation of Discrete and Binary Images
    • June
    • D. Schonfeld and J. Goutsias, "Morphological Representation of Discrete and Binary Images," IEEE Trans. Signal Processing, vol. 39, no. 6, pp. 1369-1379, June 1991.
    • (1991) IEEE Trans. Signal Processing , vol.39 , Issue.6 , pp. 1369-1379
    • Schonfeld, D.1    Goutsias, J.2
  • 52
  • 55
    • 85076142325 scopus 로고
    • Connected Operators and Pyramids
    • J. Serra and P. Salembier, "Connected Operators and Pyramids," Proc. SPIE, vol. 2030, pp. 65-76, 1993.
    • (1993) Proc. SPIE , vol.2030 , pp. 65-76
    • Serra, J.1    Salembier, P.2
  • 56
    • 9544254865 scopus 로고    scopus 로고
    • F.Y. Shih and S. Cheng, Adaptive Mathematical Morphology for Edge Linking, Int'l J. Information Sciences Informatics and Computer Science, 167, pp. 9-21, Dec. 2004.
    • F.Y. Shih and S. Cheng, "Adaptive Mathematical Morphology for Edge Linking," Int'l J. Information Sciences Informatics and Computer Science, vol. 167, pp. 9-21, Dec. 2004.
  • 57
    • 0027088616 scopus 로고
    • Generalized Skeleton Representation and Adaptive Rectangular Decomposition of Binary Images
    • J.C. Serra, ed, June
    • K. Shoji, "Generalized Skeleton Representation and Adaptive Rectangular Decomposition of Binary Images," Proc. SPIE in Image Algebra and Morphological Image Processing, J.C. Serra, ed., vol. 1769, pp. 404-415, June 1992.
    • (1992) Proc. SPIE in Image Algebra and Morphological Image Processing , vol.1769 , pp. 404-415
    • Shoji, K.1
  • 58
    • 0027576715 scopus 로고
    • Adaptive Mathematical Morphology for Range Imagery
    • Apr
    • J.G. Verly and R.L. Delanoy, "Adaptive Mathematical Morphology for Range Imagery," IEEE Trans. Image Processing, vol. 2, no. 2, pp. 272-275, Apr. 1993.
    • (1993) IEEE Trans. Image Processing , vol.2 , Issue.2 , pp. 272-275
    • Verly, J.G.1    Delanoy, R.L.2
  • 59
    • 0027576716 scopus 로고
    • Morphological Grayscale Reconstruction in Image Analysis: Applications and Efficient Algorithms
    • Apr
    • L. Vincent, "Morphological Grayscale Reconstruction in Image Analysis: Applications and Efficient Algorithms," IEEE Trans. Image Processing vol. 2, no. 2, pp. 176-201, Apr. 1993.
    • (1993) IEEE Trans. Image Processing , vol.2 , Issue.2 , pp. 176-201
    • Vincent, L.1
  • 60
    • 32944480008 scopus 로고    scopus 로고
    • Morphology-Based Multifractal Estimation for Texture Segmentation
    • Mar
    • Y. Xia, D. Feng, and R. Zhao, "Morphology-Based Multifractal Estimation for Texture Segmentation," IEEE Trans. Image Processing, vol. 15, no. 3, pp. 614-623, Mar. 2006.
    • (2006) IEEE Trans. Image Processing , vol.15 , Issue.3 , pp. 614-623
    • Xia, Y.1    Feng, D.2    Zhao, R.3
  • 61
    • 10844222919 scopus 로고    scopus 로고
    • A Generalized Discrete Morphological Skeleton Transform with Multiple Structuring Elements for the Extraction of Structural Shape Components
    • Dec
    • J. Xu, "A Generalized Discrete Morphological Skeleton Transform with Multiple Structuring Elements for the Extraction of Structural Shape Components," IEEE Trans. Image Processing, vol. 12, no. 2, pp. 1677-1686, Dec. 2003.
    • (2003) IEEE Trans. Image Processing , vol.12 , Issue.2 , pp. 1677-1686
    • Xu, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.