메뉴 건너뛰기




Volumn 25, Issue 4 SPEC. ISS., 2007, Pages 496-511

Morphology for matrix data: Ordering versus PDE-based approach

Author keywords

Diffusion tensor MRI; Dilation; Erosion; Loewner ordering; Mathematical morphology; Matrix valued images; Nonlinear partial differential equation

Indexed keywords

IMAGE ANALYSIS; IMAGE SEGMENTATION; MAGNETIC RESONANCE IMAGING; MATRIX ALGEBRA; PARTIAL DIFFERENTIAL EQUATIONS;

EID: 33846588484     PISSN: 02628856     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.imavis.2006.06.002     Document Type: Article
Times cited : (33)

References (44)
  • 1
    • 23044482368 scopus 로고    scopus 로고
    • An introduction to computational diffusion MRI: the diffusion tensor and beyond
    • Weickert J., and Hagen H. (Eds), Springer, Berlin
    • Alexander D.C. An introduction to computational diffusion MRI: the diffusion tensor and beyond. In: Weickert J., and Hagen H. (Eds). Visualization and Processing of Tensor Fields (2006), Springer, Berlin 77-100
    • (2006) Visualization and Processing of Tensor Fields , pp. 77-100
    • Alexander, D.C.1
  • 2
    • 0141542021 scopus 로고    scopus 로고
    • A Course in Convexity
    • American Mathematical Society, Providence
    • Barvinok A. A Course in Convexity. Graduate Studies in Mathematics vol. 54 (2002), American Mathematical Society, Providence
    • (2002) Graduate Studies in Mathematics , vol.54
    • Barvinok, A.1
  • 3
    • 0029403019 scopus 로고
    • Inferring microstructural features and the physical state of tissues from diffusion-weighted images
    • Basser P.J. Inferring microstructural features and the physical state of tissues from diffusion-weighted images. Nucl. Magn. Reson. Biomed. 8 (1995) 333-334
    • (1995) Nucl. Magn. Reson. Biomed. , vol.8 , pp. 333-334
    • Basser, P.J.1
  • 4
    • 0028154030 scopus 로고
    • MR diffusion tensor spectroscopy and imaging
    • Basser P.J., Mattiello J., and LeBihan D. MR diffusion tensor spectroscopy and imaging. Biophys. J. 66 (1994) 259-267
    • (1994) Biophys. J. , vol.66 , pp. 259-267
    • Basser, P.J.1    Mattiello, J.2    LeBihan, D.3
  • 5
    • 0026202914 scopus 로고
    • Multidimensional orientation estimation with applications to texture analysis and optical flow
    • Bigün J., Granlund G.H., and Wiklund J. Multidimensional orientation estimation with applications to texture analysis and optical flow. IEEE Trans. Pattern Anal. Mach. Intell. 13 8 (1991) 775-790
    • (1991) IEEE Trans. Pattern Anal. Mach. Intell. , vol.13 , Issue.8 , pp. 775-790
    • Bigün, J.1    Granlund, G.H.2    Wiklund, J.3
  • 6
    • 35248892929 scopus 로고    scopus 로고
    • Unsupervised segmentation incorporating colour, texture, and motion
    • Computer Analysis of Images and Patterns. Petkov N., and Westenberg M.A. (Eds), Springer, Berlin
    • Brox T., Rousson M., Deriche R., and Weickert J. Unsupervised segmentation incorporating colour, texture, and motion. In: Petkov N., and Westenberg M.A. (Eds). Computer Analysis of Images and Patterns. Lecture Notes in Computer Science vol. 2756 (2003), Springer, Berlin 353-360
    • (2003) Lecture Notes in Computer Science , vol.2756 , pp. 353-360
    • Brox, T.1    Rousson, M.2    Deriche, R.3    Weickert, J.4
  • 7
    • 84878591254 scopus 로고    scopus 로고
    • Nonlinear matrix diffusion for optic flow estimation
    • Pattern Recognition. Van Gool L. (Ed), Springer, Berlin
    • Brox T., and Weickert J. Nonlinear matrix diffusion for optic flow estimation. In: Van Gool L. (Ed). Pattern Recognition. Lecture Notes in Computer Science vol. 2449 (2002), Springer, Berlin 446-453
    • (2002) Lecture Notes in Computer Science , vol.2449 , pp. 446-453
    • Brox, T.1    Weickert, J.2
  • 8
    • 77953606897 scopus 로고    scopus 로고
    • Mathematical morphology based on the Loewner ordering for tensor data
    • Mathematical Morphology: 40 Years On. Ronse C., Najman L., and Decencière E. (Eds), Springer, Dordrecht
    • Burgeth B., Papenberg N., Bruhn A., Welk M., Feddern C., and Weickert J. Mathematical morphology based on the Loewner ordering for tensor data. In: Ronse C., Najman L., and Decencière E. (Eds). Mathematical Morphology: 40 Years On. Computational Imaging and Vision vol. 30 (2005), Springer, Dordrecht 407-418
    • (2005) Computational Imaging and Vision , vol.30 , pp. 407-418
    • Burgeth, B.1    Papenberg, N.2    Bruhn, A.3    Welk, M.4    Feddern, C.5    Weickert, J.6
  • 9
    • 33646872897 scopus 로고    scopus 로고
    • Morphological operations on matrix-valued images
    • Computer Vision - ECCV 2004. Pajdla T., and Matas J. (Eds), Springer, Berlin
    • Burgeth B., Welk M., Feddern C., and Weickert J. Morphological operations on matrix-valued images. In: Pajdla T., and Matas J. (Eds). Computer Vision - ECCV 2004. Lecture Notes in Computer Science vol. 3024 (2004), Springer, Berlin 155-167
    • (2004) Lecture Notes in Computer Science , vol.3024 , pp. 155-167
    • Burgeth, B.1    Welk, M.2    Feddern, C.3    Weickert, J.4
  • 10
    • 85138902587 scopus 로고    scopus 로고
    • B. Burgeth, M. Welk, C. Feddern, J. Weickert, Mathematical morphology on tensor data using the Loewner ordering, in: H. Hagen, J. Weickert (Eds.), Visualization and Processing of Tensor Fields: Springer-Verlag, Berlin, 2006.
  • 11
    • 84937398889 scopus 로고    scopus 로고
    • A regularization scheme for diffusion tensor magnetic resonance images
    • Information Processing in Medical Imaging - IPMI 2001. Insana M.F., and Leahy R.M. (Eds), Springer, Berlin
    • Coulon O., Alexander D.C., and Arridge S.A. A regularization scheme for diffusion tensor magnetic resonance images. In: Insana M.F., and Leahy R.M. (Eds). Information Processing in Medical Imaging - IPMI 2001. Lecture Notes in Computer Science vol. 2082 (2001), Springer, Berlin 92-105
    • (2001) Lecture Notes in Computer Science , vol.2082 , pp. 92-105
    • Coulon, O.1    Alexander, D.C.2    Arridge, S.A.3
  • 12
    • 84995336884 scopus 로고    scopus 로고
    • C. Feddern, J. Weickert, B. Burgeth, M. Welk, Curvature-driven PDE methods for matrix-valued images, Technical Report 104, Department of Mathematics, Saarland University, Saarbrücken, Germany, May 2004.
  • 13
    • 84995347624 scopus 로고    scopus 로고
    • W. Förstner, E. Gülch, A fast operator for detection and precise location of distinct points, corners and centres of circular features, in: Proc. ISPRS Intercommission Conference on Fast Processing of Photogrammetric Data, Interlaken, Switzerland, June 1987, pp. 281-305.
  • 14
    • 84995325988 scopus 로고    scopus 로고
    • B. Gärtner, , WebPage last visited: February 28th, 2006.
  • 16
    • 0004217902 scopus 로고    scopus 로고
    • Goutsias J., Vincent L., and Bloomberg D.S. (Eds), Kluwer, Dordrecht
    • In: Goutsias J., Vincent L., and Bloomberg D.S. (Eds). Mathematical Morphology and its Applications to Image and Signal Processing. Computational Imaging and Vision vol. 18 (2000), Kluwer, Dordrecht
    • (2000) Computational Imaging and Vision , vol.18
  • 18
    • 84958173670 scopus 로고    scopus 로고
    • Edge preserving regularization and tracking for diffusion tensor imaging
    • Medical Image Computing and Computer-Assisted Intervention - MICCAI 2001. Niessen W.J., and Viergever M.A. (Eds), Springer, Berlin
    • Hahn K., Pigarin S., and Pütz B. Edge preserving regularization and tracking for diffusion tensor imaging. In: Niessen W.J., and Viergever M.A. (Eds). Medical Image Computing and Computer-Assisted Intervention - MICCAI 2001. Lecture Notes in Computer Science vol. 2208 (2001), Springer, Berlin 195-203
    • (2001) Lecture Notes in Computer Science , vol.2208 , pp. 195-203
    • Hahn, K.1    Pigarin, S.2    Pütz, B.3
  • 19
    • 84995324365 scopus 로고    scopus 로고
    • C.G. Harris, M. Stephens, A combined corner and edge detector, in: Proc. Fourth Alvey Vision Conference, Manchester, England, August 1988, pp. 147-152.
  • 21
    • 33749555618 scopus 로고    scopus 로고
    • Heijmans H.J.A.M., and Roerdink J.B.T.M. (Eds), Kluwer, Dordrecht
    • In: Heijmans H.J.A.M., and Roerdink J.B.T.M. (Eds). Mathematical Morphology and its Applications to Image and Signal Processing. Computational Imaging and Vision vol. 12 (1998), Kluwer, Dordrecht
    • (1998) Computational Imaging and Vision , vol.12
  • 23
  • 24
    • 0016520162 scopus 로고
    • Iterations of a non-linear transformation for enhancement of digital images
    • Kramer H.P., and Bruckner J.B. Iterations of a non-linear transformation for enhancement of digital images. Pattern Recogn. 7 (1975) 53-58
    • (1975) Pattern Recogn. , vol.7 , pp. 53-58
    • Kramer, H.P.1    Bruckner, J.B.2
  • 28
    • 44749084234 scopus 로고
    • Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
    • 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
    • (1988) J. Comput. Phys. , vol.79 , pp. 12-49
    • Osher, S.1    Sethian, J.A.2
  • 29
  • 32
    • 0042433488 scopus 로고    scopus 로고
    • M. Rousson, T. Brox, R. Deriche, Active unsupervised texture segmentation on a diffusion based feature space, in: Proc. 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 2, Madison, WI, IEEE Computer Society Press, June 2003, pp. 699-704.
  • 35
    • 84995303645 scopus 로고    scopus 로고
    • J. Serra, Echantillonnage et estimation des phénoménes de transition minier, PhD thesis, University of Nancy, France, 1967.
  • 39
    • 84995359502 scopus 로고    scopus 로고
    • H. Talbot, R. Beare (Eds.), in: Proc. Sixth International Symposium on Mathematical Morphology and its Applications. Sydney, Australia, April 2002. .
  • 40
    • 0035680367 scopus 로고    scopus 로고
    • D. Tschumperlé, R. Deriche, Diffusion tensor regularization with constraints preservation, in: Proc. 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 1, Kauai, HI, IEEE Computer Society Press, pp. 948-953.
  • 42
    • 24644465521 scopus 로고    scopus 로고
    • Diffusion and regularization of vector- and matrix-valued images
    • Inverse Problems, Image Analysis, and Medical Imaging. Nashed M.Z., and Scherzer O. (Eds), AMS, Providence
    • Weickert J., and Brox T. Diffusion and regularization of vector- and matrix-valued images. In: Nashed M.Z., and Scherzer O. (Eds). Inverse Problems, Image Analysis, and Medical Imaging. Contemporary Mathematics vol. 313 (2002), AMS, Providence 251-268
    • (2002) Contemporary Mathematics , vol.313 , pp. 251-268
    • Weickert, J.1    Brox, T.2
  • 43
    • 35248878185 scopus 로고    scopus 로고
    • Median filtering of tensor-valued images
    • Pattern Recognition. Michaelis B., and Krell G. (Eds), Springer, Berlin
    • Welk M., Feddern C., Burgeth B., and Weickert J. Median filtering of tensor-valued images. In: Michaelis B., and Krell G. (Eds). Pattern Recognition. Lecture Notes in Computer Science vol. 2781 (2003), Springer, Berlin 17-24
    • (2003) Lecture Notes in Computer Science , vol.2781 , pp. 17-24
    • Welk, M.1    Feddern, C.2    Burgeth, B.3    Weickert, J.4
  • 44
    • 84957104087 scopus 로고    scopus 로고
    • Image processing for diffusion tensor magnetic resonance imaging
    • Medical Image Computing and Computer-Assisted Intervention - MIC-CAI 1999. Taylor C., and Colchester A. (Eds), Springer, Berlin
    • Westin C.-F., Maier S.E., Khidhir B., Everett P., Jolesz F.A., and Kikinis R. Image processing for diffusion tensor magnetic resonance imaging. In: Taylor C., and Colchester A. (Eds). Medical Image Computing and Computer-Assisted Intervention - MIC-CAI 1999. Lecture Notes in Computer Science vol. 1679 (1999), Springer, Berlin 441-452
    • (1999) Lecture Notes in Computer Science , vol.1679 , pp. 441-452
    • Westin, C.-F.1    Maier, S.E.2    Khidhir, B.3    Everett, P.4    Jolesz, F.A.5    Kikinis, R.6


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.