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A lattice approach to image segmentation

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Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
PL
Kratowa metoda segmentacji obrazów
Konferencja
PELINCEC International Workshop on "Image Processing in Industrial Information Technology- Methods and Applications" Warsaw, 14-15.10.2004
Języki publikacji
EN
Abstrakty
EN
This lecture comprises two parts. Firstly, after a formal definition of segmentation as the largest partition of the space according to a criterion and a function, the notion of a morphological connection is reminded. It is used as an input to a central theorem of the paper (Theorem 7), that identifies segmentation with some classes of connections. Just as connections, the segmentations can then be regrouped by suprema and infima. The generality of the theorem makes it valid for all functions from any space to any other one. Two propositions make precise the AND and OR combinations of connective criteria. The segmentation classes turn out to be independent of their location in the measuring held, assuming that a convenient neighbourhood is experimentally accessible. The second part studies the notion of a connected operator, in a more restricted framework than previously. It provides segmentations with more flexibility, and allows us to make them depend on parameters. Hierarchies of connected filters are built, whose the partitions increase when going up in the pyramid, and where the various levels are structured as semi-groups.
PL
Artykuł sktada się z dwóch części. W pierwszej po formalnej definicji segmentacji przypomniano pojęcie morfologicznego połączenia. Pojęcie to jest wykorzystane jako punkt wyjścia do głównego wyniku tj. twierdzenia 7, które identyfikuje segmentację z pewnymi klasami połączeń. Druga część artykułu analizuje pojęcie operatora połączonego w sposób bardziej rygorystyczny niż poprzednio. Daje to segmentacji więcej elastyczności i pozwala nam uczynić ją zależną od parametrów.
Rocznik
Strony
47--54
Opis fizyczny
Bibliogr. 21 poz., rys.
Twórcy
autor
  • Centre de Morphologie Mathematique, Ecole des Mines de Paris, Fontainebleau, France
Bibliografia
  • [1] Birkhoff G., Lattice theory, A.M.S. Colloq. publ., 3rd edition, vol. 25, (1983).
  • [2] Braga-Neto U.M. , Goutsias J., A Multiscale approach to Connectivity, Computer Vision and Image Understanding, 89 (2003) 70-107.
  • [3] Choquet G. Topology Academic Press, (1966).
  • [4] Crespo J., Serra J., Schafer R.W. Theoretical aspects of morphological filters by reconstruction. Signal Processing, Vol. 47, No 2, (1995), 201-225
  • [5] Crespo J., Schafer R.W., Se ra J., Gratin Ch., Meyer F. The fiat zone approach: A general low-level region merging segmentation method. Signal Processing, 62, (1997), 37-60.
  • [6] Heijmans H.J .A.M. Connected morphological operators for binary images. Computer Vision and Image Understanding, 73, (1999), 99-120.
  • [7] Maragos P. and Meyer F. Nonlinear PDEs and numerical algorithms for modeling levelings and reconstructions filters Scale-Space Theories in Computer Vision, Proceedings Scale-Space'99. Berlin: Springer., N. Mads, et al., Eds. Lecture Notes in Computer Science, (1982),363-374.
  • [8] Matheron G.Les treillis compacts. Tech. rep. N-23/90/G, Ecole des Mines de Paris, Part 1, (1990), part 2, (1996).
  • [9] Meyer F. Minimum spanning forests for morphological segmentation. In Mathematical Morphology and its applications to image and signal processing, Maragos P. et al. eds., Kluwer,(1996).
  • [10] Meyer F., The levelings. In Mathematical Morphology and its applications to image and signal processing. Kluwer, (1998).
  • [11] Meyer F., An overview of morphological segmentation. International Journal of Pattern Recognition and Artificial Intelligence, (2001). 15(7): 1089-1118.
  • [12] Pardas M., Serra J., Torres L.Connectivity filters for image sequences. In SPIE, Vol. 1769, (1992), pp. 318-329.
  • [13] Ronse C., Set theoretical algebraic approaches to connectivity in continuous or digital spaces. JMIV, (1998), Vol. 8 n°l, pp. 41-58.
  • [14] Salembier P. and Serra J., Flat zones filtering, connected operators, and filters by reconstruction IEEE Transactions on Image Processing. August (1995), vol. 4, n° 8, 1153-1160 .
  • [15] Salembier P. and Marques F. Region-based representations of image and video: Segmentation tools for multimedia services IEEE Transactions on circuits and systems for video technology, vol. 9, no 8, (l999) pp.1147-1167
  • [16] Serra J., Image analysis and mathematical morphology, part II: theoretical advances, J. Serra ed., Acad. Press, 1988.
  • [17] Serra J . Connectivity on complete lattices. Journal of Mathematical Imaging and Vision 9, (1998), pp 231-251
  • [18] Serra J. Set connections and discrete filtering (Proc. DGCI 1999) Lecture Notes in Computer Science, Vol. 1568, G. Bertrand, M. Couprie and L Perroton (eds.), Springer, 1999, pp 191-206.
  • [19] Serra J . Connectivity for sets and functions Fundam.enta Informaticae, 41 (2000) 147-186
  • [20] Sternberg S.R. Morphology for grey-tone functions, Computer Vision, Graphics and Image Processing 35, (1986) 333-355,
  • [21] Vincent L.Morphological grayscale reconstruction in image analysis: Applications and efficient algorithms. IEEE Transactions in Image Processing, Vol. 2, (1993), 176-201.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAR0-0008-0010
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