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International Workshop on Graph-Based Representations in Pattern Recognition

GbRPR 2005: Graph-Based Representations in Pattern Recognition pp 92–121Cite as

Representing and Segmenting 2D Images by Means of Planar Maps with Discrete Embeddings: From Model to Applications

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 3434))

Abstract

Representing the regions of a segmented image is an important aspect of image segmentation. Several different models have been proposed to represent the regions of a segmented image but most of them are dedicated to a specific method. Among the non hierarchical models, the model of planar maps with discrete embedding is certainly the most versatile one. Maps have the great advantage to provide a continuity of representation from the abstract mathematical model to the concrete implementation. They encode and provide most of topological and geometrical features required by segmentation algorithms and can be efficiently updated. In this paper we give an overview of the use of planar maps with discrete embedding in the context of image segmentation and we show how to design, implement and use a general environment for 2D image segmentation, from the mathematical model up to a real application. The model, data structure, algorithms and API described in this paper are currently implemented in a software which will be available under LGPL in the course of year 2005.

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References

  1. Ahronovitz, E., Aubert, J.P., Fiorio, C.: The star-topology: a topology for image analysis. In: 5th DGCI Proceedings, pp. 107–116 (1995)

    Google Scholar 

  2. Ang, C., Samet, H., Shaffer, C.A.: A new region expansion for quadtrees. IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI-12(7), 682–686 (1990)

    Article  Google Scholar 

  3. Baldy, C., Douek, P., Croisille, P., Magnin, I.E., Revel, D., Amiel, M.: Automated myocardial edge detection from breath-hold cine-mr images: Evaluation of left ventricular volumes and mass. Magnetic Resonance Imaging 12(4), 589–598 (1994)

    Article  Google Scholar 

  4. Baudelaire, P., Gangnet, M.: Planar maps: an interaction paradigm for graphic design. In: Proc. of CHI 1989, pp. 313–318. Addison-Wesley, Reading (1989)

    Google Scholar 

  5. Benois-Pineau, J., Braquelaire, A., Ali-Mhammad, A.: Interactive fine object-based segmentation of generic video scenes for object-based indexing. In: Izquierdo, E. (ed.) Proc. of WIAMIS 2003, pp. 200–203 (2003)

    Google Scholar 

  6. Benois-Pineau, J., Peretie, G., Braquelaire, A.: Adaptive video pre-processing for bit-rate reduction in object-based predictive coding schemes. In: Proc. of the 7th World Multiconference on Systemics, Cybernetics and Informatics, Orlando, Florida, July 2003, pp. 27–30 (2003)

    Google Scholar 

  7. Bertrand, Y., Damiand, G., Fiorio, C.: Topological encoding of 3d segmented images. In: Nyström, I., Sanniti di Baja, G., Borgefors, G. (eds.) DGCI 2000. LNCS, vol. 1953, pp. 311–324. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  8. Bertrand, Y., Damiand, G., Fiorio, C.: Topological map: minimal encoding of 3D segmented images. In: Proc. of GBR 2001, pp. 63–73 (2001), ISBN 887146579-2

    Google Scholar 

  9. Beveridge, J.R., Griffith, J., Kohler, R., Hanson, A.R., Riseman, E.M.: Segmenting images using localised histograms and region merging. International Journal of Computer Vision 2, 311–347 (1989)

    Article  Google Scholar 

  10. Bieri, H.: Hyperimages – an alternative to the conventional digital images. In: Eurographics 1990 proceedings, pp. 341–352 (1990)

    Google Scholar 

  11. Bister, M., Cornelis, J., Rosenfeld, A.: A critical view of pyramid segmentation algorithms. Pattern Recognit Letter 11(9), 605–617 (1990)

    Article  MATH  Google Scholar 

  12. Braquelaire, A., Damiand, G., Domenger, J.P., Vidil, F.: Comparaison and convergence of two topological models for 3D image segmentation. In: Proc. of GBR 2003, pp. 32–43 (2003), ISBN 887146579-2

    Google Scholar 

  13. Braquelaire, A., Desbarats, P., Domenger, J.P.: 3D split and merge with 3-maps. In: Proc. of GBR 2001, pp. 32–43 (2001), ISBN 887146579-2

    Google Scholar 

  14. Braquelaire, J.P., Brun, L.: Image segmentation with topological maps and inter-pixel representation. Journal on Visual Communication and Image Representation 9(1), 62–79 (1998)

    Article  Google Scholar 

  15. Braquelaire, J.P., Brun, L., Vialard, A.: Inter-pixel euclidean paths for image analysis. In: Miguet, S., Ubéda, S., Montanvert, A. (eds.) DGCI 1996. LNCS, vol. 1176, pp. 193–204. Springer, Heidelberg (1996)

    Google Scholar 

  16. Braquelaire, J.P., Desbarats, P., Domenger, J.P., Wütrich, C.: A topological structuring for aggregates of 3D discrete objects. In: Proc. of GBR 1999, Osterreichische Computer Gesellschaft, pp. 193–202 (1999), ISBN 3-8580-126-2

    Google Scholar 

  17. Braquelaire, J.P., Domenger, J.P.: Intersection of discrete contours. In: Proc. of Compugraphics 1991, pp. 434–444 (1991)

    Google Scholar 

  18. Braquelaire, J.P., Guitton, P.: A model for image structuration. In: Proc. of Computer Graphics International 1988, pp. 426–435. Springer, Heidelberg (1988)

    Google Scholar 

  19. Braquelaire, J.P., Guitton, P.: 2\(\frac{1}{2}\) scene update by insertion of contour. Computer and Graphics 15(1), 41–48 (1991)

    Article  Google Scholar 

  20. Braquelaire, J.P., Domenger, J.P.: Representation of segmented images with discrete geometric maps. Image and vision Computing 17, 715–735 (1999)

    Article  Google Scholar 

  21. Braquelaire, J.P., Vialard, A.: Euclidean paths: a new representation of boundary of discrete regions. Graphical Models and Images Processing 61, 16–43 (1999)

    Article  MATH  Google Scholar 

  22. Brice, R., Fennema, C.L.: Scene analysis using regions. Artificial intelligence 1, 205–226 (1970)

    Article  Google Scholar 

  23. Brun, L.: Segmentation d’images couleur à base topologique. PhD thesis, Université Bordeaux 1 (December 1996)

    Google Scholar 

  24. Brun, L., Domenger, J.P.: A new split and merge algorithm based on discrete map. In: Proc.of WSCG 1997, pp. 21–30 (1997)

    Google Scholar 

  25. Brun, L., Domenger, J.P., Braquelaire, J.P.: Discrete maps: a framework for region segmentation algorithms. In: Jolion, J.M., Kropatsch, W. (eds.) Proc. of Graph based Representations, GbR 1997, pp. 83–92. Springer, Heidelberg (1997)

    Google Scholar 

  26. Brun, L., Domenger, J.P., Mokhtari, M.: Incremental modifications on segmented image defined by discrete maps. Journal of visual commmunication and Image representation 14, 251–290 (2003)

    Article  Google Scholar 

  27. Brun, L., Kropatsch, W.G.: Introduction to combinatorial pyramids. In: Bertrand, G., Imiya, A., Klette, R. (eds.) Digital and Image Geometry. LNCS, vol. 2243, pp. 108–127. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  28. Cassen, C.: Développement d’une méthode de segmentation applicable aux images d’IRM cardiaque. PhD thesis, Université Bordeaux 1 (2001)

    Google Scholar 

  29. Cassen, C., Domenger, J.P., Braquelaire, A., Barat, J.L.: Left ventricular segmentation in mri images. In: Proc. of ISPA 2001, 2nd IEEE Region 8 Eurasip symposium image and signal processing and image analysis (2001)

    Google Scholar 

  30. Chang, L.W., Leu, K.L.: A fast algorithm for the restoration of images based on chain codes descriptions and its applications. Computer Vision, Graphics and Image Processing: Image Understanding 50, 296–307 (1990)

    Google Scholar 

  31. Cohen, L.D.: On active contour models and ballons. Computer Vision, Graphics and Image Processing: Image Understanding 53(2), 211–218 (1991)

    MATH  Google Scholar 

  32. Cori, R.: Un code pour les graphes planaires et ses applications. Thèse d’état de l’université Paris VII, and Astŕisque 27 (1973/1975)

    Google Scholar 

  33. Damiand, G.: Définition et étude d’un modèle topologique minimal de représentation d’images 2D et 3D. Thèse de doctorat, Université Montpellier II (Décembre 2001)

    Google Scholar 

  34. Desbarats, P.: Strucuration d’images segmentées 3D discrtes. Thèse de doctorat, Université Bordeaux 1 (Décembre 2001)

    Google Scholar 

  35. Desbarats, P., Domenger, J.-P.: Retrieving and using topological characteristics from 3D discrete images. In: Proceedings of the 7th Computer Vision Winter Workshop, pp. 130–139, PRIP-TR-72 (2002)

    Google Scholar 

  36. Domenger, J.-P.: Conception et implémentation du noyau graphique d’un environnement 2D\(\frac{1}{2}\) d’édition d’images discrètes. PhD thesis, Univ. Bordeaux 1 (Avril 1992)

    Google Scholar 

  37. Dyer, R.C., Rosenfeld, A., Hanan, S.: Region representation: Boundary codes from quadtrees. ACM: Graphics and Image Processing 23(3), 171–179 (1980)

    MATH  Google Scholar 

  38. Ferri, F., Vidal, E.: Colour image segmentation and labeling through multiedit-condensing. PRL 13, 561–568 (1992)

    Google Scholar 

  39. Fiorio, C.: Approche interpixel en analyse d’images: une topologie et des algorithmes de segmentation. Thèse de doctorat, Université Montpellier II (Novembre 1995)

    Google Scholar 

  40. Fiorio, C.: A topologically consistent representaion for image analysis: the topological graph of frontiers. In: Miguet, S., Ubéda, S., Montanvert, A. (eds.) DGCI 1996. Lectures Notes in Computer Sciences, vol. 1176. Springer, Heidelberg (1996)

    Google Scholar 

  41. Fleagle, S.R., Thedens, D.R., Stanford, W., Thompson, B.H., Weston, J.M., Patel, P.P., Skorton, D.J.: Automated myocardial edge detection on mr images: Accuracy in consecutive dubjects. Journal of Magnetic Resonance Imaging 3, 738–741 (1993)

    Article  Google Scholar 

  42. Freeman, H.: On the encoding of arbitrary geometric configurations. IRE Trans. Electr. Compu. 10, 260–268 (1961)

    Article  MathSciNet  Google Scholar 

  43. Gangnet, M., Hervé, J.C., Pudet, T., VanThong, J.M.: Incremental computation of planar maps. In: Proc. of SIGGRAPH 1989 (1989)

    Google Scholar 

  44. Gangnet, M., Van Thong, J.M.: Robust boolean operations on 2D paths. In: Proc. of COMPUGRAPHICS 1991, pp. 434–444 (1991)

    Google Scholar 

  45. Gath, I., Hoory, D.: Fuzzy clustering of elliptic ring-shaped clusters. Pattern Recognition Letters 16, 721–741 (1995)

    Article  Google Scholar 

  46. Hunter, G.M., Steiglitz, K.: Operations on images using quad trees. IEEE Trans. On Pattern Analysis and Machine Intelligence 1(2), 145–153 (1979)

    Article  Google Scholar 

  47. Jasiobedzki, P.: Adaptive adjacency graphs. In: Proceedings, SPIE Geometric methods in Computer Vision, San Diego, CA (1993)

    Google Scholar 

  48. Jolion, J.M., Montanvert, A.: The adaptative pyramid: A framework for 2D image analysis. Computer Vision, Graphics and Image Processing: Image Understanding 55(3), 339–348 (1992)

    MATH  Google Scholar 

  49. Keeler, K.C.: Map Representations and Optimal Encoding for Image Segmentation. Phd thesis, Harvard University (1990)

    Google Scholar 

  50. Khalimsky, E., Kopperman, R., Meyer, P.R.: Boundaries in digital planes. Journal of applied Math. and Stocastic Analysis 3, 27–55 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  51. Khalimsky, E., Kopperman, R., Meyer, P.R.: Computer graphics and connected topologies on finite ordered sets. Topology and its Applications 36, 1–17 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  52. Kong, T.Y., Rosenfeld, A.: Digital topology: Introduction and survey. Computer Vision, Graphics and Image Processing: Image Understanding 48, 357–390 (1989)

    Google Scholar 

  53. Köthe, U.: Xpmaps and topological segmentation – a unified approach to finite topologies in plane. In: Braquelaire, A., Lachaud, J.-O., Vialard, A. (eds.) DGCI 2002. LNCS, vol. 2301, pp. 22–33. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  54. Kovalevsky, V.A.: Finite topology as applied to image analysis. Computer Vision, Graphics and Image Processing: Image Understanding 46, 141–161 (1989)

    Google Scholar 

  55. Krämer, P., Benois-Pineau, J., Domenger, J.P.: Scene similarity measure for video content segmentation in the framework of rough indexing paradigme. In: Proc of AMR 2004, pp. 144–155 (2004)

    Google Scholar 

  56. Kropatsch, W.: Preserving contours in dual pyramids, pp. 563–565 (1988)

    Google Scholar 

  57. Kropatsch, W.: Building irregular pyramids by dual graph contraction. IEEE Proc. Vision, Image and Signal Processing 142(6), 366–374 (1995)

    Article  Google Scholar 

  58. Lienhardt, P.: N-dimensional generalized combinatorial maps and cellular quasimanifold. Int. Journ. of Comp. Geom. and Appl., 275–324 (1994)

    Google Scholar 

  59. Lipson, P., Yuille, A.L., Keefe, D.O., Cavanaugh, J., Taaffe, J., Rosenthal, D.: Deformable templates for feature extraction from medical images. In: Faugeras, O. (ed.) ECCV 1990. LNCS, vol. 427, pp. 413–417. Springer, Heidelberg (1990)

    Chapter  Google Scholar 

  60. Loomis, R.G.: Boundary networks. Communications of the ACM 8(1), 44–48 (1965)

    Article  MATH  Google Scholar 

  61. Meer, P.: Stochastic image pyramids. Computer Vision Graphics Image Processing 45, 269–294 (1989)

    Article  Google Scholar 

  62. Merrill, R.D.: Representation of contours and regions for efficient computer search. Communications of the ACM 16(2), 69–82 (1973)

    Article  MathSciNet  Google Scholar 

  63. Montanvert, A., Meer, P., Rosenfeld, A.: Hierarchical image analysis using irregular tesselations. PAMI 13(4), 307–316 (1991)

    Google Scholar 

  64. Morse, P.: Concepts of use in contour map processing. Communications of the ACM 12(3), 147–152 (1969)

    Article  MATH  Google Scholar 

  65. Nicol, C.J.: A systolic approach for real time connected component labeling. Computeer vision and Image understanding 61(1), 17–31 (1995)

    Article  Google Scholar 

  66. Pavlidis, T.: Algorithms for Graphics and Image Processing. Computer Science, Washington (1982)

    Google Scholar 

  67. Pietikainen, M., Rosenfeld, A., Walter, I.: Split and link algorithms for image segmentation. Pattern Recognition 15(4), 287–298 (1982)

    Article  Google Scholar 

  68. Raman, S.V., Sarkar, S., Boyer, K.L.: Hypothesizing structures in edge-focused cerebral magnetic resonance images using graph-theoretic cycle enumeration. CVGIP: Image Understanding 57(1), 81–98 (1993)

    Article  Google Scholar 

  69. Rosenfeld, A.: Digital topology. Amer. math. monthly 86, 621–630 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  70. Rosenfeld, A.: Picture Languages. Academic Press, London (1979)

    MATH  Google Scholar 

  71. Rosenfeld, A., Kak, A.: Digital Picture Processing, vol. 2. Academic Press, London (1982)

    Google Scholar 

  72. Samet, H.: Region representation: Quadtrees from boundary codes. ACM: Graphics and Image Processing 23(3), 163–170 (1980)

    MATH  Google Scholar 

  73. Sebbahi, A., Herment, A., de Cesare, A., Mousseaux, E.: Multimodality cardiovascular image segmentation using a deformable contour model. Computerized Medical Imaging and Graphics 21(2), 79–89 (1997)

    Article  Google Scholar 

  74. Shapiro, L.G.: Connected component labeling and adjacency graph construction. In: Kong, Rosenfeld (eds.) Topological Algorithms for Digital Image Processing, Machine Intelligence and Pattern Recognition, vol. 19. Elsevier, Amsterdam (1996)

    Google Scholar 

  75. Singleton, K.R., Pohost, G.M.: Automatic cardiac mr image segmentation using edge detection by tissue classification in pixel neigborhoods. Magnetic Resonance in Medecine 37, 418–424 (1997)

    Article  Google Scholar 

  76. Suk, M.: A new segmentation technique based on partition mode test. PaRe 16(5), 469–480 (1983)

    Google Scholar 

  77. Tanimoto, S.L.: Image data structures. In: Tanimoto, S.L., Klinger, A. (eds.) Structured Computer Vision, pp. 31–56. Academic Press, New York (1980)

    Google Scholar 

  78. Tutte, W.T.: A census of planar maps. Canad. J. Math. 15, 249–271 (1963)

    Article  MATH  MathSciNet  Google Scholar 

  79. Vialard, A.: Chemins euclidiens: Un modèle de représentation des contours discrets. Phd thesis, Université Bordeaux 1 (1996)

    Google Scholar 

  80. Vialard, A.: Geometrical parameters extraction from discrete paths. In: Miguet, S., Ubéda, S., Montanvert, A. (eds.) DGCI 1996. LNCS, vol. 1176, pp. 24–35. Springer, Heidelberg (1996)

    Google Scholar 

  81. Vialard, A., Braquelaire, J.P.: Transformations géométriques de courbes discrètes 2D. In 3èmes journées de l’AFIG (Marseille) (1995)

    Google Scholar 

  82. Willersinn, D., Kropatsch, W.G.: Dual graph contraction for irregular pyramids. In: International Conference on Pattern Recogntion D: Parallel Computing, Jerusalem, Israel, pp. 251–256 (1994); International Association for Pattern Recognition

    Google Scholar 

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Authors and Affiliations

  1. LaBRI, Laboratoire Bordelais de Recherche en Informatique, UMR 5800, Université Bordeaux 1, 351, cours de la Libération, 33405, Talence, France

    Achille Braquelaire

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  1. Achille Braquelaire
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  1. GREYC CNRS UMR 6072, Image Team, Université de Caen Basse-Normandie, 6, Boulevard Maréchal Juin, 14050, Caen Cedex, France

    Luc Brun

  2. Dipartimento di Ingegneria dell’Informazione ed Ingegneria Elettrica, Università di Salerno, via P.te Don Melillo, I-84084, Fisciano, SA), Italy

    Mario Vento

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Braquelaire, A. (2005). Representing and Segmenting 2D Images by Means of Planar Maps with Discrete Embeddings: From Model to Applications. In: Brun, L., Vento, M. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2005. Lecture Notes in Computer Science, vol 3434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31988-7_10

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  • DOI: https://doi.org/10.1007/978-3-540-31988-7_10

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