Computing Homology Group Generators of Images Using Irregular Graph Pyramids

Conference object English OPEN
Peltier , Samuel; Ion , Adrian; Haxhimusa , Yll; Kropatsch , Walter; Damiand , Guillaume;
  • Publisher: Springer Berlin / Heidelberg
  • Related identifiers: doi: 10.1007/978-3-540-72903-7_26
  • Subject: [ INFO.INFO-DS ] Computer Science [cs]/Data Structures and Algorithms [cs.DS]

International audience; We introduce a method for computing homology groups and their generators of a 2D image, using a hierarchical structure i.e. irregular graph pyramid. Starting from an image, a hierarchy of the image is built, by two operations that preserve homolo... View more
  • References (21)
    21 references, page 1 of 3

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

    2. Kovalevsky, V.A.: Digital Geometry Based on the Topology of Abstract Cellular Complexes. In Chassery, J.M., Francon, J., Montanvert, A., R´eveill`es, J.P., eds.: G´eometrie Discr`ete en Imagery, Fondements et Applications, Strasbourg, France (1993) 259-284

    3. Agoston, M.K.: Algebraic Topology, a first course. Pure and applied mathematics. Marcel Dekker Ed. (1976)

    4. Allili, M., Mischaikow, K., Tannenbaum, A.: Cubical homology and the topological classification of 2d and 3d imagery. In: Proceedings of International Conference Image Processing. Volume 2. (2001) 173-176

    5. Sonka, M., Hlavac, V., Boyle, R.: Image Processing, Analysis and Machine Vision. Brooks/Cole Publishing Company (1999)

    6. Kaczynksi, T., Mischaikow, K., Mrozek, M.: Computational Homology. Springer (2004)

    7. Niethammer, M., Stein, A.N., Kalies, W.D., Pilarczyk, P., Mischaikow, K., Tannenbaum, A.: Analysis of blood vessels topology by cubical homology. In: Proceedings of International Conference Image Processing. Volume 2. (2002) 969-972

    8. Damiand, G., Peltier, S., Fuchs, L.: Computing homology for surfaces with generalized maps: Application to 3d images. In: Procedings of 2nd International Symposium on Visual Computing. Volume 4292 of LNCS., Lake Tahoe, Nevada, USA, Springer-verlag (2006) 1151-1160

    9. Munkres, J.R.: Elements of algebraic topology. Perseus Books (1984)

    10. Jolion, J.M., Rosenfeld, A.: A Pyramid Framework for Early Vision. Kluwer (1994)

  • Metrics
Share - Bookmark