Abstract
In recent works, a new notion of component-graph has been introduced to extend the data structure of component-tree –and the induced antiextensive filtering methodologies– from grey-level images to multivalued ones. In this article, we briefly recall the main structural key-points of component-graphs, and we present the initial algorithmic results that open the way to the actual development of component-graph-based antiextensive filtering procedures.
The research leading to these results has received funding from the French Agence Nationale de la Recherche (Grant Agreement ANR-2010-BLAN-0205 03).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aho, A.V., Garey, M.R., Ullman, J.D.: The transitive reduction of a directed graph. SIAM J. Comput. 1(2), 131–137 (1972)
Angulo, J.: Geometric algebra colour image representations and derived total orderings for morphological operators–Part I: Colour quaternions. J. Vis. Commun. Image R. 21(1), 33–48 (2010)
Aptoula, E., Lefèvre, S.: A comparative study on multivariate mathematical morphology. Pattern Recogn. 40(11), 2914–2929 (2007)
Berger, C., Géraud, T., Levillain, R., Widynski, N., Baillard, A., Bertin, E.: Effective component tree computation with application to pattern recognition in astronomical imaging. In: ICIP, pp. 41–44 (2007)
Carlinet, E.: Extending the tree of shapes on colors. Master’s thesis, ENS Cachan (2012)
Cousty, J., Bertrand, G., Najman, L., Couprie, M.: Watershed cuts: Thinnings, shortest path forests, and topological watersheds. IEEE Trans. Pattern Anal. Mach. Intell. 32(5), 925–939 (2010)
Goutsias, J., Heijmans, H.J.A.M., Sivakumar, K.: Morphological operators for image sequences. Comp. Vis. Imag. Under. 62(3), 326–346 (1995)
Heijmans, H.: Theoretical aspects of gray level morphology. IEEE Trans. Pattern Anal. Mach. Intell. 13(6), 568–592 (1991)
Jones, R.: Connected filtering and segmentation using component trees. Comp. Vis. Imag. Under. 75(3), 215–228 (1999)
Monasse, P., Guichard, F.: Scale-space from a level lines tree. J. Vis. Commun. Image R. 11(2), 224–236 (2000)
Naegel, B., Passat, N.: Component-trees and multi-value images: A comparative study. In: Wilkinson, M.H.F., Roerdink, J.B.T.M. (eds.) ISMM 2009. LNCS, vol. 5720, pp. 261–271. Springer, Heidelberg (2009)
Najman, L., Couprie, M.: Building the component tree in quasi-linear time. IEEE Trans. Image Proc. 15(11), 3531–3539 (2006)
Passat, N., Naegel, B.: An extension of component-trees to partial orders. In: ICIP, pp. 3981–3984 (2009)
Passat, N., Naegel, B.: Component-trees and multivalued images: Structural properties. Technical report, INRIA-00611714 (2012), http://hal.inria.fr/inria-00611714
Ronse, C., Agnus, V.: Morphology on label images: Flat-type operators and connections. J. Math. Imaging Vis. 22(2), 283–307 (2005)
Salembier, P., Garrido, L.: Binary partition tree as an efficient representation for image processing, segmentation and information retrieval. IEEE Trans. Image Proc. 9(4), 561–576 (2000)
Salembier, P., Oliveras, A., Garrido, L.: Anti-extensive connected operators for image and sequence processing. IEEE Trans. Image Proc. 7(4), 555–570 (1998)
Soille, P.: Constrained connectivity for hierarchical image partitioning and simplification. IEEE Trans. Pattern Anal. Mach. Intell. 30(7), 1132–1145 (2008)
Urbach, E.R., Roerdink, J.B.T.M., Wilkinson, M.H.F.: Connected shape-size pattern spectra for rotation and scale-invariant classification of gray-scale images. IEEE Trans. Pattern Anal. Mach. Intell. 29(2), 272–285 (2007)
Velasco-Forero, S., Angulo, J.: Supervised ordering in ℝp: Application to morphological processing of hyperspectral images. IEEE Trans. Image Proc. 20(11), 3301–3308 (2011)
Wilkinson, M.H.F., Gao, H., Hesselink, W.H., Jonker, J.-E., Meijster, A.: Concurrent computation of attribute filters on shared memory parallel machines. IEEE Trans. Pattern Anal. Mach. Intell. 30(10), 1800–1813 (2008)
Xu, Y., Géraud, T., Najman, L.: Morphological filtering in shape spaces: Applications using tree-based image representations. In: ICPR, pp. 485–488 (2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Naegel, B., Passat, N. (2013). Towards Connected Filtering Based on Component-Graphs. In: Hendriks, C.L.L., Borgefors, G., Strand, R. (eds) Mathematical Morphology and Its Applications to Signal and Image Processing. ISMM 2013. Lecture Notes in Computer Science, vol 7883. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38294-9_30
Download citation
DOI: https://doi.org/10.1007/978-3-642-38294-9_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38293-2
Online ISBN: 978-3-642-38294-9
eBook Packages: Computer ScienceComputer Science (R0)