Abstract
Hierarchical image representations have been addressed by various models by the past, the max-tree being probably its best representative within the scope of Mathematical Morphology. However, the max-tree model requires to impose an ordering relation between pixels, from the lowest values (root) to the highest (leaves). Recently, the α-tree model has been introduced to avoid such an ordering. Indeed, it relies on image quasi-flat zones, and as such focuses on local dissimilarities. It has led to successful attempts in remote sensing and video segmentation. In this paper, we deal with the problem of α-tree computation, and propose several efficient schemes which help to ensure real-time (or near-real time) morphological image processing.
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
Martin, D., Fowlkes, C., Tal, D., Malik, J.: A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: Proceedings of the 8th International Conference on Computer Vision, Vancouver, Canada, vol. 2, pp. 416–425 (July 2001)
Matas, P., Dokladalova, E., Akil, M., Georgiev, V., Poupa, M.: Parallel hardware implementation of connected component tree computation. In: 2010 International Conference on Field Programmable Logic and Applications (FPL), August 31-September 2, pp. 64–69 (2010)
Merciol, F., Lefèvre, S.: Fast image and video segmentation based on α-tree multiscale representation. In: International Conference on Signal Image Technology Internet Systems, Naples, Italy (November 2012)
Najman, L., Couprie, M.: Building the component tree in quasi-linear time. IEEE Transactions on Image Processing 15(11), 3531–3539 (2006)
Ouzounis, G., Syrris, V., Gueguen, L., Soille, P.: The switchboard platform for interactive image information mining. In: Soille, P., Iapaolo, M., Marchetti, P., Datcu, M. (eds.) Proc. of 8th Conference on Image Information Mining, pp. 26–30. ESA-EUSC-JRC (October 2012)
Ouzounis, G.K., Soille, P.: Pattern spectra from partition pyramids and hierarchies. In: Soille, P., Pesaresi, M., Ouzounis, G.K. (eds.) ISMM 2011. LNCS, vol. 6671, pp. 108–119. Springer, Heidelberg (2011)
Perret, B., Lefèvre, S., Collet, C., Slezak, E.: Hyperconnections and hierarchical representations for grayscale and multiband image processing. IEEE Transactions on Image Processing 21(1), 14–27 (2012)
Salembier, P., Garrido, L.: Binary partition tree as an efficient representation for image processing, segmentation, and information retrieval. IEEE Transactions on Image Processing 9(4), 561–576 (2000)
Salembier, P., Oliveras, A., Garrido, L.: Anti-extensive connected operators for image and sequence processing. IEEE Transactions on Image Processing 7(4), 555–570 (1998)
Serra, J.: Anamorphoses and function lattices. In: Dougherty, E.R. (ed.) Mathematical Morphology in Image Processing, ch. 13, pp. 483–523. Marcel Dekker, New York (1993)
Soille, P.: Constrained connectivity for hierarchical image partitioning and simplification. IEEE Transactions on Pattern Analysis and Machine Intelligence 30(7), 1132–1145 (2008)
Soille, P., Grazzini, J.: Constrained connectivity and transition regions. In: Wilkinson, M.H.F., Roerdink, J.B.T.M. (eds.) ISMM 2009. LNCS, vol. 5720, pp. 59–69. Springer, Heidelberg (2009)
Soille, P., Najman, L.: On morphological hierarchical representations for image processing and spatial data clustering. In: Köthe, U., Montanvert, A., Soille, P. (eds.) WADGMM 2010. LNCS, vol. 7346, pp. 43–67. Springer, Heidelberg (2012)
Tarjan, R.E.: Efficiency of a good but not linear set union algorithm. Journal of the ACM 22, 215–225 (1975)
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
Havel, J., Merciol, F., Lefèvre, S. (2013). Efficient Schemes for Computing α-tree Representations. 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_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-38294-9_10
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)