Abstract
In this paper connected operators from mathematical morphology are extended to a wider class of operators, which are based on connectivities in higher dimension spaces, similar to scale spaces which will be called attribute spaces. Though some properties of connected filters are lost, granulometries can be defined under certain conditions, and pattern spectra in most cases. The advantage of this approach is that regions can be split into constituent parts before filtering more naturally than by using partitioning connectivities.
Keywords
- Mathematical morphology
- multi-scale analysis
- connected filters
- perceptual grouping
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References
U. Braga-Neto and J. Goutsias. A multiscale approach to connectivity. Comp. Vis. Image Understand., 89:70–107, 2003.
E. J. Breen and R. Jones. Attribute openings, thinnings and granulometries. Comp. Vis. Image Understand., 64(3):377–389, 1996.
H. J. A. M. Heijmans. Connected morphological operators for binary images. Comp. Vis. Image Understand., 73:99–120, 1999.
T. Y. Kong and A. Rosenfeld. Digital topology: Introduction and survey. Comp. Vision Graph. Image Proc., 48:357–393, 1989.
P. Maragos. Pattern spectrum and multiscale shape representation. IEEE Trans. Pattern Anal. Mach. Intell., 11:701–715, 1989.
P. Maragos and R. D. Ziff. Threshold decomposition in morphological image analysis. IEEE Trans. Pattern Anal. Mach. Intell., 12(5), 1990.
P. Monasse and F. Guichard. Fast computation of a contrast invariant image representation. IEEE Trans. Image Proc., 9:860–872, 2000.
P. Salembier, A. Oliveras, and L. Garrido. Anti-extensive connected operators for image and sequence processing. IEEE Trans. Image Proc., 7:555–570, 1998.
P. Salembier and J. Serra. Flat zones filtering, connected operators, and filters by reconstruction. IEEE Trans. Image Proc., 4:1153–1160, 1995.
J. Serra. Connectivity on complete lattices. J. Math. Imag. Vis., 9(3):231–251, 1998.
A. Sofou, C. Tzafestas, and P. Maragos. Segmentation of soilsection images using connected operators. In Int. Conf. Image Proc. 2001, pages 1087–1090, 2001.
C. S. Tzafestas and P. Maragos. Shape connectivity: Multiscale analysis and application to generalized granulometries. J. Math. Imag. Vis., 17:109–129, 2002.
E. R. Urbach and M. H. F. Wilkinson. Shape-only granulometries and grey-scale shape filters. In Proc. Int. Symp. Math. Morphology (ISMM) 2002, pages 305–314, 2002.
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Wilkinson, M.H. (2005). Attribute-Space Connected Filters. In: Ronse, C., Najman, L., Decencière, E. (eds) Mathematical Morphology: 40 Years On. Computational Imaging and Vision, vol 30. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3443-1_9
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DOI: https://doi.org/10.1007/1-4020-3443-1_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3442-8
Online ISBN: 978-1-4020-3443-5
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