Abstract
In this paper we propose a series of novel morphological operators that are anisotropic, and adapt themselves to the local orientation in the image. This new morphology is therefore rotation invariant; i.e. rotation of the image before or after the operation yields the same result.We present relevant properties required by morphology, as well as other properties shared with common morphological operators. Two of these new operators are increasing, idempotent and absorbing, which are required properties for a morphological operator to be used as a sieve. A sieve is a sequence of filters of increasing size parameter, that can be used to construct size distributions.As an example of the usefulness of these newoperators, we show how a sieve can be build to estimate a particle or pore length distribution, as well as the elongation of those features.
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References
J. Serra. Image Analysis and Mathematical Morphology. Academic Press, London, 1982.
C.L. Luengo Hendriks and L.J. van Vliet. A rotation-invariant morphology using anisotropic structuring elements. in preparation.
R. van den Boomgaard. Mathematical Morphology: Extensions Towards Computer Vision. Ph.d. thesis, University of Amsterdam, Amsterdam, 1992.
P. Soille. Morphological Image Analysis. Springer-Verlag, Berlin, 1999.
G. Matheron. Random Sets and Integral Geometry. JohnWiley and Sons, NewYork, 1975.
P. Soille. Morphological operators with discrete line segments. In G. Borgefors, I. Nyström, and G. Sanniti di Baja, editors, DGCI 2000, 9th Discrete Geometry for Computer Imagery, volume 1953 of LNCS, pages 78–98, Uppsala, Sweden, 2000.
J.A. Bangham, P. Chardaire, C.J. Pye, and P.D. Ling. Multiscale nonlinear decomposition: The sieve decomposition theorem. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18(5):529–539,1996.
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© 2001 Springer-Verlag Berlin Heidelberg
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Hendriks, C.L.L., van Vliet, L.J. (2001). A Rotation-Invariant Morphology for Shape Analysis of Anisotropic Objects and Structures. In: Arcelli, C., Cordella, L.P., di Baja, G.S. (eds) Visual Form 2001. IWVF 2001. Lecture Notes in Computer Science, vol 2059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45129-3_34
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DOI: https://doi.org/10.1007/3-540-45129-3_34
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