Abstract
Binary mathematical morphology is a set theoretical approach to multidimensional signal processing. It enables extraction of shape features and is thus a well known and successfully applied kind of operation for image processing and recognition tasks. Nevertheless, a system theoretical treatment of these operations seems to be difficult, due to its mathematical origin of integral geometry. A system theoretical description of binary mathematical morphology is given in the present paper that allows to design realizations of binary morphological operations following methods from classical linear systems theory in a very favorable way. The advantage of the proposed correspondence description is exemplary shown in the development of a matching technique for shape varying object clusters.
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References
Q.-S. Chen M. Defrise F. Deconinck (1994 (December)) ArticleTitleSymmetric phase-only matched filtering of fourier-mellin transforms for image registration and recognition IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI 16 IssueID12 1156–1168 Occurrence Handle10.1109/34.387491
H. Hadwiger (1950) ArticleTitleMinkowskische Addition und Subtraktion beliebiger Punktemengen und die Theoreme von Erhard Schmidt Mathematische Zeitschrift 53 210–218 Occurrence Handle10.1007/BF01175656 Occurrence Handle0040.38301 Occurrence Handle12,631f
H. Hadwiger (1957) Vorlesungen über Inhalt, Oberfläche und Isoperimetrie Springer Verlag Berlin
P. Maragos R.W. Schafer (1987(August)) ArticleTitleMorphological filters – Part I: their set-theoretic analysis and relations to linear shift-invariant filters. IEEE Transactions on Acoustics, Speech and Singal Processing, ASSP 35 IssueID8 1153–1169 Occurrence Handle10.1109/TASSP.1987.1165259 Occurrence Handle88f:94011
G. Matheron (1975) Random sets and integral geometry Wiley New York, USA
H. Minkowski (1903) ArticleTitleVolumen und Oberfläche Mathematische Annalen 57 447–495 Occurrence Handle10.1007/BF01445180 Occurrence Handle34.0649 Occurrence Handle1511220
H. Minkowski (1911) Gesammelte abhandlungen Teubner Verlag Berlin
G.X. Ritter J.N. Wilson (1996) Handbook of computer vision algorithms in image algebra CRC Press New York, USA
J. Serra (1982) Image analysis and mathematical morphology Academic Press London, Great Britain
Velten, J., & Kummert, A. (2004, July). Implementation of a high-performance hardware architecture for binary morphological image processing operations. In Proceedings of the 47th IEEE International Midwest Symposium on Circuits and Systems, MWSCAS, vol. 2, pp. 241–244, Hiroshima, Japan, 2004.
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Published online: April 2006
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Velten, J., Kummert, A. A Multi-dimensional Systems Theory Framework for Binary Mathematical Morphology. Multidim Syst Sign Process 17, 211–217 (2006). https://doi.org/10.1007/s11045-005-6229-2
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DOI: https://doi.org/10.1007/s11045-005-6229-2