Abstract
Geometrical properties of subsets of digital pictures play an important role in image analysis. Mathematical morphology is an approach to image processing which consists in transformations of subsets of digital pictures to facilitate subsequent processing [1,4,7,9,10,11,15,16,17]. In this paper a linear operator represented by a boolean circulant Toeplitz matrix, which transforms an ordered discrete even set of n points into its symmetric form with the common centroid is described.
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References
A. Arcelli and G. Massorati, “Regular arcs in digital contours”, CGIP, no. 4, pp. 339-360, 1975.
L. Berezin and N. Zhidkoy, Computing methods, Oxford: Pergamon Press, 1965.
P. Davies, Circulant matrices, New York: Wiley, 1979.
I. Hargittai, Symmetry, New York: Pergamon Press, 1986.
H. Freeman, “Computer processing of line-drawing images”, Computing Surveys, no.6, pp.57-97, 1974.
M.K. Hu, “Visual pattern recognition by moment invariants”, IRE Trans. on Infor. Theory, no.8, pp. 1-12, 1962.
R. Klette, “The m-dimensional grid point space”, CGIP, vol. 30, pp. 1–12, 1985.
S. Maitra, “Moment invariants”, Proc. IEEE, vol. 64, pp. 697–699, 1979.
A. Rosenfeld and J. LPfaltz, “Distance functions on digital pictures”, Pattern Recognition, vol. 1, pp. 35–51, 1968.
A. Rosenfeld, “Arcs and curves in digital pictures”, JACM, 1, pp. 146–160, 1973.
A. Rosenfeld, “Adjency in digital pictures”, Inform. Control, vol. 26, pp. 1264–1269, 1974.
A. Rosenfeld and A. C. Kak, Digital picture processing, New York: Academic Press, 1976.
A. Rosenfeld, Picture languages, New York: Academic Press, 1979.
F. Sloboda, “Toeplitz matrices, homothety and least squares approximation”, in Parallel Computing: Methods, Algorithms and Applications, D.J. Evans and C. Sutti, Eds., Bristol: Adam Hilger, 1989.
J. Sklansky and V. Gonzales, “Fast polygonal approximation of digitized curves”, Pattern recognition, no.12, pp.327-331, 1980.
J. Sklansky, R.L. Chazin and B.J. Hansen, “Minimum perimeter polygon of digitized silhouettes”, IEEE Trans. on Comp., no.3, pp.260-268, 1972.
G.T. Toussaint, Computational morphology, Amsterdam: North Holland, 1988.
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© 1992 Springer Science+Business Media New York
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Sloboda, F. (1992). On Symmetric Forms of Discrete Sets of Points and Digital Curves. In: Arcelli, C., Cordella, L.P., di Baja, G.S. (eds) Visual Form. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0715-8_49
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DOI: https://doi.org/10.1007/978-1-4899-0715-8_49
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