Abstract
For a given real triangle T its discretization on a discrete point set S consists of points from S which fall into T. If the number of such points is finite, the obtained discretization of T will be called discrete triangle.
In this paper we show that the discrete moments having the order up to 3 characterize uniquely the corresponding discrete triangle if the discretizationing set S is fixed.
Of a particular interest is the case when S is the integer grid, i.e., S = Z 2. Then the discretization of a triangle T is called digital triangle. It turns out that the proposed characterization preserves a coding of digital triangles from an integer grid of a given size, say m x m within an O(log m) amount of memory space per coded digital triangle. That is the theoretical minimum.
The author is also with the Mathematical institute of Serbian Academy of Sciences, Belgrade.
Chapter PDF
Similar content being viewed by others
References
Dorst, L., Smeulders, A. W. M.: Discrete representation of straight lines. IEEE Trans. Pattern Anal. Machine Intell. 6 (1984) 450–463.
Forchhammer, S., Kim, C. E.: Digital squares. IEEE Trans. Pattern Anal. Machine Intell. 22 (1988) 672–674.
Hu, M., Visual pattern recognition by moment invariants, IRE Trans. Inf. Theory 8 (1962) 179–187.
Ivić, A., Koplowitz, J., Žunić, J.: On the number of digital convex polygons inscribed into an (m,m)-grid. IEEE Trans. on Information Theory. 40 (1994) 1681–1686.
Jiang, X. Y., Bunke, H.: Simple and fast computation of moments. Pattern Recognition. 24 (1991) 801–806.
Leu, J.-G.: Computing a shape’s moments from its boundary. Pattern Recognition. 24 (1991) 949–957.
Lindenbaum, M., Koplowitz, J.: A new parametrization of digital straight lines. IEEE Trans. Pattern Anal. Machine Intell. 13 (1991) 847–852.
Mamistvalov, A. G.: n-Dimensional moment invariants and conceptual mathematical theory of recognition n-dimensional solids. IEEE Trans. Pattern Anal. Machine Intell. 20 (1998) 819–831.
Nakamura, A., Aizawa, K.: Digital squares. Computer Vision, Graphics Image Processing 49 (1990) 357–368.
Singer, M. H.: A general approach to moment calculation for polygons and line segments. Pattern Recognition. 26 (1993). 1019–1028.
Worring, M., Smeulders, A. W. M.: Digitized circular arcs: Characterization and parameter estimation. IEEE Trans. Pattern Anal. Machine Intell. 17 (1995) 587–598.
Žunić, J., Acketa, M. D.: A general coding scheme for families of digital curve segments. Graphical Models and Image Processing 60 (1998) 437–460.
Žunić, J., Sladoje, N.: Efficiency of Characterizing Ellipses and Ellipsoids by Discrete Moments. IEEE Trans. Pattern Anal. Machine Intell. 22 (2000) 407–414.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Žunić, J. (2002). On Characterization of Discrete Triangles by Discrete Moments. In: Braquelaire, A., Lachaud, JO., Vialard, A. (eds) Discrete Geometry for Computer Imagery. DGCI 2002. Lecture Notes in Computer Science, vol 2301. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45986-3_21
Download citation
DOI: https://doi.org/10.1007/3-540-45986-3_21
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43380-4
Online ISBN: 978-3-540-45986-6
eBook Packages: Springer Book Archive