Abstract
The method here proposed is based on the idea that the object of interest is first decomposed in a set of cubes under d∞. This decomposition is known to form a partition. The required moments are computed as a sum of the moments of the partition. The moments of each cube can be computed in terms of a set of very simple expressions using the center of the cube and its radio. The method provides integral accuracy by applying the exact definition of moments over each cube of the partition. One interesting feature of our proposal is that once the partition is obtained, moment computation is faster than with earlier methods.
Francisco Cuevas is in a post-doctoral stay at the Centra de Investigatión en Computatión of the Instituto Politécnico Nacional.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
M. K. Hu, Visual pattern recognition by moment invariants, IRE Transactions on Information Theory, 179–187, 1962.
C. H. Lo and H. S. Don, 3-D moment forms: Their construction and application to object identification and positioning, IEEE Transactions on Pattern Analysis and Machine Intelligence, 11:1 53-1064, 1989.
S. C. Pei and L. G. Liou, Using moments to acquire the motion parameters of a deformable object without correspondences, Image Vision and Computing, 12:475–485, 1994.
J. Shen and B. C. Li, Fast determination of center and radius of spherical surface by use of moments, in Proceedings of the 8th Scandinavian Conference on Image Analysis, Tromso, Norway, pp. 565–572, 1993.
D. Cyganski, S. J. Kreda and J. A. Orr, Solving for the general linear transformation relating 3-D objects from the minimum moments, in SPIE Intelligent Robots and Computer Vision VII, Proceedings of the SPIE, Vol. 1002, pp. 204–211, Bellingham, WA, 1988.
B. C. Li, The moment calculation of polyhedra, Pattern Recognition, 26:1229–1233, 1993.
B. C. Li and J. Shen, Pascal triangle transform approach to the calculation of 3D moments, CVGIP: Graphical Models and Image Processing, 54:301–307, 1992.
B. C. Li and S. D. Ma, Efficient computation of 3D moments, in Proceedings of 12 the International Conference on Pattern Recognition, Vol 1, pp. 22–26, 1994.
Z. L. Budrikis and M. Hatamian, Moment calculations by digital filters, AT&T Bell Lab. Tech. J. 63:217–229, 1984.
L. Yang and F. Albregtsen and T. Taxt, Fast computation of three-dimensional geometric moments using a discrete divergence theorem and a generalization to higuer dimensions, CGVIP: Graphical models and image processing, 59(2):97–108, 1997.
H. Sossa, C. Yañez and J. L Díaz, Computing geometric moments using morphological erosions, Pattern Recogntition, 34(2), 2001.
M. Dai, P. Baylou and M. Najim, An efficient algorithm for computation of shape moments from run-length codes or chain codes, Pattern Recognition, 25(10): 1119–1128, 1992.
J. Flusser, Refined moment calculation using image block representation, IEEE Transactions on Image Processing, 9(11): 1977–1978, 2000.
J. D. Díaz de León and J. H. Sossa, Mathematical Morphology based on linear combined metric spaces on Z2 (Part I): Fast distance transforms, Journal of Mathematical Imaging and Vision, 12:137–154, 2000.
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
Azuela, J.H.S., de la Rosa, F.C., Benitez, H. (2002). Efficient Computation of 3-D Moments in Terms of an Object’s Partition. In: Caelli, T., Amin, A., Duin, R.P.W., de Ridder, D., Kamel, M. (eds) Structural, Syntactic, and Statistical Pattern Recognition. SSPR /SPR 2002. Lecture Notes in Computer Science, vol 2396. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-70659-3_31
Download citation
DOI: https://doi.org/10.1007/3-540-70659-3_31
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44011-6
Online ISBN: 978-3-540-70659-5
eBook Packages: Springer Book Archive