Shape Features of 2D Figures

Abstract:

The symmetry-diagram was originally defined for symmetry recognition. As a consequence it has been proven that the symmetry-diagram shows the unique shape property of the two-dimensional (2D) figures. The symmetry-diagram is different in the case of 2D figures having a different shape. It is very sensitive to the smallest change in the shape. The only exception for its applicability is the 2D figure having two or more concentric boundary loops.

• Periodical: Materials Science Forum (Volume 659)
• Pages: 459-466
• DOI: https://doi.org/10.4028/www.scientific.net/MSF.659.459
• Online since: September 2010
• Authors: Zoltán Szakál, Ibolya Zsoldos
• Keywords: Shape Factor, Symmetry Detection, Symmetry Diagram

References

[1] Fischmeister H. F. (1974): Shape factors in quantitative microscopy, Zeitschrift für Metallkunde, Vol. 65, 558-562 p.

[2] Beddow J. K., Vetter A. F., Sissopn K. (1976a): Powder Metallurgy Review, Part I., Particle shape analysis, Powder Metallurgy International, Vol. 8, No. 2, 69-76. p.

[3] Beddow J. K., Vetter A. F., Sissopn K. (1976b): Powder Metallurgy Review, Part I., Particle shape analysis, Powder Metallurgy International, Vol. 8, No. 3, 107-109 p.

[4] Underwood E. E. (1976): Quantitative shape parameters for microstructural fetures, The Microscope, Vol. 24, 49-64 p.

[5] Pavlidis T. (1978): Survey. A review of algorithm for shape analysis, Computer Graphics and Images Processing, Vol. 7, 243-258 p.

[6] Roósz A., Réti T. (1978): A sztereometrikus metallográfia és mai alkalmazási lehetőségei, Bányászati és Kohászati Lapok, Kohászat, Vol. 111, No. 7, 308-313 p.

[7] Réti T. (1983): Mikroszkópos részecskék alakjának minősítése, Bányászati és Kohászati Lapok, Kohászat, Vol. 116 No. 12, 549-557 p.

[8] Exner H. E. (1987): Shape - A key problem in quantifying microstusture, Acta Stereologica, Vol. 6/III, 1023-1028 p.

[9] Flook A. (1987): The quantitative measurement of particle shape, Acta Stereologica, Vol. 6/III, 1009-1021 p.

[10] Sonka M., Hlavac V., Boyle R. (1993): Image Processing, Analysis and Machine Vision, Chapman and Hall Computing, London.

[11] Santolo L. A. (1976): Integral Geometry and Geometric Probability, Addision-Wsley, Reading, Massachusetts.

[12] Pratt W. K. (1987): Digital Image Processing, John Wiley and Sons, New York, 525-534 p.

[13] Parker J. R. (1994): Practical Computer Vision Using C, John Wiley and Sons, New York.

[14] Gácsi Z. (2001): Szereológia és képelemzés, Well-Press Kiadó Kft., 205-232 p.

[15] Nemes N. J. (1998): A tér a társadalomtudományban, Hirsner Rezső Szociálpolitikai Egyesület Kiadó, Budapest, 143.

[16] Csepeli ZS., Gácsi Z., Karalik GY., Lőrinczi J., Zsámbok D. (2001): Stereological characterisation of steel wide strip microstructures after normalising and thermomechanical rolling, Anyagok világa. Vol. 2. No 2.

DOI: 10.4028/www.scientific.net/msf.414-415.63

[17] Zahn C., Roskies R. Z. (1972): Fourier descriptors for plane closed curves, IEEE Trans. Computers, Vol. 21, 269-281 p.

DOI: 10.1109/tc.1972.5008949

[18] Bennett J. R., Mac Donald, J. S. (1975): On the mesurement of curvature in a quantized environment, IEEE Trasaction on Computers, Vol. 24. 803-819 p.

[19] Granlund G. H. (1972): Fourier preprocessing for hand print character recognition, IEEE Transaction on computers, Vol. C-21. 195-201p.

DOI: 10.1109/tc.1972.5008926

[20] Richard C. W., Hemami H. (1974): Identification of the three-dimensional objects Fourier descriptors of the boundary curve, IEEE Trasaction on System, Man, and Cybernetics, Vol. SMC-4. 371-378 p.

DOI: 10.1109/tsmc.1974.5408458

[21] Persoon E., Fu K S. (1977): Shape discrimination using Fourier Descriptors, IEEE Transaction on System, Man, and Cybernetics, Vol. SMC-7. 170-179 p.

DOI: 10.1109/tsmc.1977.4309681

[22] Réti T., Czinege I. (1989): Shape characterization of particles via generalized Fourier analysis, Journal of Microscopy, Vol. 156, 15-32 p.

DOI: 10.1111/j.1365-2818.1989.tb02903.x

[23] Tang X. (1998): Multiple competitive learning network fusion for object classification, IEEE Transactions on System, Man, and Cybernetics Part B, Vol. 28, 532-543 p.

DOI: 10.1109/3477.704292

[24] Szakal Z., Zsoldos I. (2008): The Symmetry-Diagram as a Tool of the Pattern Recognition, International Journal of Mathematical Models and Methods in Applied Sciences, Issue 4, Volume 2, 523-532 p.