Abstract
Quantification of shape remains an area of active study in the field of image analysis and machine vision. We present a comparative survey of three approaches to shape measurement: classical dimensionless ratios, harmonic analysis, and invariant moments, showing their suitability for classification of objects and other statistical analyses, including quantitative structure-property relationships. We show that for topologically simple shapes and well controlled imaging conditions, all three methods can provide robust classification of objects.
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References
S. Loncaric, “A survey of shape analysis techniques,” Pattern Recognition, 31 (8) (1998), 983–1001.
M. R. Teague, “Image analysis via the general theory of moments,” Journal of the Optical Society of America, 70 (8) (1980), 920–930.
M. K. Hu, “Visual pattern recognition by moment invariants,” IEEE Transactions on Information Theory, 8 (2) (1962), 179–187.
J. Flusser and T. Suk, “Pattern recognition by affine moment invariants,” Pattern Recognition, 26 (1) (1993), 167–174.
J. Flusser, “On the independence of rotation moment invariants,” Pattern Recognition, 33 (9) (2000), 1405–1410.
H. P. Schwartz and K. C. Shane, “Measurement of particle shape by Fourier analysis,” Sedimentology, 13 (3–4) (1969), 213–231.
R. Ehrlich and B. Weinberg, “An Exact Method for Characterization of Grain Shape,” SEPM Journal of Sedimentary Research, 40 (1) (1970), 205–212.
A. J. Haines and J. S. Crampton, “Improvements To The Method Of Fourier Shape Analysis As Applied In Morphometric Studies,” Palaeontology, 43 (4) (2000), 765–783.
P. E. Lestrel, Ed., Fourier Descriptors and Their Applications in Biology (Cambridge, UK: Cambridge University Press, 1997.)
F. B. Neal and J. C. Russ, Measuring Shape (Boca Raton, FL: CRC Press, 2012), 337–347.
C. Brechbühler, “Parametrization of Closed Surfaces for 3-D Shape Description,” Computer Vision and Image Understanding, 61 (2) (1995), 154–170.
N. Canterakis, “3D Zernike moments and Zernike affine invariants for 3D image analysis and recognition,” (Paper presented at the 11th Scandinavian Conference on Image Analysis, 1999.)
B. Ruthensteiner, N. Baeumler, and D. G. Barnes, “Interactive 3D volume rendering in biomedical publications.,” Micron, 41 (7) (2010), 886.e1–886.e17.
A. Ziegler, M. Ogurreck, T. Steinke, F. Beckmann, S. Prohaska, and A. Ziegler, “Opportunities and challenges for digital morphology.,” Biology direct, 5 (2010), 45.
K. Libbrecht, Field Guide to Snowflakes (St. Paul, MN: Voyageur Press, 2006), 102–107.
F. Kuhl and C. Giardina, “Elliptic Fourier features of a closed contour,” Computer Graphics and Image Processing, 18 (3) (1982), 236–258.
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© 2012 TMS (The Minerals, Metals & Materials Society)
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Neal, F.B., Russ, J.C. (2012). Shape Analysis and the Classification of Objects. In: De Graef, M., Poulsen, H.F., Lewis, A., Simmons, J., Spanos, G. (eds) Proceedings of the 1st International Conference on 3D Materials Science. Springer, Cham. https://doi.org/10.1007/978-3-319-48762-5_21
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DOI: https://doi.org/10.1007/978-3-319-48762-5_21
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-48573-7
Online ISBN: 978-3-319-48762-5
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