Abstract
A measurement system, which consisted of a CCD laser displacement sensor and two pulse stages, was constructed to obtain three-dimensional (3-D) surface data of Citrus fruit. Fruits of 58 species of three specimens each were measured. By expanding the data measured in a series of spherical harmonic functions, a set of expansion coefficients to characterize the object shape was obtained. The data was normalized to make the coefficients be independent of the x- and y-coordinates of the object. To summarize the information about shape contained in the62 coefficients, a principal component analysis of the standardized spherical harmonic coefficients of each fruit was made. The contribution of each of the first seven principal components was found to exceed that of a single variable. The first three principal components had a cumulative contribution of 0.823.Analysis of variance showed that the variance due to between-species as tested against the variance due to within-species was significant for the 1st,2nd, 3rd, 4th, 7thcomponent score and the volume. A scatter diagram of the 1st and 2nd principal components failed to group the species studied.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Brechbühler, C., G. Gerig & O. Kubler, 1995. Parametrization of closed surfaces for 3–D shape description. Computer Vision, Graphics and Image Processing 61(2): 154–170.
Fan, J. & L.B. Wolff, 1997. Surface curvature and shape reconstruction from unknown multiple illumination and integrability. Computer Vision and Image Understanding 65(2): 347–359.
Furuta, N., S. Ninomiya, N. Takahashi, H. Ohmori & Y. Ukai, 1995. Quantitative evaluation of soybean (Glycine max L.Merr.) leaflet shape by principal component scores based on elliptic Fourier descriptor. Breeding Science 45: 315–320.
Iwata, H., S. Niikura, S. Matsuura, Y. Takano & Y. Ukai, 1998. Evaluation of variation of root shape of Japanese radish (Raphanus sativus L.) based on image analysis using elliptic Fourier descriptors. Euphytica 102: 143–149.
Kuhl, F.P. & C.R. Giardina, 1982. Elliptic Fourier features of a closed contour. Computer Graphics and Image Processing 18: 236–258.
Masuda, H., 1985. Size and shape of particles. J Soc Powder Tech Japan 22: 42–50.
Max, N.L. & E.D. Getzoff, 1988. Spherical harmonic molecular surfaces. IEEE Conf Computer Graphics and Applications July: 42–50.
Ninomiya, S., R. Ohsawa & M. Yoshida, 1995. Evaluation of buckwheat and Tartary buckwheat kernel shape by the elliptic Fourier method. In: T. Matano & A. Ujihara (Eds.), Current Advances in Buckwheat Research, pp. 389–396. Shinshu University Press, Matsumoto.
Rosenfeld, A. & A.C. Kak, 1976. Digital Picture Processing. Academic Press, New York. pp. 406–407.
Sakai, N. & S. Yonekawa, 1991. Three dimensional image analysis of the shape of soybean seed. Journal of Food Engineering 15: 221–234.
Tanaka, C., 1933. Citrus studies, 3rd Edition, Yokendo, Tokyo. pp. 38–178.
Takahashi, I., 1964. Citrus, Yokendo, Tokyo. pp. 58–120.
Yu, Z., H. Iwata, W. Ding, T. Yoshida, Y. Ukai & T. Akihama, 1997. Genetic evaluation of Citrus fruit shape by analysis based on elliptic Fourier Descriptor. Breeding Science, 47 (Suppl. 2): 257.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ding, W., Nesumi, H., Takano, Y. et al. Quantitative evaluation of the three-dimensional fruit shape and size of Citrus species based on spherical harmonic descriptors. Euphytica 114, 103–115 (2000). https://doi.org/10.1023/A:1003963214304
Issue Date:
DOI: https://doi.org/10.1023/A:1003963214304