Quantitative evaluation of the three-dimensional fruit shape and size of Citrus species based on spherical harmonic descriptors

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 the 62 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 1(st), 2(nd), 3(rd), 4(th), 7(th) component score and the volume. A scatter diagram of the 1(s)t and 2(nd) principal components failed to group the species studied.