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 an d two pulse stages, was constructed to obtain three-dimensional (3-D) surfa ce 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 independ ent of the x- and y-coordinates of the object. To summarize the information about shape contained in the 62 coefficients, a principal component analys is of the standardized spherical harmonic coefficients of each fruit was ma de. The contribution of each of the first seven principal components was fo und to exceed that of a single variable. The first three principal componen ts 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) co mponent score and the volume. A scatter diagram of the 1(s)t and 2(nd) prin cipal components failed to group the species studied.