Calcuates symmetry indices on OutCoe objects

For OutCoe objects obtained with efourier, calculates several indices on the matrix of coefficients: AD, the sum of absolute values of harmonic coefficients A and D; BC same thing for B and C; amp the sum of the absolute value of all harmonic coefficients and sym which is the ratio of AD over amp. See references below for more details.

Usage

symmetry(OutCoe)

Arguments

OutCoe: efourier objects

Value

a matrix with 4 colums described above.

Note

What we call symmetry here is bilateral symmetry. By comparing coefficients resulting from efourier, with AD responsible for amplitude of the Fourier functions, and BC for their phase, it results in the plane and for fitted/reconstructed shapes that symmetry. As long as your shapes are aligned along their bilateral symmetry axis, you can use the approach coined by Iwata et al., and here implemented in Momocs.

References

Below: the first mention, and two applications.

Iwata, H., Niikura, S., Matsuura, S., Takano, Y., & Ukai, Y. (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.
Iwata, H., Nesumi, H., Ninomiya, S., Takano, Y., & Ukai, Y. (2002). The Evaluation of Genotype x Environment Interactions of Citrus Leaf Morphology Using Image Analysis and Elliptic Fourier Descriptors. Breeding Science, 52(2), 89-94. doi:10.1270/jsbbs.52.89
Yoshioka, Y., Iwata, H., Ohsawa, R., & Ninomiya, S. (2004). Analysis of petal shape variation of Primula sieboldii by elliptic fourier descriptors and principal component analysis. Annals of Botany, 94(5), 657-64. doi:10.1093/aob/mch190

Examples

bot.f <- efourier(bot, 12)
#> 'norm=TRUE' is used and this may be troublesome. See ?efourier #Details
res <- symmetry(bot.f)
hist(res[, 'sym'])