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Normalized Fourier coefficients

Source: R/utils_efourier.R
efourier_norm.Rd

The first harmonic defines an ellipse that best fits the outlines. One can use the parameters of the first harmonic to “normalize” the data so that they can be invariant to size, rotation, and starting position of the outline trace. This approach is referred to in the literature as the normalized elliptic Fourier. efourier_norm() calculates a new set of Fourier coefficients An, Bn, Cn, Dn that one can use for further multivariate analyses (Claude, 2008).

Usage

efourier_norm(x, start = FALSE)

Arguments

x

An object computed with efourier().

start

Logical value telling whether the position of the starting point has to be preserved or not.

Value

A list with the following components:

  • A, B, C, D for harmonic coefficients.

  • size the magnitude of the semi-major axis of the first fitting ellipse.

  • theta angle, in radians, between the starting and the semi-major axis of the first fitting ellipse.

  • psi orientation of the first fitting ellipse

  • a0 and c0, harmonic coefficients.

  • lnef the concatenation of coefficients.

  • nharm the number of harmonics used.

Details

Adapted from Claude (2008). pp. 226.

References

Claude, J. (2008) Morphometrics with R, Use R! series, Springer 316 pp.

Examples

if (interactive() && requireNamespace("EBImage")) {
library(pliman)
leaf1 <- contours[[4]]
plot_polygon(leaf1)

# compute the Fourier coefficients
ef <- efourier(leaf1)
efourier_coefs(ef)

# Normalized Fourier coefficients

efn <- efourier_norm(ef)
efourier_coefs(efn)
}