Computes an spectrum of harmonic Fourier power. The power is proportional to the harmonic amplitude and can be considered as a measure of shape information. As the rank of harmonic increases, the power decreases and adds less and less information. We can evaluate the number of harmonics that we must select, so their cumulative power gathers 99% of the total cumulative power (Claude, 2008).

## Usage

efourier_power(
x,
first = TRUE,
thresh = c(0.8, 0.85, 0.9, 0.95, 0.99, 0.999),
plot = TRUE,
ncol = NULL,
nrow = NULL
)

## Arguments

x

An object of class efouriercomputed with efourier().

first

Logical argument indicating whether to include the first harmonic for computing the power. See Details.

thresh

A numeric vector indicating the threshold power. The number of harmonics needed for such thresholds will then be computed.

plot

Logical argument indicating whether to produce a plot.

ncol, nrow

The number of rows or columns in the plot grid. Defaults to NULL, i.e., a square grid is produced.

## Value

A list with the objects:

• cum_power, a data.frame object with the accumulated power depending on the number of harmonics

## Details

Most of the shape "information" is contained in the first harmonic. This is not surprising because this is the harmonic that best fits the outline, and the size of ellipses decreases as for explaining successive residual variation. However, one may think that the first ellipse does not contain relevant shape information, especially when differences one wants to investigate concern complex outlines. By using first = FALSE it is possible to remove the first harmonic for this computation. When working on a set of outlines, high-rank-harmonics can contain information that may allow groups to be distinguished (Claude, 2008).

Adapted from Claude (2008). pp. 229.

## References

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

## Examples

library(pliman)
pw <- efourier(contours) |> efourier_power()