Elliptical Fourier Analysis

Computes Elliptical Fourier Analysis of closed outlines based on x and y-coordinates coordinates.

Usage

efourier(x, nharm = 10, align = FALSE, center = FALSE, smooth_iter = 0)

Arguments

x

A matrix, a data.frame a list of perimeter coordinates, often produced with object_contour() or a vector of landmarks produced with landmarks() or landmarks_regradi().

nharm

An integer indicating the number of harmonics to use. Defaults to 10.

align

Align the objects before computing Fourier analysis? Defaults to FALSE. If TRUE, the object is first aligned along the major caliper with poly_align().

center

Center the objects on the origin before computing Fourier analysis? Defaults to FALSE. If TRUE, the object is first centered on the origin with poly_center().

smooth_iter

The number of smoothing iterations to perform. This will smooth the perimeter of the objects using poly_smooth().

Value

A list of class efourier with:

• the harmonic coefficients (an, bn, cn and dn)

• the estimates of the coordinates of the centroid of the configuration (a0 and c0).

• The number of rows (points) of the perimeter outline (nr).

• The number of harmonics used (nharm).

• The original coordinates (coords).

If x is a list of perimeter coordinates, a list of efourier objects will be returned as an object of class iefourier_lst.

Details

Adapted from Claude (2008). pp. 222-223.

References

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

Kuhl, F. P., and Giardina, C. R. (1982). Elliptic Fourier features of a closed contour. Computer Graphics and Image Processing 18, 236-258. doi: doi:10.1016/0146-664X(82)90034-X

Examples

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

#### default options
# 10 harmonics (default)
# without alignment

ef <- efourier(leaf1)
efourier_coefs(ef)

# object is aligned along the major caliper with `poly_align()`
# object is centered on the origin with `poly_center()`
# using a list of object coordinates
ef2 <- efourier(contours, align = TRUE, center = TRUE)
efourier_coefs(ef2)

# reconstruct the perimeter of the object
# Use only the first one for simplicity
plot_polygon(contours[[1]] |> poly_align() |> poly_center())
efourier_inv(ef2[[1]]) |> plot_contour(col = "red", lwd = 4)
}