Description Usage Arguments Details Value Note References See Also Examples
View source: R/coreoutefourier.R
efourier
computes Elliptical Fourier Analysis (or Transforms or EFT)
from a matrix (or a list) of (x; y) coordinates.
1 2 3 4 5 6 7 8 
x 
A 
... 
useless here 
nb.h 

smooth.it 

verbose 

norm 
whether to normalize the coefficients using efourier_norm 
start 
logical whether to consider the first point as homologous 
For the maths behind see the paper in JSS.
Normalization of coefficients has long been a matter of trouble,
and not only for newcomers. There are two ways of normalizing outlines: the first,
and by far the msot used, is to use a "numerical" alignment, directly on the
matrix of coefficients. The coefficients of the first harmonic are consumed
by this process but harmonics of higher rank are normalized in terms of size
and rotation. This is sometimes referred as using the "first ellipse", as the
harmonics define an ellipse in the plane, and the first one is the mother of all
ellipses, on which all others "roll" along. This approach is really convenient
as it is done easily by most software (if not the only option) and by Momocs too.
It is the default option of efourier
.
But here is the pitfall: if your shapes are prone to bad aligments among all
the first ellipses, this will result in poorly (or even not at all) "homologous" coefficients.
The shapes prone to this are either (at least roughly) circular and/or with a strong
bilateral symmetry. You can try to use stack
on the Coe
object
returned by efourier
. Also, when plotting PCA using Momocs,
this will be strikingly clear though. This phenomenon will result in two clusters,
and more strikingly into upsidedown (or 180 degrees rotated)
shapes on the morphospace. If this happen, you should seriously consider
aligning your shapes before the efourier
step,
and performing the latter with no normalization (norm = FALSE
), since
it has been done before.
You have several options to align your shapes, using control points (or landmarks),
of Procrustes alignment (see fgProcrustes
) through their calliper
length (see coo_aligncalliper
), etc. You should also make the first
point homologous either with coo_slide
or coo_slidedirection
to minimize any subsequent problems.
I will dedicate (some day) a vignette or a paper to this problem.
A list with these components:
an 

bn 

cn 

dn 

ao 

co 

Directly borrowed for Claude (2008), and also called efourier
there.
Claude, J. (2008) Morphometrics with R, Use R! series, Springer 316 pp. Ferson S, Rohlf FJ, Koehn RK. 1985. Measuring shape variation of twodimensional outlines. Systematic Biology 34: 5968.
Other efourier: efourier_i
,
efourier_norm
, efourier_shape
1 2 3 4 5 6 7 
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.