dfourier: Discrete cosinus transform

In vbonhomme/Momocs: Morphometrics using R

Discrete cosinus transform

Description

Calculates discrete cosine transforms, as introduced by Dommergues and colleagues, on a shape (mainly open outlines).

Usage

dfourier(coo, nb.h)

## Default S3 method:
dfourier(coo, nb.h)

## S3 method for class 'Opn'
dfourier(coo, nb.h)

## S3 method for class 'list'
dfourier(coo, nb.h)

## S3 method for class 'Coo'
dfourier(coo, nb.h)

Arguments

coo	a matrix (or a list) of (x; y) coordinates
nb.h	numeric the number of harmonics to calculate

Value

a list with the following components:

• an the A harmonic coefficients

• bn the B harmonic coefficients

• mod the modules of the points

• arg the arguments of the points

Note

This method has been only poorly tested in Momocs and should be considered as experimental. Yet improved by a factor 10, this method is still long to execute. It will be improved in further releases but it should not be so painful right now. It also explains the progress bar. Shapes should be aligned before performing the dct transform.

Silent message and progress bars (if any) with options("verbose"=FALSE).

References

• Dommergues, C. H., Dommergues, J.-L., & Verrecchia, E. P. (2007). The Discrete Cosine Transform, a Fourier-related Method for Morphometric Analysis of Open Contours. Mathematical Geology, 39(8), 749-763. doi:10.1007/s11004-007-9124-6

• Many thanks to Remi Laffont for the translation in R).

See Also

Other dfourier: dfourier_i(), dfourier_shape()

Examples

o <- olea %>% slice(1:5) # for the sake of speed
od <- dfourier(o)
od
op <- PCA(od)
plot(op, 1)

# dfourier and inverse dfourier
o <- olea[1]
o <- coo_bookstein(o)
coo_plot(o)
o.dfourier <- dfourier(o, nb.h=12)
o.dfourier
o.i <- dfourier_i(o.dfourier)
o.i <- coo_bookstein(o.i)
coo_draw(o.i, border='red')

#future calibrate_reconstructions
o <- olea[1]
h.range <- 2:13
coo <- list()
for (i in seq(along=h.range)){
coo[[i]] <- dfourier_i(dfourier(o, nb.h=h.range[i]))}
names(coo) <- paste0('h', h.range)
panel(Opn(coo), borders=col_india(12), names=TRUE)
title('Discrete Cosine Transforms')

vbonhomme/Momocs documentation built on Nov. 13, 2023, 8:54 p.m.