Morpho (version 2.12)

procSym: Procrustes registration

Description

procSym performs Procrustes superimposition including sliding of semi-landmarks on curves/outlines in 2D and 3D.

Usage

procSym(
  dataarray,
  scale = TRUE,
  reflect = TRUE,
  CSinit = TRUE,
  orp = TRUE,
  proctol = 1e-05,
  tol = 1e-05,
  pairedLM = NULL,
  sizeshape = FALSE,
  use.lm = NULL,
  center.part = FALSE,
  weights = NULL,
  centerweight = FALSE,
  pcAlign = TRUE,
  distfun = c("angle", "riemann"),
  SMvector = NULL,
  outlines = NULL,
  deselect = FALSE,
  recursive = TRUE,
  iterations = 0,
  initproc = FALSE,
  bending = TRUE,
  stepsize = 1
)

Value

size

a vector containing the Centroid Size of the configurations

rotated

k x m x n array of the rotated configurations

Sym

k x m x n array of the Symmetrical component - only available for the "Symmetry"-Option (when pairedLM is defined)

Asym

k x m x n array of the Asymmetrical component. It contains the per-landmark asymmetric displacement for each specimen. Only available for the "Symmetry"-Option (when pairedLM is defined)

asymmean

k x m matrix of mean asymmetric deviation from symmetric mean

mshape

sample meanshape

symmean

meanshape of symmetrized configurations

tan

if orp=TRUE: Residuals in tangentspace else, Procrustes residuals - only available without the "Symmetrie"-Option

PCs

Principal Components - if sizeshape=TRUE, the first variable of the PCs is size information (as log transformed Centroid Size)

PCsym

Principal Components of the Symmetrical Component

PCasym

Principal Components of the Asymmetrical Component

PCscores

PC scores

PCscore_sym

PC scores of the Symmetrical Component

PCscore_asym

PC scores of the Asymmetrical Component

eigenvalues

eigenvalues of the Covariance matrix

eigensym

eigenvalues of the "Symmetrical" Covariance matrix

eigenasym

eigenvalues of the "Asymmetrical" Covariance matrix

Variance

Table of the explained Variance by the PCs

SymVar

Table of the explained "Symmetrical" Variance by the PCs

AsymVar

Table of the explained "Asymmetrical" Variance by the PCs

orpdata

k x m x n array of the rotated configurations projected into tangent space

rho

vector of Riemannian distance from the mean

dataslide

array containing slidden Landmarks in the original space - not yet processed by a Procrustes analysis. Only available if a sliding process was requested

meanlogCS

mean log-transformed centroid size

Arguments

dataarray

Input k x m x n real array, where k is the number of points, m is the number of dimensions, and n is the sample size.

scale

logical: indicating if scaling is requested to minimize the General Procrustes distance. To avoid all scaling, one has to set CSinit=FALSE, too.

reflect

logical: allow reflections.

CSinit

logical: if TRUE, all configurations are initially scaled to Unit Centroid Size.

orp

logical: if TRUE, an orthogonal projection at the meanshape into tangent space is performed.

proctol

numeric: Threshold for convergence in the alignment process

tol

numeric: Threshold for convergence in the sliding process

pairedLM

A X x 2 matrix containing the indices (rownumbers) of the paired LM. E.g. the left column contains the lefthand landmarks, while the right side contains the corresponding right hand landmarks.

sizeshape

Logical: if TRUE, a log transformed variable of Centroid Size will be added to the shapedata as first variable before performing the PCA.

use.lm

vector of integers to define a subset of landmarks to be used for Procrustes registration.

center.part

Logical: if TRUE, the data superimposed by the subset defined by use.lm will be centered according to the centroid of the complete configuration. Otherwise orp will be set to FALSE to avoid erroneous projection into tangent space.

weights

numeric vector: assign per landmark weights.

centerweight

logical: if TRUE, the landmark configuration is scaled according to weights during the rotation process, instead of being scaled to the Centroid size.

pcAlign

logical: if TRUE, the shapes are aligned by the principal axis of the first specimen

distfun

character: "riemann" requests a Riemannian distance for calculating distances to mean, while "angle" uses an approximation by calculating the angle between rotated shapes on the unit sphere.

SMvector

A vector containing the landmarks on the curve(s) that are allowed to slide

outlines

A vector (or if threre are several curves) a list of vectors (containing the rowindices) of the (Semi-)landmarks forming the curve(s) in the successive position on the curve - including the beginning and end points, that are not allowed to slide.

deselect

Logical: if TRUE, the SMvector is interpreted as those landmarks, that are not allowed to slide.

recursive

Logical: if TRUE, during the iterations of the sliding process, the outcome of the previous iteration will be used. Otherwise the original configuration will be used in all iterations.

iterations

integer: select manually how many iterations will be performed during the sliding process (usefull, when there is very slow convergence). 0 means iteration until convergence.

initproc

Logical: indicating if the first Relaxation step is performed against the mean of an initial Procrustes superimposition. Symmetric configurations will be relaxed against a perfectly symmetrical mean.

bending

if TRUE, bending energy will be minimized, Procrustes distance otherwise (not suggested with large shape differences)

stepsize

integer: dampening factor for the sliding. Useful to keep semi-landmarks from sliding too far off the surface. The displacement is calculated as
stepsize * displacement.

Author

Stefan Schlager

Details

This function performs Procrustes registration, allowing a variety of options, including scaling, orthogonal projection into tangentspace and relaxation of semi-landmarks on curves (without reprojection onto the surface/actual outline). It also allows the superimpositioning to be performed using only a subset of the available landmark. For taking into account object symmetry, pairedLM needs to be set. This generates an object of class "symproc". Otherwise an object of class "nosymproc".

References

Dryden IL, and Mardia KV. 1998. Statistical shape analysis. Chichester.

Klingenberg CP, Barluenga M, and Meyer A. 2002. Shape analysis of symmetric structures: quantifying variation among individuals and asymmetry. Evolution 56(10):1909-1920.

Gunz, P., P. Mitteroecker, and F. L. Bookstein. 2005. Semilandmarks in Three Dimensions, in Modern Morphometrics in Physical Anthropology. Edited by D. E. Slice, pp. 73-98. New York: Kluwer Academic/Plenum Publishers.

See Also

slider3d

Examples

require(rgl)
data(boneData)

### do an analysis of symmetric landmarks
## visualize landmarks on surface
if (FALSE) {
 spheres3d(boneLM[,,1])
wire3d(skull_0144_ch_fe.mesh,col=3)
## get landmark numbers
text3d(boneLM[,,1],text=paste(1:10),adj = 1, cex=3)
}
## determine paired Landmarks left side:
left <- c(4,6,8)
## determine corresponding Landmarks on the right side:
# important: keep same order
right <- c(3,5,7)
pairedLM <- cbind(left,right)
symproc <- procSym(boneLM, pairedLM=pairedLM)
if (FALSE) {
## visualize first 3 PCs of symmetric shape
pcaplot3d(symproc, sym=TRUE)
## visualize first 3 PCs of asymmetric shape
pcaplot3d(symproc, sym=FALSE)

## visualze distribution of symmetric PCscores population
pop <- name2factor(boneLM, which=3)
if (require(car)) {
spm(~symproc$PCscore_sym[,1:5], groups=pop)
## visualze distribution of asymmetric PCscores population
spm(~symproc$PCscore_asym[,1:5], groups=pop)
}
}