relWarps: calculate relative Warp analysis

In Morpho: Calculations and Visualisations Related to Geometric Morphometrics

calculate relative Warp analysis

Description

After Procrustes registration the data is scaled by the bending energy or its inverse to emphasize global/local differences when exploring a sample's shape.

Usage

relWarps(
  data,
  scale = TRUE,
  CSinit = TRUE,
  alpha = 1,
  tol = 1e-10,
  orp = TRUE,
  pcAlign = TRUE,
  computeBasis = TRUE,
  noalign = FALSE
)

Arguments

data	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
CSinit	Logical: if TRUE, all configurations are initially scaled to Unit Centroid Size.
alpha	integer: power of the bending energy matrix. If alpha = 0 then standard Procrustes PCA is carried out. If alpha = 1 then large scale differences are emphasized, if alpha = -1 then small scale variations are emphasised.
tol	tolerance for the eigenvalues of the bending energy matrix to be zero
orp	logical: request orthogonal projection into tangent space.
pcAlign	logical: if TRUE, the shapes are aligned by the principal axis of the first specimen
computeBasis	logical: whether to compute the basis of the resulting vector space (takes a lot of memory and time for configurations with > 1000 coordinates.
noalign	logical: if TRUE, data is assumed to be already aligned and alignment and orthogonal projection are skipped.

Value

bescores	relative warp scores (PC-scores if alpha = 0)
uniscores	uniform scores, NULL if alpha = 0
Var	non-affine variation explained by each relative warp
mshape	sample's conensus shape
rotated	Procrustes superimposed data
bePCs	vector basis of nonaffine shape variation- relative warps (plain PCs if alpha = 0)
uniPCs	vector basis of affine shape variation - uniform component. NULL if alpha = 0

Author(s)

Stefan Schlager

References

Bookstein FL 1989. Principal Warps: Thin-plate splines and the decomposition of deformations. IEEE Transactions on pattern analysis and machine intelligence 11.

Bookstein FL, 1991. Morphometric tools for landmark data. Geometry and biology. Cambridge Univ. Press, Cambridge.

Rohlf FJ, Bookstein FL 2003. Computing the Uniform Component of Shape Variation. Systematic Biology 52:66-69.

Examples

data(boneData)
pop <- name2factor(boneLM,which=3)
rW <- relWarps(boneLM, alpha = -1)
## Not run: 
if (require(car)) {
# plot first 5 relative warps scores grouped by population
spm(rW$bescores[,1:5],group=pop)
# plot uniform component scores grouped by population
spm(rW$uniscores[,1:5],group=pop)
}
##plot non-affine variance associated with each relative warp
barplot(rW$Var[,2], xlab="relative Warps")
## visualize first relative warp +-3 sd of the scores
rw1 <- restoreShapes(as.matrix(c(-3,3)*sd(rW$bescores[,1])),rW$bePCs[,1,drop=FALSE],rW$mshape)
deformGrid3d(rw1[,,1],rw1[,,2],ngrid=5)

## 2D example:
if (require(shapes)) {
data <- bindArr(gorf.dat, gorm.dat, along=3)
sex <- factor(c(rep("fem", dim(gorf.dat)[3]), rep("male",dim(gorm.dat)[3])))
rW <- relWarps(data, alpha = -1)
if (require(car)) {
# plot first 3 relative warps scores grouped by population
spm(rW$bescores[,1:3],group=sex)
# plot uniform component scores grouped by population
spm(rW$uniscores[,1:2],group=sex)
}
##plot non-affine variance associated with each relative warp
barplot(rW$Var[,2], xlab="relative Warps")
## visualize first relative warp +-3 sd of the scores
rw1 <- restoreShapes(as.matrix(c(-3,3)*sd(rW$bescores[,1])),rW$bePCs[,1,drop=FALSE],rW$mshape)
deformGrid2d(rw1[,,1],rw1[,,2],ngrid=10)
}
## End(Not run)

Morpho documentation built on Feb. 16, 2023, 10:51 p.m.