Morpho (version 2.1)

relWarps: 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)

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.

Value

• bescores
  relative warp scores
• uniscores
  uniform scores
• 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
• uniPCs
  vector basis of affine shape variation - uniform component

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)
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")

## 2D example:
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)
# 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")