shapes (version 1.2.7)

tpsgrid: Thin-plate spline transformation grids

Description

Thin-plate spline transformation grids from one set of landmarks to another.

Usage

tpsgrid(TT, YY, xbegin=-999, ybegin=-999, xwidth=-999, opt=1, ext=0.1, ngrid=22, 
                  cex=1, pch=20, col=2,zslice=0, mag=1, axes3=FALSE)

Value

No returned value

Arguments

TT

First object (source): (k x m matrix)

YY

Second object (target): (k x m matrix)

xbegin

lowest x value for plot: if -999 then a value is determined

ybegin

lowest y value for plot: if -999 then a value is determined

xwidth

width of plot: if -999 then a value is determined

opt

Option 1: (just deformed grid on YY is displayed), option 2: both grids are displayed

ext

Amount of border on plot in 2D case.

ngrid

Number of grid points: size is ngrid * (ngrid -1)

cex

Point size

pch

Point symbol

col

Point colour

zslice

For 3D case the scaled z co-ordinate(s) for the grid slice(s). The values are on a standardized scale as a proportion of height from the middle of the z-axis to the top and bottom. Values in the range -1 to 1 would be sensible.

mag

Exaggerate effect (mag > 1). Standard effect has mag=1.

axes3

Logical. If TRUE then the axes are plotted in a 3D plot.

Author

Ian Dryden

Details

A square grid on the first configuration is deformed smoothly using a pair of thin-plate splines in 2D, or a triple of splines in 3D, to a curved grid on the second object. For 3D data the grid is placed at a constant z-value on the first figuure, indicated by the value of zslice.

For 2D data the covariance function in the thin-plate spline is $sigma(h) = |h|^2 log |h|^2$ and in 3D it is given by $sigma(h) = -| h |$.

References

Bookstein, F.L. (1989). Principal warps: thin-plate splines and the decomposition of deformations, IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, 567--585.

Dryden, I.L. and Mardia, K.V. (2016). Statistical Shape Analysis, with Applications in R (Second Edition). Wiley, Chichester. Chapter 12.

See Also

procGPA

Examples

data(gorf.dat)
data(gorm.dat)

#TPS grid with shape change exaggerated (2x)
gorf<-procGPA(gorf.dat)
gorm<-procGPA(gorm.dat)
TT<-gorf$mshape
YY<-gorm$mshape
tpsgrid(TT,YY,mag=2) 
title("TPS grid: Female mean (left) to Male mean (right)")