tpsgrid {shapes}R Documentation

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)

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.

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 $sigma(h) = -| h |$.

Value

No returned value

Author(s)

Ian Dryden

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. (1998) Statistical Shape Analysis. Wiley, Chichester. Chapter 10.

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)")   


[Package shapes version 1.1-5 Index]