procOPA {shapes} | R Documentation |
Ordinary Procrustes analysis
Description
Ordinary Procustes analysis : the matching of one configuration to another using translation, rotation and (possibly) scale. Reflections can also be included if desired. The function matches configuration B onto A by least squares.
Usage
procOPA(A, B, scale = TRUE, reflect = FALSE)
Arguments
A |
k x m matrix (or complex k-vector for 2D data), of k landmarks in m dimensions. This is the reference figure. |
B |
k x m matrix (or complex k-vector for 2D data). This is the figure which is to be transformed. |
scale |
logical indicating if scaling is required |
reflect |
logical indicating if reflection is allowed |
Value
A list with components:
R |
The estimated rotation matrix (may be an orthogonal matrix if reflection is allowed) |
s |
The estimated scale matrix |
Ahat |
The centred configuration A |
Bhat |
The Procrustes registered configuration B |
OSS |
The ordinary Procrustes sum of squares, which is $\|Ahat-Bhat\|^2$ |
rmsd |
rmsd = sqrt(OSS/(km)) |
Author(s)
Ian Dryden
References
Dryden, I.L. and Mardia, K.V. (2016). Statistical Shape Analysis, with applications in R (Second Edition). Wiley, Chichester. Chapter 7.
See Also
procGPA,riemdist,tpsgrid
Examples
data(digit3.dat)
A<-digit3.dat[,,1]
B<-digit3.dat[,,2]
ans<-procOPA(A,B)
plotshapes(A,B,joinline=1:13)
plotshapes(ans$Ahat,ans$Bhat,joinline=1:13)
#Sooty Mangabey data
data(sooty.dat)
A<-sooty.dat[,,1] #juvenile
B<-sooty.dat[,,2] #adult
par(mfrow=c(1,3))
par(pty="s")
plot(A,xlim=c(-2000,3000),ylim=c(-2000,3000),xlab=" ",ylab=" ")
lines(A[c(1:12,1),])
points(B)
lines(B[c(1:12,1),],lty=2)
title("Juvenile (-------) Adult (- - - -)")
#match B onto A
out<-procOPA(A,B)
#rotation angle
print(atan2(out$R[1,2],out$R[1,1])*180/pi)
#scale
print(out$s)
plot(A,xlim=c(-2000,3000),ylim=c(-2000,3000),xlab=" ",ylab=" ")
lines(A[c(1:12,1),])
points(out$Bhat)
lines(out$Bhat[c(1:12,1),],lty=2)
title("Match adult onto juvenile")
#match A onto B
out<-procOPA(B,A)
#rotation angle
print(atan2(out$R[1,2],out$R[1,1])*180/pi)
#scale
print(out$s)
plot(B,xlim=c(-2000,3000),ylim=c(-2000,3000),xlab=" ",ylab=" ")
lines(B[c(1:12,1),],lty=2)
points(out$Bhat)
lines(out$Bhat[c(1:12,1),])
title("Match juvenile onto adult")