Morphometric Data - An Invariant Approach to Statistical Analysis of Shapes - page 60

K D ) . This means
that if we translate an object, the mean matrix gets translated by
the same amount, but the variance-covariance matrix remains
unaffected.
b) Effect of rotation: XR ~ N ( MR,

a) Effect of translation: X

1 t ~ N ( M 1 t,

D R ) . This means that
rotation of an object affects the mean as well as the variance-
covariance matrix.
c) Effect of translation and rotation combined: XR

K R T

1 t ~ N ( MR

D R ) . This means that rotation and translation of an
object affects both the mean and the variance-covariance
matrix.

1 t , K R T