Statistical Models for Landmark Coordinate Data - An Invariant Approach to Statistical Analysis of Shapes - page 118

STEP 1: Calculate the centered matrices X 1 c , X 2 c ,…, X n c where
X i c

LX i .
STEP 2: Calculate the centered inner product matrices
B i X i c ( X i c ) T . Notice that these centered inner product matri-

ces are 2

2 symmetric matrices. Let B 11, i , B 22, i , B 12, i be the
three distinct elements of B i .
STEP 3: Calculate the following quantities:

n
å

B 11 = 1
n

B 11, i

i = 1

n
å

B 22 = 1
n

B 22, i

i = 1

n
å

B 12 = 1
n

B 12, i

i = 1

n
å

var( B 11 ) = 1
n

( B 11, i - B 11 ) 2

i = 1

n
å

var( B 22 ) = 1

( B 22, i - B 22 ) 2

n

i = 1

n
å

var( B 12 ) = 1

( B 12, i - B 12 ) 2

n

i = 1

n
å

cov( B 11 , B 22 ) = 1
n

( B 11, i - B 11 )( B 22, i - B 22 )

i = 1

n
å

cov( B 11, B 12 ) = 1 ( B 11, i - B 11 )( B 12, i - B 12 )

n

i = 1

n
å

cov( B 22 , B 12 ) = 1 ( B 22, i - B 22 )( B 12, i - B 12 )

n

i = 1