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the terminology of 'size' and 'shape' that follows from the use of scaling
factors is not precise (Mosimann, 1979; Lele, 1991). Surrogate mea-
sures for 'size' are many (e.g., volume, weight, length) and the use of
each will result in a different size-corrected shape. Keeping this impre-
cision in mind, we adopt the common usage of the terms 'size' and
'shape' in the following discussion.
Suppose we calculate the geometric mean of all distances in
FM(A)
and refer to the geometric mean as 'size.' Let
S(A)
{
FM
(
A
)}
1
/
L
ij
denote the 'size' of object
A
. Using the ongoing example, the geometric
mean or size of form
A
is 1.12. Similarly, let
S (B)
denote the 'size' of
form
B
. In the example above,
S
(
B
)
1.64. Now consider the matrix
FM A
SA
()
()
ij
SM
()
A
We consider
SM
ij
(A)
to represent the 'scaled form
ij
of
A
' or the
shape matrix
of
A
. Similarly, we define
as the shape matrix of
B
. These matrices are given as:
and
One can describe the form difference between objects
A
and
B
by
using two quantities.
quantifies the 'size difference'
between forms
A
and
B
, while the shape difference between forms is
given by a shape difference matrix whose elements represent the abso-
lute difference between like-linear distances of the two shape matrices,
SDM
ij
(B,A)
=
SM
ij
(B) - SM
ij
(A)
. In our example, the shape difference
matrix is:
0
0 32
.
0 284
.
SDM
ij
(, )
B A
032
.
0
0097
.
0 284
.
0 097
.
0
4.7.4 Estimation of form difference using EDMA
Up to this point, we have been discussing the comparison of single
forms and have operated under the assumption that the true means are
available. Remember, however, that in practice the true means are
never available. All that are available are rotated and translated ver-
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