Biology Reference

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Defining the difference between two forms

Let us begin with two forms, A and B. We will set the landmark coor-

dinates for forms A and B to differ only in the position of landmark 2,

so that the coordinate locations for these two forms are:

FM (A)
and
FM (B)
denote the form matrices corresponding to the

two objects. Recall that
FM
ij
(A)
is the distance between landmarks
i

and
j
in object
A
and that
FM
ij
(B)
is the corresponding distance in

object
B
. The form matrices for the above objects are:

01 1

10

02 1

20

FM A

()

.

1

FM B

()

.

3

1

1 41

.

0

1

2 23

.

0

We present three possible ways to express form difference using the

form matrices, FM (A) and FM (B).

Arithmetic form difference

The difference between forms can be expressed as the arithmetic dif-

ference between like linear distances in the two forms. The collection

of these differences can be expressed as a matrix consisting of elements

that correspond to the arithmetic difference between like linear dis-

tances in the two objects. For example, the absolute form difference

matrix,
AFDM (B, A)

FM
ij
(B)

FM
ij
(A)
, for the above two objects, is

given as:

01 0

10

AFDM B A

(, )

.

2

0

0 82

.

0

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