Biology Reference
In-Depth Information
Uniform (Affine) Components
There are six distinct types of uniform deformations for landmarks in two dimen-
sions, and they are independent of each other (meaning that they are mutually orthogo-
nal).
Figure 5.4
shows these six operations carried out on a square configuration of
landmarks. The first four are the familiar ones that do not alter shape: translation along
two perpendicular axes (
Figure 5.4A,B
), scaling (
Figure 5.4C
) and rotation (
Figure 5.4D
).
These are all used in superimposing shapes. The other two uniform deformations do
alter shape: compression/dilation (
Figure 5.4E
) and shear (
Figure 5.4F
). Compression/
dilation refers to the case in which one direction has expanded (the vertical or
Y-direction in
Figure 5.4E
) while the other has contracted (the horizontal or X-direction).
Shearing refers to translating landmarks along one axis by a distance proportional to
their location along the other axis.
(A)
(B)
(C)
(D)
(E)
(F)
FIGURE 5.4
The six uniform (affine) transformations: (A) translation along the vertical axis; (B) translation
along the horizontal axis; (C) scaling; (D) rotation; (E) compression/dilation; (F) shearing. The original (or refer-
ence) square is shown with dotted lines, while the deformed shape is shown with solid lines.
