Morphometric Data - An Invariant Approach to Statistical Analysis of Shapes - page 23

marks can be constructed. Let us say that data are being collected from
the pelvis. Several features of the pelvis can serve as traditional land-
marks (e.g., McHenry and Corrunccini, 1978; Li and Richtsmeier,
1996), but the large alar surfaces are void of landmarks. Figure 2.5
shows several landmarks located on a human innominate (hip) bone. A
landmark can be constructed by using the location of two traditional
landmarks, say anterior superior iliac spine and posterior superior
iliac spine (marked by open circles on either side of the bone in Figure
2.5 ) and connecting these points by an arc that stretches along the sur-
face of the iliac crest. A single midpoint along this arc (as shown in
Figure 2.5 ) or several points at specific intervals along the arc can be
identified and their location recorded as a constructed landmark. The
same could be done using a combination of any of the traditional land-
marks defined on a form. A string that hugs a surface can be useful in
defining constructed points. The “string” can be an actual one, hand-
held by the researcher, or can take the form of an algorithm that
computes the shortest distance between the two traditional landmarks
along a given surface captured in digital format.
Constructed landmarks are those that might easily be placed by
computer-based algorithms for landmark locating. Although computer
automation of data collection would significantly reduce the amount of
time required for data collection, caution must be taken. Biological
variability can figure into landmark location in unexpected ways. For
example, if a point were defined as lying midway along the shortest
possible distance between two points, it is possible that the shortest
distance between two points may not cross the surface of interest, but
instead pass through or wrap around an alternate surface. When total
automation of landmark data collection by computer algorithm is a
viable option, continued supervision by the researcher is critical in cor-
rectly locating all landmarks.
Whether located by a human or a computer, the biological and sta-
tistical properties of constructed landmarks are different than those of
traditional landmarks, and this needs to be considered during data col-
lection, analysis, and interpretation. As suggested above, a lack of
correspondence between constructed landmarks collected on different
forms may occur. The locus midway between two landmarks along a
surface on one object may not correspond biologically with a locus mid-
way between the same two points along the homologous surface of
another object. Error in the location of constructed landmarks is
dependent upon error in the location of each of the traditional land-
marks and error in the placement of the constructed landmark.