Morphometric Data - An Invariant Approach to Statistical Analysis of Shapes - page 21

b) Fuzzy landmarks:
A fuzzy landmark is a point corresponding to a biological structure
that is precisely delineated and that corresponds to a locus of some bio-
logical significance, but that occupies an area that is larger than a
single point in the observer's reference system (Valeri et al., 1998). The
definition of a fuzzy landmark usually includes a positional reference
(e.g., centroid, apex) that corresponds with a place on the feature that
best represents it as a point. Because fuzzy landmarks must be locat-
ed on a larger structure or surface, there is the possibility that more
measurement error will be included in their location (see Valeri et al.,
1998). Fuzzy landmarks become necessary when portions of the form
under study are made up of relatively large, smooth surfaces or fea-
tures and do not include sufficient traditional landmarks. Biological
examples of such features include the squamous portion of mammalian
cranial bones, the articular surface of the astragulus, the articular sur-
face of the capitulum of the humerus, the basin between two shearing
facets on a tooth, the outer capsule of pome fruits, the external surface
of some crab carapaces, the leading edge of a canine tooth, and the
ischial tuberosity. The example in Figure 2.4 shows the left frontal
Figure 2.4 Three-dimensional reconstruction of a computed tomography scan of an
infant showing an example of a fuzzy landmark. The frontal boss is a swelling on each
frontal bone. It is a rather large area. The black points shown in the figure depict the
placement of a single point to localize this feature in a series of data collection trials.
The white point provides an estimate of the average location of these trials.