Further Applications of EDMA - An Invariant Approach to Statistical Analysis of Shapes - page 260

CHAPTER 7
Further Applications of EDMA
Theodore M. Cole III
Department of Basic Medical Science
University of Missouri-Kansas City
Dr. Tim Cole has been one of our collaborators in our work with EDMA.
In this chapter, he summarizes some recent extensions of EDMA
methodology to new research areas. These extensions are still under
development and the discussion here is necessarily preliminary.
7.1 The study of asymmetry
Bilateral symmetry of the musculoskeletal system is a phylogenetical-
ly widespread characteristic of many complex organisms (Palmer,
1996). There is a midline plane of symmetry that divides the body into
right and left halves, so that one half is essentially a mirror image of
the other. However, asymmetries in form are frequently observed both
in natural populations of organisms and in clinical settings. Some of
these asymmetries can be very subtle. For example, while normal
human faces may appear symmetric on casual inspection, some slight
differences between sides can always be found. In other cases, there
may be asymmetries that are immediately obvious. Some large-scale,
conspicuous asymmetries may occur in normally symmetric structures
because of developmental anomalies (e.g., hemifacial microsomia), and
there are also dramatic asymmetries that occur normally in natural
populations (e.g., the skulls of flounders).
There are three basic patterns of asymmetry, all of which are
defined at the level of the sample or population: fluctuating asymme-
try , directional asymmetry , and antisymmetry (Palmer, 1996). These
patterns are distinguished on the basis of: 1) the degree of asymmetry,