Comparison of shape and form is a fundamental issue in biology and medicine. Comparing shape and form of organisms means to compare their geometry and to draw conclusions on the reasons for differences and the processes involved in the changes from one into another.
Three guiding principles:
1. The forms to be compared shall be captured as accurate as possible
Measurements based on digital data can be taken efficiently and accurately, they can be taken in regions not accessible on real specimens, and previously unattended regions can be captured using another type of landmarks (semilandmarks).
2. When groups are compared, as many as possible individuals shall be included
A large number of specimens can be compared at once. Comparing
two specimens is a relatively easy task but in most applications,
groups have to be compared with other groups or a new specimen should
be assigned to a group. The one-by-one comparisons can go easily into
the thousands while the sample size increases.
The practical question is therefore: Can we extract a generalized configuration for a specific group of specimens? A larger number of specimens allows to apply statistics and can be used to create a formalized "reference model" for a particular group which includes information on mean configuration, variability, and probability distribution that can be used for comparison, estimation of missing data, and classification.
3. Comparisons of form are always in a context of the processes that govern those forms
The particular formal technique of landmark points, recently extended to the idea of semilandmarks, enforces one particular rule for keeping comparisons under the control of biological theory, namely comparing like to like (the corresponding parts). This approach also handles other common biological explanations such as integration or symmetry.
GMM is a subdiscipline of statistics that is concerned with the analysis of shape and shape changes of geometrical objects.