Form representions and means for landmarks: A survey and comparative study

The form of an object may be briefly defined as the totality of all geometrical features in the object. Thus different images (as two-dimensional objects) can be said to have the same form provided they convey identical geometrical information, regardless of the coordinates used to express this information. In this paper, we survey some of the principal approaches to the representation and statistical analysis of forms of landmark data which can be extracted from images directly or by means of computer tomography. In particular, we survey the various ways in which forms can be pooled by form averaging. We propose a set of criteria for an ideal mean form, and study the available methods in light of these criteria. An annotated bibliography is provided as a guide to various theoretical and applied papers on the subject.