Size and Shape Spaces for Landmark Data in Two Dimensions

摘要: Biometric studies of the forms organisms usually consider size and shape variations in geometric configuration landmarks, points that correspond biologically from form to form. The variables may be usefully considered linear vector space spanned by set all distances between pairs landmarks. a single triangle $\Delta ABC$ landmarks reduced pair coordinates locating vertex $C$ coordinate system with landmark $A$ sent (0,0) $B$ (1,0). A useful is span such for various triples On convenient null model identical circular normal perturbations at each independently, one variable $S$, which taken as mean square interlandmark distances, has covariance zero every variable. Then associations tested $F$ ratio multiple regression $S$ on any basis space. For existence difference or change Hotelling's $T^2$ applied triangle. When statistically significant, it interpreted measured along directions an angle averaging $90^\circ$ samples forms. One will bear greatest rate forms, other least. Analysis configurations more than three reduces consideration involving most These techniques are demonstrated study growth head 62 Ann Arbor youth. Each comparison interest summarized its own orthogonal system, biorthogonal grid pair.