Morphometric Tools for Landmark Data: Geometry and Biology by Fred L. Bookstein

By Fred L. Bookstein

Morphometrics is the statistical research of organic form and form swap. Its richest facts are landmarks, issues, comparable to the bridge of the nostril, that experience organic names in addition to geometric destinations. This ebook is the 1st systematic survey of morphometric equipment for landmark info.

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In the limit of small changes, these are exact Euclidean circles about the identity transformation in that subspace. Thus, all such changes are detected by the common T2 or F with the same full efficiency, regardless of direction. The shape coordinates, and the feature space of the uniform transformations, are now nearly a decade old, having been introduced in manuscripts written in the early 1980s. Their extension to the more complex subspaces has occupied me considerably since then. This book is the first presentation of all this material in coherent survey form.

That is, landmarks are quite a bit more than instructions for measurement; they are the places at which one's explanations of biological processes ought to be grounded. At the same time, they are "less than" measurements, in that the transition from their locations to proper statistical variables must be made with great care. The chapter goes on to review the three main categories of landmarks commonly encountered in practice: anatomical points (discrete juxtapositions of distinct tissues), maxima of curvature or other relicts of local morphogenetic processes, and more ambiguous records of processes at a distance - extremal diameters, centers of circles that are tangent to the outline at more than one point, and the like.

3. 5. Third finding of the phenytoin-face study. The uniform component of shape variation, case by case, resembles that for Endocanthion alone (finding 1), but with greater group overlap. " Information from Endocanthion has been omitted from this estimate. 5) resembles what we have already seen for the most sensitive landmark, Endocanthion, separately. The difference between the exposed group and the unexposed is aligned with the displacement from the vaguely elliptical scatter of U's to the somewhat differently shaped ellipse of E's.

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