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**Size and shape spaces for landmark data in two dimensions (with discussion).**
*(English)*
Zbl 0614.62144

This highly theoretical 40 pages long paper is followed by a 20 pages long discussion of its subject by 5 other statisticians: David G. Kendall, Noel Cressie, Gregory Campbell, Paul D. Sampson, and Colin Goodall. The subject is mathematical formalisms to be used in morphometrics, i.e. the study of the geometrical form of biological organisms including man. E.g. in studying the effects of maternal alcohol consumption during pregnancy on the health of the off-spring their facial photographs have been analysed. From the ”landmarks” selected by the biologists (e.g. the tip of the nose) the morphometricians task is to construct a set of numerical descriptor variables for size and shape so that these quantities may be compared quantitatively within and between groups, e.g. of different sex and age. Starting with the distances and triangles between pairs and triples, respectively, of landmarks a ”formidable mathematics” is developed. It is illustrated by applying it to a study of growth of the head of 62 school children from 8 to 14 years subjected to X-ray photography of their crania. However, one misses the medical purpose of this specific investigation. One also wonders whether such applications of X-rays may not be dangerous to the children [cf. e.g., the reviewer and D. D. Skov, ”Kernkraft”, Teil 2: Biologische Probleme, Springer (1987)].

Reviewer: N.Arley

### MSC:

62P10 | Applications of statistics to biology and medical sciences; meta analysis |