This project will continue the development of a class of statistical methods for morphometrics, the quantitative analysis of biological shape. These methods all exploit landmark data, locations of biologically corresponding (homologous) points in all the forms of a series or study. Such data are routinely available from many modes of medical image analysis. Work during the current funding period showed that changes or variability in any configuration of landmarks may be divide into a uniform and a nonuniform part. These are algebraically distinctive pieces of the thin-plate splines that very effectively interpolate deformations from the landmark data. Variation or change of the nonuniform part is calibrated by a certain bending energy that incorporates the geometric scales at which changes at the separate landmarks are coordinated; the uniform part may be considered to have bending energy zero. The adaptations of factor and component analysis that this decomposition supports fully exploit the special structure of landmark data, just as the earlier methods carefully adapted the general linear model to this context. In the new funding period, we will explore several extensions of these feature spaces for studies of shape variability and the statistical methods they support. We will rigorously consider the relation between the two ways in which one can parameterize """"""""blobs"""""""" in medical images: as locations or as patterns of gray levels. We will explore models for """"""""growth centers"""""""", bulges, and other processes which involve directed divergences among many landmark locations and curves or surfaces at once. We will extend the hypotheses for which rigorous machinery is available to include questions of asymmetry and correlations of form with scalar fields; and we will carefully explore ties between the landmark-based methods and other approaches of image summary, such as """"""""stacks"""""""" of successive blurs, under study at other medical imaging research centers. The visualization of the landmark-based biometric machinery will be transferred in extenso to a very powerful graphics computer, the Stellar GS1000, in order to support interactive analysis of three-dimensional data. These new morphometric methods will be applied in demonstration studies from craniofacial growth, craniofacial anomalies, and neurology. The methods should greatly increase the efficiency with which morphological information may be exploited, alone or in combination with other measures, in biomedical studies of the large-scale shapes of organs, their variability, their changes over time, or their covariation with causes or effects.
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