Variety of Geologic Silhouette Shapes Distinguishable by Multiple Rotations Method of Quantitative Shape Analysis Text: ABSTRACT

Abstract

Silhouette shapes are two-dimensional projections of three-dimensional objects such as sand grains, gravel, and fossils. Within-the-margin markings such as chamber boundaries, sutures, or ribs are ignored. Comparisons between populations of objects from similar and different origins (i.e., environments, species or genera, growth series, etc) is aided by quantifying the shapes. The Multiple Rotations Method (MRM) uses a variation of eigenshapes, which is capable of distinguishing most of the subtle variations that the trained eye can detect. With a video-digitizer and microcomputer, MRM is fast, more accurate, and more objective than the human eye. The resulting shape descriptors comprise 5 or 6 numbers per object that can be stored and retrieved to compare with simila descriptions of other objects. The original-shape outlines can be reconstituted sufficiently for gross recognition from these few numerical descriptors. Thus, a semi-automated data-retrieval system becomes feasible, with silhouette-shape descriptions as one of several recognition criteria. MRM consists of four rotations: (1) rotation about a center to a comparable orientation; (2) a principal-components rotation to reduce the many original shape descriptors to a few; (3) a VARIMAX orthogonal-factor rotation to achieve simple structure; and (4) a rotation to achieve factor scores on individual objects. A variety of subtly different shapes includes sand grains from several locations, ages, and environments, and fossils of several types. This variety illustrates the feasibility of quantitative comparisons by MRM. End_of_Article - Last_Page 464------------