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The AAPG/Datapages Combined Publications Database

AAPG Bulletin


Volume: 68 (1984)

Issue: 4. (April)

First Page: 464

Last Page: 464

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

Author(s): D. G. Collins, J. M. Parks


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.

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Copyright 1997 American Association of Petroleum Geologists