Mr. Lauren E. Levine Profile

Lauren E. Levine

Mathematician at Air Force Research Lab

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Proceedings Article | 1 August 2002 Paper

Label-invariant approach to procrustes analysis

Lauren Levine, Gregory Arnold, Kirk Sturtz

Proceedings Volume 4727, (2002) https://doi.org/10.1117/12.478693

KEYWORDS: Shape analysis, Automatic target recognition, Matrices, Analytical research, Sensors, Nose, Feature extraction, Optical spheres, Distance measurement, Data modeling

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Procrustes Analysis (least-squares mapping) is typically used as a method of comparing the shape of two objects. This method relies on matching corresponding points (landmarks) from the data associated with each object. Typically, landmarks are physically meaningful locations (e.g. end of a nose) whose relationship to the whole object is known. Corresponding landmarks would be the same physical location on the two different individuals, and therefore Procrustes analysis is a reasonable method of measuring relative shape. However, in the application of automatic target recognition, the correspondence of landmarks is unknown. In other words, the description of the shape of an object is dependent upon the labeling of landmarks, an undesirable characteristic. In an attempt to circumvent the labeling problem (without exhaustively computing the factorial number of correspondences), this paper presents a label-invariant method of shape analysis. The label-invariant method presented in this paper uses measurements which are related to the measurements used in Procrustes Analysis. The label-invariant approach of shape measurement yields near-optimal results. A relation exists between Procrustes Analysis and the label-invariant measurements, however the relationship is not one to one. The goal is to further understand the implications of the nearly optimal results, and to further glean these intermediate results to form a measure of shape that is efficient and one to one with the Procrustes metric.

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