Studies of Shapes with Bilateral Symmetry

Sheets, D.H.*; Zelditch, M.L.: Studies of Shapes with Bilateral Symmetry

The first step in any comparison of shapes is putting them in a common framework or registration, which is done by superimposition. Superimposition involves placing shapes on top of each other, mathematically rescaling them, and sometimes rotating them so that they differ as little as possible from each other. This allows for mathematical comparison of shape, eliminating differences in size or position of the object. The most common methods of superposition are based on minimizing the morphometric difference between two shapes. We show how these approaches can produce biologically unreasonable superpositions when organisms are bilaterally symmetric. The problem is that the methods do not respect that axis of symmetry. We suggest an alternative approach to superimposition that does respect axes of symmetry. This alternative is likely to be most useful in cases of bilateral symmetry, but may also be useful whenever workers wish to prevent biologically implausible rotations of shapes. Software developed for several superposition methods will be shown and made available.

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