Application of Harmonized Elliptic Fourier Transform Coefficients for Comparing the Shapes of Biological Structures (Example of the Attachment Organs of Monogenea).

The elliptic Fourier transform is a common method of describing the shape of objects by an unique sequence of coefficients that allow comparing the shapes by mathematical methods. However, the raw coefficients contain unnecessary data unrelated to the shape, which does not provide a correct comparison. For this reason, the coefficients are normalized. This removes some of the superfluous data, but leaves information about mirror symmetry and the order in which the contour vertices are declared, that are encoded in the signs of the coefficients. This also interferes with shape comparison. The paper describes an algorithm for harmonizing the coefficients, leveling the influence of the information mentioned. Based on the example of attachment organs of monogeneans, the advantages of using harmonized coefficients for comparing the shapes of biological structures are shown. [ABSTRACT FROM AUTHOR]