Application of harmonized elliptic Fourier transform coefficients for comparing the shapes of biological structures (on the example of the attachment organs of monogenea)

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, raw coefficients contain unnecessary data unrelated to the shape, which does not provide a correct comparison. For this reason the coefficients are normalised. 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 interfere with shape comparison. The paper describes an algorithm for harmonizing the coefficients, leveling the influence of the mentioned information. On the example of attachment organs of monogeneas, the advantages of using harmonized coefficients for comparing the shapes of biological structures are shown.