Wavelet analysis of ammonoid sutures

Abstract

A morphometric method based on a continuous wavelet transform is introduced for describing the form of ammonoid suture lines. A series of y-coordinate data along the suture line placed in a common reference system was used as the descriptor function of the cumulative chordal length along the suture line. The wavelet transform is defined as an inner product between the descriptor function and a finite-length localized waveform, termed a "daughter wavelet." The absolute values of wavelet transforms, or amplitudes, were computed for individual daughter wavelets with various wavelengths and positions, and a series of amplitudes for different frequencies was used as a shape function in characterizing the suture shape and was summarized into a few principal components.

Ammonoid Septa and Sutures

“…Eigenshape analysis was employed by Ubukata et al (2009) to quantitatively characterize ammonoid sutures. The same was attempted by Ubukata et al (2014) using wavelet analysis. Undoubtedly, there is still room for research to facilitate the quantification of similarity between sutures, be it between or within taxa or between or within individuals (throughout ontogeny).…”

Buckman’s Rules of Covariation

“…b Intergrading morphological series of Sonninia adicra (Bajocian) illustrating the covariation pattern between ornamentation robustness and whorl section (modified after Westermann 1966 The suture line (imprint of septa on the conch) has been variously quantified: by simple indices such as the number of lobes (e.g., Batt 1991;Saunders et al 1999) or by more complex indices such as fractal indices (e.g., Garcia-Ruiz et al 1990;Boyajian and Lutz 1992;Pérez-Claros 2005;Pérez-Claros et al 2002, by Fourier analysis (Gildner 2003;Allen 2006;Ubukata et al 2014), by geospatial information systems (Manship 2004;Yacobucci and Manship 2011), or by Eigenshape analysis (Ubukata et al 2010). Despite all these tools, the correlation between whorl shape, coiling and suture indentation has rarely been quantified within species.…”

Power scaling of ammonitic suture patterns from Cretaceous Ancyloceratina: constraints on septal/sutural complexity

“…While the shape of suture patterns can be quantified in many useful ways (Westermann ; Yacobucci & Manship ; Ubukata et al . , ), fractal analysis is chosen herein because it particularly reflects the scaling properties of a pattern. Ammonitic sutures often exhibit intricate corrugations over a range of length scales which can be quantified by a power scaling exponent or fractal dimension (Fig.…”