Morphometry and statistical treatments
Form constitutes a holistic parameter from which a lot of information retrieved : growth conditions, speciation, recording of environmental parameters, etc. Nevertheless, understanding a form, which is aboveall a qualitative parameter, is a difficult task. Mathematics provide all the necessary fundamental tools and concepts to make the extraction of quantitative form variables possible : this is the aim of morphometry. The Biogeosciences Laboratory has developed methods in this area using tools such as the DCT (Discrete Cosine Transform), the Fourier Transform, the wavelet transform, and fractal analysis. These methods have been applied to objects without landmarks such as mollusk shells and corals (Figure 1). Finally, the Biogeosciences Laboratory develops methods of multivariate statistical analysis with applications for data acquired both in the field and laboratory.
For more information:
Vancolen S. & Verrecchia E.P. (2008): Does prism width from the shell prismatic layer have a random distribution? Geo Marine Letters 28, 383-393.
Chappatte D. & Verrecchia, E.P. (2009): Discrete simulation of biogeochemical exchanges in a microbial mat. IAMG 2009 Computational Methods for the Earth, Energy and Environmental Sciences, August 23-28, Stanford University, USA.
Dommergues C.H., Dommergues J.-L. & Verrecchia E.P. (2007). The discrete cosine transform, a Fourier-related method for morphometric analysis of open contours. Mathematical Geology 39, 749-763.
Martin-Garin B., Lathuilière B., Verrecchia E.P. & Geister J. (2007): Use of fractal dimension to quantify coral shape. Coral Reefs 26, 541-550.
Verrecchia E.P. (2005): Multiresolution analysis of shell growth increments to detect natural cycles. pp.273-293 in Francus P. (eds.) Image and paleoenvironmental reconstuction. Developments in Paleoenvironmental Research Book Series 7. Kluwer Academic Plubishers, Amsterdam.
Verrecchia E.P. (2003): Image analysis and morphometry of geological objects. Mathematical Geology 35, 759-762.