Overview

CartesianDiatom-EFA is a free, open-source, customizable and independent Microsoft Excel 97-2003 program designed and written by RKE to conduct and facilitate a highly visual elliptical Fourier analysis of outlines. The programmatic implementation of the EFA is based on Kuhl & Giardina (1982), Rohlf & Archie (1984), Ferson et al. (1986), Rohlf (1990) and Schmittbuhl et al. (2003) written in Visual Basic for Applications (VBA) code.

The progam interfaces with tpsDIG and ImageJ image analysis software to manage the import of data into Excel. CartesianDiatom-EFA accepts up to 7,500 pairs of x,y-coordinates collected semiautomatically or manually in either clockwise or counterclockwise traces. All diatom outlines brought into CartesianDiatom-EFA can be centered, rotated and reflected so that their center is at the origin of the coordinate system, their apical axes are parallel to the x-axis, and, if the valves are asymmetrical, the larger portions of their reflections about the transapical and apical axes are to the left-of-center and above-center, respectively. Reorientation using user-defined (pseudo)landmarks is permitted. The trace of all outlines is also automatically normalized to originate at the extreme intersection of the positive x-axis and the outline and to proceed clockwise. Outlines can be smoothed using moving average and median filters (in windows ranging from 3 to 25 values) and can be sampled to provide a set of 10 to 1,000 equally spaced points for EFA. Size normalization can be effected based on interlandmark distance, principal axis, semi-major axis of the best fitting ellipse and area. A preview mode permits a visual exploratory comparison of the original and smoothed-and-sampled outlines of any selected valve outline. The above procedures are generic and can be customized by CartesianDiatom to accomodate the demands of particular taxa.

The EFA is conducted on either the original outline of x,y coordinates (if the number is < 1000) or a smoothed-and-sampled outline of x,y coordinates and extracts as many as 30 harmonics (with 4 coefficients per harmonic). For each harmonic the goodness-of-fit between reproduced and smoothed-and-sampled outlines is measured and summarized statistically. For a selected valve another preview mode facilitates the rapid graphic comparison of outlines reproduced using k and (k-1) harmonics superimposed on the original and smoothed-and-sampled outlines. This permits assessing the effects of the highest order harmonic (e.g., k=16 harmonics) chosen compared to the next lower order harmonic (e.g., (k-1)=15 harmonics) in reproducing the outline. Because historically the Fourier coefficients have been characterized as difficult to interpret, we have included also the "elliptical descriptors" of Schmittbuhl et al. (2003), which are readily interpretable as the familiar parameters of ellipses for each harmonic.

The results of the EFA are exported to separate worksheets in a format amenable as input to programs for multivariate analyses, such as principal components or discriminant analyses. The Results worksheet contains basic valve identifier and descriptive information, Fourier coefficients and harmonic amplitudes. A second worksheet stores the Schmittbuhl elliptical descriptors, which can also be subjected to multivariate analyses. These results are available in preview mode for selected valves prior to their export. The EFA may be conducted on selected valves individually or on all valves in the data set as a group, in which case worksheet and graphic output are suppressed, except for the export of the results.

The program additionally includes the ability to reproduce and display outlines based on the Fourier coefficients for selected valves, either singly or in groups of up to 25 valves simultaneously.

Help is provided liberally within the program in ToolTips and pop-up forms and is available more extensively in on-line documentation and downloadable Adobe pdf files.