The discrete cosine transform, a Fourier-related method for morphometric analysis of open contours

The discrete cosine transform (DCT) is described and then tested to see whether it is a suitable Fourier-related method for morphometric analysis of open outlines. While most Fourier methods are mainly effective with closed outlines, the DCT can handle open curves too, making it useful for quantitative descriptions of a broad range of natural objects. Like other Fourier-type methods, the DCT yields informative numerical signatures; the shape serves as input for subsequent multivariate analysis, with, for example, principal component analysis (PCA). To test the DCT as a morphometric tool, a set of 32 ammonite ribs was analyzed. The ammonites, representing 16 different species belonging to nine genera, were from the Hildoceratidae, a major Lower Jurassic family with essentially falcoid s.l. ribs, whose taxonomy is based largely on their ornamentation. Species were selected to illustrate the broad spectrum of ribbing patterns from almost straight to falcate via sigmoidal or falcoid, exhibited by the NW European Hildoceratidae. The first six harmonic amplitudes computed by the DCT were processed by PCA. The first three factorial axes of the PCA accounted for 87.2% of the total variance. Projections of the specimens on the first two factorial planes provide a well structured plot of the entire morphospace, demonstrating that the DCT is a promising and effective tool for morphometry.