Parametric fitting and morphometric analysis of 3D open curves based on discrete cosine transform

Abstract

Fourier transform methods are usually adopted to fit 2D closed curves representing samples’ profiles to be studied in morphometric analysis. As for problems concerning 3D open curves, landmark-based methods are widely used. In this paper, a parametric method based on discrete cosine transform (DCT) is proposed to serve as a morphometric tool for 3D open curves. DCT transforms real signal (coordinates) into a combination of cosine functions. DCT describes the shape of a curve with coefficients generated from the fitting curve. Four examples are introduced to be fitted with DCT. The first example is 3D spiral curves with different shapes, added random disturbances to make this model more general. A curve alignment is also utilized to eliminate the non-shape effect. The other three examples of suture curves abstracted from 3D human skulls on which semilandmarks and landmarks are aligned with General Procrustes Analysis (GPA) to eliminate the effect brought by location, size, and orientation. These 3D curves with different diagnoses are matched with DCT. Coefficients generated in the fitting result are analyzed with between-group principal component analysis (bgPCA) and one-way permutational multivariate analysis of variance (PERMANOVA). Different groups of four examples are separated and present significant differences in the results of one-way PERMANOVA. Statistical analyses demonstrate that DCT is promising in morphometric analysis of 3D open curves.