Shape Fitting and Morphometric Analysis of Open Curves Based on Discrete Cosine Transform

Fourier series have been widely used in morphometric analysis to fit and describe 2D closed curves that represent the profiles of the samples to be studied. As for problems concerning open profiles, researchers either connect the endpoints of the curves and treat them as closed curves, or adopt other analysis techniques such as landmark-based geometric methods. This paper presents a method to fit 2D and 3D open curves based on discrete cosine transform (DCT), which transforms the input coordinate signals to output ones. The 2D example is normalized with general procrustes analysis (GPA) before fitted with DCT. DCT can describe shapes with the coefficients produced in fitting results. A total of 90 2D open curves that represent leaf profiles of 9 genera are fitted using DCT method. A stepwise Fisher discriminant analysis (FDA) is then conducted for genus classification. DCT method is also applied to 3D cochlear centerlines, lambdoidal sutures and nasal-apertures of human skulls. The results prove that DCT method is capable of fitting chaotic curves or smooth curves that are difficult to find or lack homologous landmarks and providing useful parameters for discrimination.