Surface Representation and Morphometric Analysis Based on Discrete Cosine Transform
Tóm tắt
Fourier series are usually employed to describe closed or open, 2D or 3D outlines of biological samples. Landmark-based morphometric methods are widely used in the analysis of 3D surfaces. There are few investigations on the representation and morphometric analysis of 3D biological sample surfaces with methods relating to Fourier series. In this paper, we firstly extend discrete cosine transform (DCT), a Fourier-related method classically used to describe 2D open curves, but here to 3D surfaces. Surfaces are transformed into 3D curves with a path connecting all points. The path can be determined manually by an analyst or by algorithms. Before being represented with DCT, non-shape effects should be eliminated. A strategy to improve the selection of coefficients to approximate surfaces is also presented. As a result, the mathematical homology of the coefficients is preserved while fast convergence of the approximation is ensured. Three 3D surface examples are transformed into 3D curves and represented with DCT. The first example is four groups of 120 simulated surfaces generated with equations, and the other two examples are 3D surfaces extracted from aligned 3D human skulls with four types of diagnoses of coronal craniosynostosis. Principal component analysis, one-way analysis of similarity, and one-way permutational multivariate analysis of variance are utilized to analyze the coefficients obtained. The results of statistical analyses suggest that DCT is an effective and stable tool in describing 3D surfaces.
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