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

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A Correction to this article was published on 09 April 2021

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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.

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The data that support the findings of this study are available in the supplementary materials.

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The code that supports the findings of this study is available in the supplementary materials.

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Acknowledgements

We want to acknowledge Emeric Gioan for providing the 3D skull data of different diagnoses. We also acknowledge Dr. Andrea Cardini and Professor Fred. L. Bookstein for advice on the statistical analysis of the fitting results. This work is supported by the National Science Foundation of China under Grant No. 51805080 and the Double first-class construction subsidies of Jiangsu province under Grant No. 4002002011.

Funding

This work is supported by the National Science Foundation of China under Grant No. 51805080 and the Double first-class construction subsidies of Jiangsu province under Grant No. 4002002011.

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Author notes

  1. Shengmin Zhou and Bingjue Li contributed equally to this work.

Authors and Affiliations

  1. School of Mechanical Engineering and Jiangsu Key Laboratory for Design and Manufacture of Micro-Nano Biomedical Instruments, Southeast University, Nanjing, 211189, People’s Republic of China

    Shengmin Zhou, Bingjue Li & Heng Nie

Authors
  1. Shengmin Zhou
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  2. Bingjue Li
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  3. Heng Nie
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Contributions

Bingjue Li proposed the concept and acquired the data. Shengmin Zhou developed the code to fit 3D curves and conduct statistical analyses. Shengmin Zhou and Bingjue Li drafted the manuscript. Heng Nie administrated the data. All the authors revised the manuscript.

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Correspondence to Bingjue Li.

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The original online version of this article was revised: Errors in equations corrected and missing references updated.

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Zhou, S., Li, B. & Nie, H. Parametric fitting and morphometric analysis of 3D open curves based on discrete cosine transform. Zoomorphology 140, 301–314 (2021). https://doi.org/10.1007/s00435-021-00520-w

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