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Longitudinal shape analysis by using the spherical coordinates

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  • M. Moghimbeygi
  • M. Golalizadeh

Abstract

One of the important topics in morphometry that received high attention recently is the longitudinal analysis of shape variation. According to Kendall's definition of shape, the shape of object appertains on non-Euclidean space, making the longitudinal study of configuration somehow difficult. However, to simplify this task, triangulation of the objects and then constructing a non-parametric regression-type model on the unit sphere is pursued in this paper. The prediction of the configurations in some time instances is done using both properties of triangulation and the size of great baselines. Moreover, minimizing a Euclidean risk function is proposed to select feasible weights in constructing smoother functions in a non-parametric smoothing manner. These will provide some proper shape growth models to analysis objects varying in time. The proposed models are applied to analysis of two real-life data sets.

Suggested Citation

  • M. Moghimbeygi & M. Golalizadeh, 2017. "Longitudinal shape analysis by using the spherical coordinates," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(7), pages 1282-1295, May.
    • Handle: RePEc:taf:japsta:v:44:y:2017:i:7:p:1282-1295
    DOI: 10.1080/02664763.2016.1201798
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    References listed on IDEAS

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    1. Alfred Kume & Ian L. Dryden & Huiling Le, 2007. "Shape-space smoothing splines for planar landmark data," Biometrika, Biometrika Trust, vol. 94(3), pages 513-528.
    2. Michael J. Prentice, 1987. "Fitting Smooth Paths to Rotation Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 325-331, November.
    3. Julian J. Faraway & Carroll‐Ann Trotman, 2011. "Shape change along geodesics with application to cleft lip surgery," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 60(5), pages 743-755, November.
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    Cited by:

    1. Meisam Moghimbeygi & Mousa Golalizadeh, 2019. "A longitudinal model for shapes through triangulation," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(1), pages 99-121, March.

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