Fitting Smooth Paths to Speherical Data

Jupp, P. E.; Kent, John T.

doi:10.2307/2347843

Cited by 140 publications

(125 citation statements)

References 16 publications

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“…This agrees with the formula (12) and gives a geometric interpretation of the control vector u in (14).…”

Section: The Rolling Mapsupporting

confidence: 88%

“…In which concerns the interpolation algorithm, the present work generalises ideas and results contained in [10,12] and [11], where only certain manifolds embedded in Euclidean spaces have been considered. The novelty of our results is the approach to solve interpolation problems on the ellipsoid through rolling motions in a non-Euclidean space.…”

Section: Discussionmentioning

confidence: 97%

“…This algorithm is based on a procedure to generate interpolating curves on manifolds embedded in Euclidean space, first described in [12] for the 2-sphere, generalised in [10] for the n-sphere and in [11] for the rotation group and Grassmann manifolds. The algorithm is based on a rolling/unrolling and wrapping/unwrapping technique that will be fully described in the last two sections.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An algorithm based on rolling to generate smooth interpolating curves on ellipsoids

Krakowski¹,

Leite²

2014

Kybernetika

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“…This agrees with the formula (12) and gives a geometric interpretation of the control vector u in (14).…”

Section: The Rolling Mapsupporting

confidence: 88%

Section: Discussionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An algorithm based on rolling to generate smooth interpolating curves on ellipsoids

Krakowski¹,

Leite²

2014

Kybernetika

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“…We develop the necessary details in the appendix and explicitly determine in a short calculation parallel transport on Kendall's space of planar shapes (which are essentially complex projective spaces) in Appendix A.2. We note that [33] computed parallel transport differently, based on which, [31] extended spline-fitting for spherical curves by [24] to shape curves. In another method [12] extended polynomial regression for intrinsic curve fitting.…”

Section: Introductionmentioning

confidence: 99%

Intrinsic MANOVA for Riemannian Manifolds with an Application to Kendall's Space of Planar Shapes

Huckemann

Hotz

Munk

2010

IEEE Trans. Pattern Anal. Mach. Intell.

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Abstract-We propose an intrinsic multi-factorial model for data on Riemannian manifolds as typically occur in the statistical analysis of shape. Due to the lack of a linear structure, linear models cannot be defined in general; to date only one-way MANOVA is available. For a general multi-factorial model, we assume that variation not explained by the model is concentrated near elements defining the effects. By determining the asymptotic distributions of respective sample covariances under parallel transport, we show that they can be compared by standard MANOVA. Often in applications, manifolds are only implicitly given as quotients where the bottom space parallel transport can be expressed through a differential equation. For Kendall's space of planar shapes, we provide an explicit solution. We illustrate our method by an intrinsic two-way MANOVA for a set of leaf shapes. While biologists can identify genotype effects by sight, we can detect height effects that are otherwise not identifiable.

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“…That is, the operations of rotating and smoothing the data are not commutative. Jupp and Kent (1987) provided a detailed critique of various strategies which use Euclidean smoothing for spherical data.…”

Section: Preliminariesmentioning

confidence: 99%

Nonparametric Regression for Spherical Data

Marzio¹,

Panzera²,

Taylor³

2014

Journal of the American Statistical Association

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We develop nonparametric smoothing for regression when both the predictor and the response variables are defined on a sphere of whatever dimension. A local polynomial fitting approach is pursued, which retains all the advantages in terms of rate optimality, interpretability, and ease of implementation widely observed in the standard setting. Our estimates have a multi-output nature, meaning that each coordinate is separately estimated, within a scheme of a regression with a linear response. The main properties include linearity and rotational equivariance. This research has been motivated by the fact that very few models describe this kind of regression. Such current methods are surely not widely employable since they have a parametric nature, and also require the same dimensionality for prediction and response spaces, along with nonrandom design. Our approach does not suffer these limitations. Real-data case studies and simulation experiments are used to illustrate the effectiveness of the method.

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Fitting Smooth Paths to Speherical Data

Cited by 140 publications

References 16 publications

An algorithm based on rolling to generate smooth interpolating curves on ellipsoids

An algorithm based on rolling to generate smooth interpolating curves on ellipsoids

Intrinsic MANOVA for Riemannian Manifolds with an Application to Kendall's Space of Planar Shapes

Nonparametric Regression for Spherical Data

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