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The Frenet-Serret framework for aligning geometric curves

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSNConference contribution/Paperpeer-review

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The Frenet-Serret framework for aligning geometric curves. / Brunel, Nicolas; Park, Juhyun.

Geometric Science of Information: 4th International Conference, GSI 2019, Toulouse, France, August 27–29, 2019, Proceedings. ed. / Frank Nielsen; Frédéric Barbaresco. Cham : Springer, 2019. p. 608-617 (Lecture Notes in Computer Science; Vol. 11712).

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSNConference contribution/Paperpeer-review

Harvard

Brunel, N & Park, J 2019, The Frenet-Serret framework for aligning geometric curves. in F Nielsen & F Barbaresco (eds), Geometric Science of Information: 4th International Conference, GSI 2019, Toulouse, France, August 27–29, 2019, Proceedings. Lecture Notes in Computer Science, vol. 11712, Springer, Cham, pp. 608-617, GSI 2019, Toulouse, France, 27/08/19. <https://www.springer.com/gp/book/9783030269791>

APA

Brunel, N., & Park, J. (2019). The Frenet-Serret framework for aligning geometric curves. In F. Nielsen, & F. Barbaresco (Eds.), Geometric Science of Information: 4th International Conference, GSI 2019, Toulouse, France, August 27–29, 2019, Proceedings (pp. 608-617). (Lecture Notes in Computer Science; Vol. 11712). Springer. https://www.springer.com/gp/book/9783030269791

Vancouver

Brunel N, Park J. The Frenet-Serret framework for aligning geometric curves. In Nielsen F, Barbaresco F, editors, Geometric Science of Information: 4th International Conference, GSI 2019, Toulouse, France, August 27–29, 2019, Proceedings. Cham: Springer. 2019. p. 608-617. (Lecture Notes in Computer Science).

Author

Brunel, Nicolas ; Park, Juhyun. / The Frenet-Serret framework for aligning geometric curves. Geometric Science of Information: 4th International Conference, GSI 2019, Toulouse, France, August 27–29, 2019, Proceedings. editor / Frank Nielsen ; Frédéric Barbaresco. Cham : Springer, 2019. pp. 608-617 (Lecture Notes in Computer Science).

Bibtex

@inproceedings{ed78523b584444f58052e4a0e150ab3b,
title = "The Frenet-Serret framework for aligning geometric curves",
abstract = "Variations of the curves and trajectories in 1D can be analysed efficiently with functional data analysis tools. The main sources of variations in 1D curves have been identified as amplitude and phase variations. Dealing with the latter gives rise to the problem of curve alignment and registration problems. It has been recognised that it is important to incorporate geometric features of the curves in developing statistical approaches to address such problems. Extending these techniques to multidimensional curves is not obvious, as the notion of multidimensional amplitude can be dened in multiple ways. We propose a framework to deal with the curve alignment in multidimensional curves as 3D objects. In particular, we propose a new distance between the curves that utilises the geometric information of the curves through the Frenet-Serret representation of the curves. This can be viewed as a generalisation of the elastic shape analysis based on the square root velocity framework. We develop an efficient computational algorithm to find an optimal alignment based on the proposed distance using dynamic programming.",
author = "Nicolas Brunel and Juhyun Park",
year = "2019",
month = aug,
day = "31",
language = "English",
isbn = "9783030269791",
series = "Lecture Notes in Computer Science",
publisher = "Springer",
pages = "608--617",
editor = "Frank Nielsen and Fr{\'e}d{\'e}ric Barbaresco",
booktitle = "Geometric Science of Information",
note = "GSI 2019 : 4th Conference on Geometric Science of Information, 4th ; Conference date: 27-08-2019 Through 29-08-2019",
url = "https://www.see.asso.fr/en/GSI2019",

}

RIS

TY - GEN

T1 - The Frenet-Serret framework for aligning geometric curves

AU - Brunel, Nicolas

AU - Park, Juhyun

PY - 2019/8/31

Y1 - 2019/8/31

N2 - Variations of the curves and trajectories in 1D can be analysed efficiently with functional data analysis tools. The main sources of variations in 1D curves have been identified as amplitude and phase variations. Dealing with the latter gives rise to the problem of curve alignment and registration problems. It has been recognised that it is important to incorporate geometric features of the curves in developing statistical approaches to address such problems. Extending these techniques to multidimensional curves is not obvious, as the notion of multidimensional amplitude can be dened in multiple ways. We propose a framework to deal with the curve alignment in multidimensional curves as 3D objects. In particular, we propose a new distance between the curves that utilises the geometric information of the curves through the Frenet-Serret representation of the curves. This can be viewed as a generalisation of the elastic shape analysis based on the square root velocity framework. We develop an efficient computational algorithm to find an optimal alignment based on the proposed distance using dynamic programming.

AB - Variations of the curves and trajectories in 1D can be analysed efficiently with functional data analysis tools. The main sources of variations in 1D curves have been identified as amplitude and phase variations. Dealing with the latter gives rise to the problem of curve alignment and registration problems. It has been recognised that it is important to incorporate geometric features of the curves in developing statistical approaches to address such problems. Extending these techniques to multidimensional curves is not obvious, as the notion of multidimensional amplitude can be dened in multiple ways. We propose a framework to deal with the curve alignment in multidimensional curves as 3D objects. In particular, we propose a new distance between the curves that utilises the geometric information of the curves through the Frenet-Serret representation of the curves. This can be viewed as a generalisation of the elastic shape analysis based on the square root velocity framework. We develop an efficient computational algorithm to find an optimal alignment based on the proposed distance using dynamic programming.

M3 - Conference contribution/Paper

SN - 9783030269791

T3 - Lecture Notes in Computer Science

SP - 608

EP - 617

BT - Geometric Science of Information

A2 - Nielsen, Frank

A2 - Barbaresco, Frédéric

PB - Springer

CY - Cham

T2 - GSI 2019

Y2 - 27 August 2019 through 29 August 2019

ER -