Frenet-Serret and the Estimation of Curvature and Torsion
- Authors
- Kim, Kwang-Rae; Kim, Peter T.; Koo, Ja-Yong; Pierrynowski, Michael R.
- Issue Date
- 8월-2013
- Publisher
- IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
- Keywords
- Binormal; biomechanics; bone pin and skin marker; differential equations; knots; normal; smooth curve; splines; tangent
- Citation
- IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING, v.7, no.4, pp.646 - 654
- Indexed
- SCIE
SCOPUS
- Journal Title
- IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING
- Volume
- 7
- Number
- 4
- Start Page
- 646
- End Page
- 654
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/102516
- DOI
- 10.1109/JSTSP.2012.2232280
- ISSN
- 1932-4553
- Abstract
- In this paper we approach the problem of analyzing space-time curves. In terms of classical geometry, the characterization of space-curves can be summarized in terms of a differential equation involving functional parameters curvature and torsion whose origins are from the Frenet-Serret framework. In particular, curvature measures the rate of change of the angle which nearby tangents make with the tangent at some point. In the situation of a straight line, curvature is zero. Torsion measures the twisting of a curve, and the vanishing of torsion describes a curve whose three dimensional range is restricted to a two-dimensional plane. By using splines, we provide consistent estimators of curves and in turn, this provides consistent estimators of curvature and torsion. We illustrate the usefulness of this approach on a biomechanics application.
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Collections - College of Political Science & Economics > Department of Statistics > 1. Journal Articles
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