Korea University Department of Statistics

2011년 1회 통계세미나 개최를 알려드리고자 합니다.

일시: 2011년 3월 30일(수) 오후 5시

장소: 고려대학교 정경관 507호

연사: Kim Kwang-Rae

(Department of Statistics, korea University)

"Frenet-Serret and the Estimation of

Curvature and Torsion" 

In this paper we approach the problem of analyzing space-time curves from a functional data analytic point of view. 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 on the other hand 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.