The statistical analysis of dynamic curves and sections

摘要

By a curve, we shall understand a one-dimensional smooth path lying in R2 or R3 which can be naturally parametrized by a real coordinate. The coordinate could represent physical time or any other variable which can be interpreted dynamically. In some cases, the curve will arise as the linear section of a higher-dimensional structure such as the planar section of a surface in R3. In this paper, we develop a model for the shape of planar curves, based on their curvatures, that is reasonably robust to the location of landmarks or knots used to approximate the contours of the curve. The measurement for the shape difference between two curves that we propose is also based on the curvatures of the curves and directly inherits the simple Euclidean property for averages.