Our methods are applied to data on the gaits of a group of 5-year-old children. We propose smooth nonparametric estimates of the eigen-functions and a suitable method of cross-validation to determine the amount of smoothing. In the estimation of the covariance structure, we are primarily concerned with models in which the first few eigenfunctions are smooth and the eigenvalues decay rapidly, so that the variability is predominantly of large scale. This method of cross-validation, which consists of deleting entire sample curves, has the advantage that it does not require that the covariance structure be known or estimated.
We suggest a variant on the usual form of cross-validation for choosing the degree of smoothing to be employed. We propose a method of estimating the mean function non-parametrically under the assumption that it is smooth.
We develop methods for the analysis of a collection of curves which are stochastically modelled as independent realizations of a random function with an unknown mean and covariance structure. Although this provided a means of automatically parameterising shape variability, the method was difficult. 1 Introduction We have previously described a method for modelling two dimensional shape, based on the statistics of chord lengths over a set of examples. We demonstrate the application of the Point Distribution Model in describing two classes of shapes. The method produces a compact flexible `Point Distribution Model' with a small number of linearly independent parameters, which can be used during image search. In this way allowed variation in shape can be included in the model. The mean positions of the points give an average shape and a number of modes of variation are deter# mined describing the main ways in which the example shapes tend to deform from the average. The technique determines the statistics of the points over a collection of example shapes. A method for building flexible shape models is presented in which a shape is represented by a set of labelled points.