  Contours may be viewed as the 2D outline of the image of an object. This type
of data arises in medical imaging as well as in computer vision and can be
modeled as data on a manifold and can be studied using statistical shape
analysis. Practically speaking, each observed contour, while theoretically
infinite dimensional, must be discretized for computations. As such, the
coordinates for each contour as obtained at k sampling times, resulting in the
contour being represented as a k-dimensional complex vector. While choosing
large values of k will result in closer approximations to the original contour,
this will also result in higher computational costs in the subsequent analysis.
The goal of this study is to determine reasonable values for k so as to keep
the computational cost low while maintaining accuracy. To do this, we consider
two methods for selecting sample points and determine lower bounds for k for
obtaining a desired level of approximation error using two different criteria.
Because this process is computationally inefficient to perform on a large
scale, we then develop models for predicting the lower bounds for k based on
simple characteristics of the contours.
