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Contours may be viewed as the 2D outline of the image of an object. This typeof data arises in medical imaging as well as in computer vision and can bemodeled as data on a manifold and can be studied using statistical shapeanalysis. Practically speaking, each observed contour, while theoreticallyinfinite dimensional, must be discretized for computations. As such, thecoordinates for each contour as obtained at k sampling times, resulting in thecontour being represented as a k-dimensional complex vector. While choosinglarge 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 keepthe computational cost low while maintaining accuracy. To do this, we considertwo methods for selecting sample points and determine lower bounds for k forobtaining a desired level of approximation error using two different criteria.Because this process is computationally inefficient to perform on a largescale, we then develop models for predicting the lower bounds for k based onsimple characteristics of the contours.

Evaluation and Prediction of Polygon Approximations of Planar Contours for Shape Analysis