Prediction of Lower Bounds for the Number of Sampling Points for Approximating Shapes of Planar Contours

• Activity Number: 360
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Imaging
• Author(s): Chalani Prematilake* and Leif Ellingson
• Companies: Texas Tech University and Texas Tech University
• Keywords: Statistical shape analysis ; Statistics in manifolds ; discretization ; planar contours ; estimation with regression modelling

Abstract

This paper is concerned about finding a lower bound for the number of sampling points for approximating similarity shapes of planar contours. Contours in this context may be thought of as the ranges of simple closed curves. While contours are by their very nature infinite-dimensional, in order for computations to be performed with digital images, discretization is unavoidable and results in some amount of approximation error. To aid in the quantification of this error, we use a polygonal approximation for the contours by evaluating the contours at k times. For a given configuration, polygons were approximated by specifying a margin of error of 0.05. We use two different criteria for polygon approximation and the resulting k-gons are kL-gon and kD-gon. Here kL, kD are the number of sampling points approximated considering the relative error of length and the relative distance, due to approximation. The objective here is to determine a relatively smaller number of sampling points that explain the most of the variation in the original contour. We explore regression models for determining a rough lower bound for the number of sampling points depending on the characteristics of original