An Approximative Calculation of Relative Convex Hulls for Surface Area Estimation of 3D Digital Objects

Abstract

Relative convex hulls have been suggested for multigrid-convergent surface area estimation. Besides the existence of a convergence theorem there is no efficient algorithmic solution so far for calculating relative convex hulls. This article discusses an approximative solution based on minimum-length polygon calculations. It is illustrated that this approximative calculation also proves (experimentally) to provide a multigrid convergent measurement. 1 Center for Image Technology and Robotics Tamaki Campus, The University of Auckland, Auckland, New Zealand. lyu011@ec.auckland.ac.nz and r.klette@auckland.ac.nz You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the CITR Tamaki web site under terms that include this permission. All other rights are reserved by the author(s). An Approximative Calculation of Relative Convex Hulls for Surface Area Estimation Linjiang Yu and Reinhard Klette