Surface area estimation of digitized 3D objects using quasi-Monte Carlo methods

A novel and efficient quasi-Monte Carlo method for estimating the surface area of digitized 3D objects in the volumetric representation is presented. It operates directly on the original digitized objects without any surface reconstruction procedure. Based on the Cauchy–Crofton formula from integral geometry, the method estimates the surface area of a volumetric object by counting the number of intersection points between the objectʹs boundary surface and a set of uniformly distributed lines generated with low-discrepancy sequences. Using a clustering technique, we also propose an effective algorithm for computing the intersection of a line with the boundary surface of volumetric objects. A number of digitized objects are used to evaluate the performance of the new method for surface area measurement.