The hidden point removal (HPR) operator introduced by Katz et al. [KTB07] provides an elegant solution for the problem of estimating the visibility of points in point samplings of surfaces. Since the method requires computing the three-dimensional convex hull of a set with the same cardinality as the original cloud, the method has been largely viewed as impractical for real-time rendering of medium to large clouds. In this paper we examine how the HPR operator can be used more efficiently by combining several image space techniques, including an approximate convex hull algorithm, cloud sampling, and GPU programming. Experiments show that this combination permits faster renderings without overly compromising the accuracy.