Visibility of noisy point cloud data

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We present a robust algorithm for estimating visibility from a given viewpoint for a point set containing concavities, non-uniformly spaced samples, and possibly corrupted with noise. Instead of performing an explicit surface reconstruction for the points set, visibility is computed based on a construction involving convex hull in a dual space, an idea inspired by the work of Katz et al. [26]. We derive theoretical bounds on the behavior of the method in the presence of noise and concavities, and use the derivations to develop a robust visibility estimation algorithm. In addition, computing visibility from a set of adaptively placed viewpoints allows us to generate locally consistent partial reconstructions. Using a graph based approximation algorithm we couple such reconstructions to extract globally consistent reconstructions. We test our method on a variety of 2D and 3D point sets of varying complexity and noise content.