Computing Shapes from Point Cloud Data

Abstract

The problem of modeling a shape from point cloud data arises in many areas of science and engineering. Recent advances in scanning technology and scientific simulations can generate sample points from a geometric domain with ease. Perhaps the most usual sampled domain is the boundary of a 3D object, which is a surface in 3D. Consequently, the problem of surface reconstruction has been a topic of intense research in recent years. In this talk we will present a surface reconstruction algorithm popularly known as Cocone that simplified and improved its predecessor called Crust. We will discuss its mathematically provable guarantees and issues related to its successful implementation.

The concepts used in Cocone have been further extended to other problems in sample based modeling. We show how these concepts can be used to decimate a point cloud dataset while preserving the shape features. We extend the Cocone theory and methods to detect the dimension of a manifold from its point samples, where the manifold is embedded in an Euclidean space. In a recent work we used the Cocone concepts to approximate the medial axis of a smooth surface from the Voronoi diagram of its point samples. We will discuss these extensions and present our theoretical and experimental results.