Shape Reconstruction from Range Images Using Alpha Shapes Ale S Hole Cek, Tomm a S Pajdla, Vv Aclav Hlavv a C

This report presents the concept of computing a \shape" of a nite set of points in the three-dimensional Euclidean space R 3. To deene the geometric notion of the \shape", a generalization of a convex hull based on an-shape of the set of points is used. An-shape is a polytope uniquely determined by the points and a parameter 2 R, that controls the desired level of detail. Constructing such shapes is based on Delaunay triangulation and can be done with the time complexity O(n 2) for given point set of size n.