Three-dimensional structure detection from anisotropic alpha-shapes

Abstract

We present an application of a family of affine diagrams to the detection of three-dimensional sampled structures embedded in a perturbated background. This family of diagrams is an extension of the Voronoi diagram, namely the anisotropic diagrams. These diagrams are defined by using a parameterized distance whose unit ball is an ellipsoidal one. The parameters, upon which depends this distance, control the elongation and the orientation of the associated ellipsoidal ball. Based on these diagrams, we define the three-dimensional anisotropic α-shape concept. This concept is an extension of the Euclidean one, it allows us to detect structures, as straight lines and planes, in a given direction. The detection of a more general polyhedral structure is obtained by merging several anisotropic α-shapes, computed for different orientations. © Springer-Verlag Berlin Heidelberg 2005.