As the number of in-house and public-domain 3D shape models increase, importance of shape-similarity based search and retrieval for 3D shapes models has increased rapidly. In this paper, we describe our preliminary findings in applying a multiresolution analysis technique to the task of shape similarity comparison of polygon soup models. We used the 3D alpha shapes algorithm to create a multire...

We introduce order-k α-hulls and αshapes — generalizations of α-hulls and α-shapes. Being also a generalization of k-hull (known in statistics as “k-depth contour”), order-k α-hull provides a link between shape reconstruction and statistical depth. As a generalization of α-hull, order-k α-hull gives a robust shape estimation by ignoring locally up to k outliers in a point set. Order-k α-shape p...

Intuitively, many wireless and sensing applications benefit from knowledge of network boundaries. Many virtual coordinate constructions rely on the furthest set of nodes as beacons. Network edges may also bound routing holes in the network, regions of failure due to environmental effects, or indicate the need for additional deployment. In this paper we solve the edge detection problem locally u...

We present a method to extract polyhedral structures from a three-dimensional set of points, even if these structures are embedded in a perturbed background. The method is based on a family of affine diagrams which is an extension of the Voronoi diagram. These diagrams, namely anisotropic diagrams, are defined by using a parameterized distance whose unit ball is an ellipsoidal one. The paramete...

Distance-dependent, pairwise, statistical potentials are based on the concept that the packing observed in known protein structures can be used as a reference for comparing different 3D models for a protein. Here, packing refers to the set of all pairs of atoms in the molecule. Among all methods developed to assess threedimensional models, statistical potentials are subject both to praise for t...

Detailed geometric models of the real world are in increasing demand. LiDAR data is appropriate to reconstruct such models. For urban reconstruction, it works well to reconstruct the individual surfaces of the scene and connect them to form the scene geometry. There are various methods for reconstructing the free-form shape of a point sample on a single surface. However, these methods do not ta...

The existing algorithms for 3D surface reconstruction from point clouds require objects with smooth surfaces and extremely dense samplings with no or only very few noise in order to guarantee a correct result. Moreover they can only be applied to single object reconstruction and not to segmentation of three or more regions. We have developed an alternative surface reconstruction method wich pre...

We present a method to extract polyhedral structures from a three-dimensional set of points, even if these structures are embedded in a perturbed background. The method is based on a family of affine diagrams which is an extension of the Voronoi diagram. These diagrams, namely anisotropic diagrams, are defined by using a parameterized distance whose unit ball is an ellipsoidal one. The paramete...

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 shap...