Probabilistic Roadmap (PRM) planners have been successful in path planning of robots with many degrees of freedom, but they behave poorly when a robot's configuration space contains narrow passages. This paper presents workspace importance sampling (WIS), a new sampling strategy for PRM planning. Our main idea is to use geometric information from a robot's workspace as "importance" values to guide sampling in the corresponding configuration space. By doing so, WIS increases the sampling density in narrow passages and decreases the sampling density in wide-open regions. We tested the new planner on rigid-body and articulated robots in 2-D and 3-D environments. Experimental results show that WIS improves the planner's performance for path planning problems with narrow passages.

Curve-skeletons are a 1D subset of the medial surface of a 3D object and are useful for many visualization tasks including virtual navigation, reduced-model formulation, visualization improvement, mesh repair, animation, etc. There are many algorithms in the literature describing extraction methodologies for different applications; however, it is unclear how general and robust they are. In this paper, we provide an overview of many curve-skeleton applications and compile a set of desired properties of such representations. We also give a taxonomy of methods and analyze the advantages and drawbacks of each class of algorithms.

In this paper, we propose a new scheme for free-form skeleton-driven global mesh deformations. First a Voronoi-based skeletal mesh is extracted from a given original mesh. Next the skeletal mesh is modified by free-form deformations. Then a desired global shape deformation is obtained by reconstructing the shape corresponding to the deformed skeletal mesh. We develop a mesh fairing procedure allowing us to avoid possible global and local self-intersections of the reconstructed mesh. Finally, using DSS [16] shape representation improves the speed and robustness of our approach.

3D scanners, iso-surface extraction procedures, and several recent geometric compression schemes sample surfaces of 3D shapes in a regular fashion, without any attempt to align the samples with the sharp edges and corners of the original shape. Consequently, the interpolating triangle meshes chamfer these sharp features and thus exhibit significant errors. The new Edge-Sharpener filter introduced here identifies the chamfer edges and subdivides them and their incident triangles by inserting new vertices and by forcing these vertices to lie on intersections of planes that locally approximate the smooth surfaces that meet at these sharp features.

In this paper, we propose a novel surface reconstruction technique based on Bayesian statistics: The measurement process as well as prior assumptions on the measured objects are modeled as probability distributions and Bayes ’ rule is used to infer a reconstruction of maximum probability. The key idea of this paper is to define both measurements and reconstructions as point clouds and describe all statistical assumptions in terms of this finite dimensional representation. This yields a discretization of the problem that can be solved using numerical optimization techniques. The resulting algorithm reconstructs both topology and geometry in form of a well-sampled point cloud with noise removed. In a final step, this representation is then converted into a triangle mesh. The proposed approach is conceptually simple and easy to extend. We apply the approach to reconstruct piecewise-smooth surfaces with sharp features and examine the performance of the algorithm on different synthetic and real-world data sets. Categories and Subject Descriptors (according to ACM CCS): I.5.1 [Models]: Statistical; I.3.5 [Computer Graphics]: Curve, surface, solid and object representations

We consolidate an unorganized point cloud with noise, outliers, non-uniformities, and in particular interference between close-by surface sheets as a preprocess to surface generation, focusing on reliable normal estimation. Our algorithm includes two new developments. First, a weighted locally optimal projection operator produces a set of denoised, outlier-free and evenly distributed particles over the original dense point cloud, so as to improve the reliability of local PCA for initial estimate of normals. Next, an iterative framework for robust normal estimation is introduced, where a priority-driven normal propagation scheme based on a new priority measure and an orientation-aware PCA work complementarily and iteratively to consolidate particle normals. The priority setting is reinforced with front stopping at thin surface features and normal flipping to enable robust handling of the close-by surface sheet problem. We demonstrate how a point cloud that is wellconsolidated by our method steers conventional surface generation schemes towards a proper interpretation of the input data. 1

A theoretical and computational framework for computing intrinsic distance functions and geodesics on submanifolds of Rd given by point clouds is introduced and developed in this paper. The basic idea is that, as shown here, intrinsic distance functions and geodesics on general co-dimension submanifolds of Rd can be accurately approximated by extrinsic Euclidean ones computed inside a thin offset band surrounding the manifold. This permits the use of computationally optimal algorithms for computing distance functions in Cartesian grids. We use these algorithms, modified to deal with spaces with boundaries, and obtain a computationally optimal approach also for the case of intrinsic distance functions on submanifolds of Rd. For point clouds, the offset band is constructed without the need to explicitly find the underlying manifold, thereby computing intrinsic distance functions and geodesics on point clouds while skipping the manifold reconstruction step. The case of point clouds representing noisy samples of a submanifold of Euclidean space is studied as well. All the underlying theoretical results are presented along with experimental examples for diverse applications and comparisons to graph-based distance algorithms.

We present a novel surface reconstruction algorithm that can recover high-quality surfaces from noisy and defective data sets without any normal or orientation information. A set of new techniques are introduced to afford extra noise tolerability, robust orientation alignment, reliable outlier removal, and satisfactory feature recovery. In our algorithm, sample points are first organized by an octree. The points are then clustered into a set of monolithically singlyoriented groups. The inside/outside orientation of each group is determined through a robust voting algorithm. We locally fit an implicit quadric surface in each octree cell. The locally fitted implicit surfaces are then blended to produce a signed distance field using the modified Shepard’s method. We develop sophisticated iterative fitting algorithms to afford improved noise tolerance both in topology recognition and geometry accuracy. Furthermore, this iterative fitting algorithm, coupled with a local model selection scheme, provides a reliable sharp feature recovery mechanism even in the presence of bad input.

Many algorithms in computer graphics improve their efficiency by using Hierarchical Space Subdivision Schemes (HS 3), such as octrees, kD-trees or BSP trees. Such HS 3 usually provide an axis-aligned subdivision of the 3D space embedding a scene or an object. However, the purely volume-based behavior of these schemes often leads to strongly imbalanced surface clustering. In this article, we introduce the VS-Tree, an alternative HS 3 providing efficient and accurate surface-based hierarchical clustering via a combination of a global 3D decomposition at coarse subdivision levels, and a local 2D decomposition at fine levels near the surface. First, we show how to efficiently construct VS-Trees over meshes and point-based surfaces, and analyze the improvement it offers for cluster-based surface simplification methods. Then we propose a new surface reconstruction algorithm based on the volume-surface classification of the VS-Tree. This new algorithm is faster than state-of-the-art reconstruction methods and provides a final semi-regular mesh comparable to the output of remeshing algorithms. 1.

The signed distance field of a surface can effectively support many geometry processing tasks such as decimation, smoothing, and Boolean operations since it provides efficient access to distance (error) estimates. In this paper we present an algorithm to compute a piecewise linear, not necessarily continuous approximation of the signed distance field for a given object. Our approach is based on an adaptive hierarchical space partition that stores a linear distance function in every leaf node. We provide positive and negative criteria for selecting the splitting planes. Consequently the algorithm adapts the leaf cells of the space partition to the geometric shape of the underlying model better than previous methods. This results in a hierarchical representation with comparably low memory consumption and which allows for fast evaluation of the distance field function.