In this paper, we describe a novel method for searching and comparing 3D objects. The method encodes the geometric and topological information in the form of a skeletal graph and uses graph matching techniques to match the skeletons and to compare them. The skeletal graphs can be manually annotated to refine or restructure the search. This helps in choosing between a topological similarity and a geometric (shape) similarity. A feature of skeletal matching is the ability to perform part-matching, and its inherent intuitiveness, which helps in defining the search and in visualizing the results. Also, the matching results, which are presented in a per-node basis can be used for driving a number of registration algorithms, most of which require a good initial guess to perform registration. In this paper, we also describe a visualization tool to aid in the selection and specification of the matched objects.

Digital 3D models of the environment are needed in rescue and inspection robotics, facility managements and architecture. This paper presents an automatic system for gaging and digitalization of 3D indoor environments. It consists of an autonomous mobile robot, a reliable 3D laser range finder and three elaborated software modules. The first module, a fast variant of the Iterative Closest Points algorithm, registers the 3D scans in a common coordinate system and relocalizes the robot. The second module, a next best view planner, computes the next nominal pose based on the acquired 3D data while avoiding complicated obstacles. The third module, a closed-loop and globally stable motor controller, navigates the mobile robot to a nominal pose on the base of odometry and avoids collisions with dynamical obstacles. The 3D laser range finder acquires a 3D scan at this pose. The proposed method allows one to digitalize large indoor environments fast and reliably without any intervention and solves the SLAM problem. The results of two 3D digitalization experiments are presented using a fast octree-based visualization method.

This paper describes a new method to extract feature lines directly from a surface point cloud. No surface reconstruction is needed in advance, only the inexpensive computation of a neighbor graph connecting nearby points.

Curve-skeletons are thinned 1D representations of 3D objects useful for many visualization tasks including virtual navigation, reduced-model formulation, visualization improvement, 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.

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A surface reconstruction algorithm takes as input a set of sample points from an unknown closed and smooth surface in 3-d space, and produces a piece-wise linear approximation of the surface that contains the sample points. Variants of this problem have received considerable attention in computer vision and computer graphics and more recently in computational geometry. In the latter area, three different algorithms (Amenta and Bern `98, and refined in Amenta, Choi, Dey and Leekha `00; Amenta, Choi and Kolluri `00; Boissonnat and Cazals `00) have been proposed. These algorithms have a correctness guarantee: if the sample is sufficiently dense then the output is a good approximation to the original surface. They have unfortunately a worst-case running time that is quadratic in the size of the input. This is so because they are based on the construction of 3-d Voronoi diagrams or Delaunay tetrahedrizations, which can have quadratic size. Even worse, according to recent work (Erickson `01), there are surfaces for which this is the case even when the sample set is "locally uniform" on the surface. In this paper, we describe a new algorithm that also has a correctness guarantee but whose worst-case running time is almost linear. In fact, O(n log n) where n is the input size. As in some of the previous algorithms, the piece-wise linear approximation produced by the new algorithm is a subset of the 3-d Delaunay tetrahedrization; however, this is obtained by computing only the relevant parts of the 3-d Delaunay structure. The algorithm first estimates for each sample point the surface normal and a parameter that is then used to "decimate" the set of samples. The resulting subset of sample points is locally uniform and so a reconstruction based on it can be compu...

Abstract: Probabilistic Roadmaps (PRM) have been successfully used to plan complex robot motions in configuration spaces of small and large dimensionalities. However, their efficiency decreases dramatically in spaces with narrow passages. This paper presents a new method – smallstep retraction – that helps PRM planners find paths through such passages. This method consists of slightly “fattening ” robot’s free space, constructing a roadmap in fattened free space, and finally repairing portions of this roadmap by retracting them out of collision into actual free space. Fattened free space is not explicitly computed. Instead, the geometric models of workspace objects (robot links and/or obstacles) are “thinned ” around their medial axis. A robot configuration lies in fattened free space if the thinned objects do not collide at this configuration. Two repair strategies are proposed. The “optimist ” strategy waits until a complete path has been found in fattened free space before repairing it. Instead, the “pessimist ” strategy repairs the roadmap as it is being built. The former is usually very fast, but may fail in some pathological cases. The latter is more reliable, but not as fast. A simple combination of the two strategies yields an integrated planner that is both fast and reliable. This planner was implemented as an extension of a pre-existing single-query PRM planner. Comparative tests show that it is significantly faster (sometimes by several orders of magnitude) than the pre-existing planner. 1.

Robust integration of range images is an important task for building high-quality 3D models. Since range images, and in particular range maps from stereo vision, may have a substantial amount of outliers, any integration approach aiming at high-quality models needs an increased level of robustness. Additionally, a certain level of regularization is required to obtain smooth surfaces. Computational efficiency and global convergence are further preferable properties. The contribution of this paper is a unified framework to solve all these issues. Our method is based on minimizing an energy functional consisting of a total variation (TV) regularization force and an L 1 data fidelity term. We present a novel and efficient numerical scheme, which combines the duality principle for the TV term with a point-wise optimization step. We demonstrate the superior performance of our algorithm on the well-known Middlebury multi-view database and additionally on real-world multi-view images. 1.

We consider the use of medial surfaces to represent symmetries of 3-D objects. This allows for a qualitative abstraction based on a directed acyclic graph of components and also a degree of invariance to a variety of transformations including the articulation of parts. We demonstrate the use of this representation for 3-D object model retrieval. Our formulation uses the geometric information

Skeleton is a lower dimensional shape description of an object. The requirements of a skeleton di#er with applications. For example, object recognition requires primitive features to make similarity comparison. On the other hand, detailed geometry descriptions are essential to reduce the approximation error for surface reconstruction. Whereas many previous works have been done, most of these methods are time consuming and sensitive to noise, or restricted to specific 3D models.