1359860
Skewed Mirror Symmetry in the 3D Reconstruction of Polyhedral Models
We aim to reconstruct three-dimensional polyhedra from axonometric line drawings. Existence of mirror symmetry in polyhedra can assist the reconstruction process. We present a new approach for determining planes of mirror symmetry of such polyhedral objects based on prior detection of their planar faces and any axes of symmetry of these faces. The axes are obtained from skewed facial symmetries, for which we also give a new method of determination.
20893351
Automatic inspection of mechanical parts using geometric models and laser range finder data
Abstract This paper addresses the problems associated in processing arrays of depth data in order to achieve the goal of automatic inspection of mechanical parts, i. e. developing general model-based inspection strategies that can be applied to a range of objects. The main problems in processing this data are segmenting out reliable primitives from the data and matching these primitives to those in a stored geometric model of an object. The ability of a 3D vision system to provide depth data accurate enough to perform automatic inspection tasks was until recently only possible at a short range from an object, typically a few centimetres. However it is now possible to produce dense data from a vision system situated further from the object, typically half a metre to a metre. Such a system is outlined. Some current model-based matching techniques are assessed for their suitability for employment in inspection type tasks. One approach is adopted and modifications that improve the efficiency and accuracy of the method for inspection purposes are presented. Finally, an inspection strategy is outlined and its performance assessed. Results are presented on both artificial and real depth data.
14838227
Sweeping of three-dimensional objects
Evaluating the volume swept out by a three-dimensional (3D) object as it moves along an arbitrary path is of interest to many areas of CAD and CAM, such as mechanism design and robot path planning. This paper shows how envelope theory from differential geometry can be used to find the volumes swept out by the individual surfaces of a solid body, and how computer algebra methods may be of use to perform the computations involved. Finally, a new algorithm is presented which shows how the results of sweeping the individual surfaces of a solid body can be combined to form a new 3D model of the swept volume. This algorithm has strong resemblance to hidden line algorithms, but works in one dimension higher.
27145850
A non-Euclidean implementation of LOGO
Abstract This paper describes an implementation of the LOGO Turtle Graphics programming environment in non-Euclidean geometry. Turtle graphics and non-Euclidean geometry are described briefly, and consideration is given to some of the details and problems of implementation. We describe the ways in which the LOGO language must be modified for a non-Euclidean environment, and the geometrical problems encountered during implementation.
16135249
Local topological beautification of reverse engineered models
Boundary representation models reconstructed from 3D range data suffer from various inaccuracies caused by noise in the data and by numerical errors in the model building software. The quality of such models can be improved in a beautification step, where geometric regularities need to be detected and imposed on the model, and defects requiring topological change need to be corrected. This paper considers changes to the topology such as the removal of short edges, small faces and sliver faces, filling of holes in the surface of the model (arising due to missing data), adjusting pinched faces, etc. A practical algorithm for detecting and correcting such problems is presented. Analysis of the algorithm and experimental results show that the algorithm is able to quickly provide the desired changes. Most of the time required for topological beautification is spent on adjusting the geometry to agree with the new topology.
2505791
Morphing based on strain field interpolation
Strain fields provide a method of deformation measurement based on physics. Using these as a tool, we can analyze deformation of objects in a measurable way. We have developed a new morphing technique based on strain field interpolation. Shape shaking and squeezing, which often happen when using linear interpolation for morphing, do not arise in our approach. We have also developed a new method to create isomorphic meshes from corresponding objects in two images. Meshes generated by this method have much fewer triangles than other methods, which greatly decreases calculation loads in the morphing process. Copyright # 2004 John Wiley & Sons, Ltd.
5430944
Distributed selfish load balancing
Suppose that a set of m tasks are to be shared as equally as possible amongst a set of n resources. A game-theoretic mechanism to find a suitable allocation is to associate each task with a "selfish agent", and require each agent to select a resource, with the cost of a resource being the number of agents to select it. Agents would then be expected to migrate from overloaded to underloaded resources, until the allocation becomes balanced.Recent work has studied the question of how this can take place within a distributed setting in which agents migrate selfishly without any centralized control. In this paper we discuss a natural protocol for the agents which combines the following desirable features: It can be implemented in a strongly distributed setting, uses no central control, and has good convergence properties. For m ≫ n, the system becomes approximately balanced (an ε-Nash equilibrium) in expected time O(log log m). We show using a martingale technique that the process converges to a perfectly balanced allocation in expected time O(log log m + n4). We also give a lower bound of Ω (max{log log m, n}) for the convergence time.
16901231
A Noise Suppression System for the AMR Speech Codec
In this paper we describe a noise reduction preprocessing algorithm for the adaptive multirate (AMR) speech codec of the GSM system. The algorithm is based on spectral weighting and explicitly takes into account the properties of the human auditory system. The weighting rule results in the smallest possible speech distortion under the constraint that the background noise should exhibit no audible distortions. The algorithm was implemented in 16 Bit fixed-point arithmetic and submitted to the ETSI AMR noise reduction standardization contest. Compared to other algorithms, our noise reduction method gave very good results in CCR tests and good results in ACR tests.
34342205
Pfaffian Algorithms for Sampling Routings on Regions with Free Boundary Conditions
Sets of non-intersecting, monotonic lattice paths, or fixed routings, provide a common representation for several combinatorial problems and have been the key element for designing sampling algorithms. Markov chain algorithms based on routings have led to efficient samplers for tilings, Eulerian orientations [8] and triangulations [9], while an algorithm which successively calculates ratios of determinants has led to a very fast method for sampling fixed routings [12]. We extend Wilson’s determinant algorithm [12] to sample free routings where the number of paths, as well as the endpoints, are allowed to vary. The algorithm is based on a technique due to Stembridge for counting free routings by calculating the Pfaffian of a suitable matrix [11] and a method of Colbourn, Myrvold and Neufeld [1] for efficiently calculating ratios of determinants. As an application, we show how to sample tilings on planar lattice regions with free boundary conditions.
94046
Rapidly mixing Markov chains for sampling contingency tables with a constant number of rows
We consider the problem of sampling almost uniformly from the set of contingency tables with given row and column sums, when the number of rows is a constant. (2002) have recently given a fully polynomial randomized approximation scheme (fpras) for the related counting problem, which only employs Markov chain methods indirectly. But they leave open the question as to whether a natural Markov chain on such tables mixes rapidly. Here we answer this question in the affirmative, and hence provide a very different proof of the main result of Cryan and Dyer. We show that the "2 /spl times/ 2 heat-bath" Markov chain is rapidly mixing. We prove this by considering first a heat-bath chain operating on a larger window. Using techniques developed by Morris and Sinclair (2002) (see also Morris (2002)) for the multidimensional knapsack problem, we show that this chain mixes rapidly. We then apply the comparison method of Diaconis and Saloff-Coste (1993) to show that the 2 /spl times/ 2 chain is rapidly mixing. As part of our analysis, we give the first proof that the 2 /spl times/ 2 chain mixes in time polynomial in the input size when both the number of rows and the number of columns is constant.
18074193
Dynamic Diffusion Load Balancing
We consider the problem of dynamic load balancing in arbitrary (connected) networks on n nodes. Our load generation model is such that during each round, n tasks are generated on arbitrary nodes, and then (possibly after some balancing) one task is deleted from every non-empty node. Notice that this model fully saturates the resources of the network in the sense that we generate just as many new tasks per round as the network is able to delete. We show that even in this situation the system is stable, in that the total load remains bounded (as a function of n alone) over time. Our proof only requires that the underlying “communication” graph be connected. (It of course also works if we generate less than n new tasks per round, but the major contribution of this paper is the fully saturated case.) We further show that the upper bound we obtain is asymptotically tight (up to a moderate multiplicative constant) by demonstrating a corresponding lower bound on the system load for the particular example of a linear array (or path). We also show some simple negative results (i.e., instability) for work-stealing based diffusion-type algorithms in this setting.