Showing papers on "Point (geometry) published in 2000"

Model Sets: A Survey

Abstract: Even when reduced to its simplest form, namely that of point sets in euclidean space, the phenomenon of genuine quasi-periodicity appears extraordinary Although it seems unfruitful to try and define the concept precisely, the following properties may be considered as representative: discreteness; extensiveness; finiteness of local complexity; repetitivity; diffractivity; aperiodicity; existence of exotic symmetry (optional)

Method and apparatus for building and using multi-dimensional index trees for multi-dimensional data objects

Abstract: A method and apparatus are provided for building a searchable multi-dimensional index tree that indexes a plurality of data objects. In one aspect of the invention, the index tree divides dataspace into three subspaces and indexes the data objects using a single dimension. If too many data objects map to the same point in that dimension, the dimension is switched to a new dimension of the data object and the data object is indexed using the new dimension. A split node having a split value is used to keep track of the indexing. In another aspect of the invention, the index tree divides dataspace into two subspaces, and equal bits are used in the split nodes to track the content of the data objects in the subspaces. If too many data objects sharing the same key within the same dimension map to a single point, then the dimension is switched to a new dimension and the data objects are indexed using the new dimension. Also disclosed is the multi-dimensional index tree itself as well as a router that uses the multi-dimensional index tree of the present invention to provide packet classification functions.

A cost model for query processing in high dimensional data spaces

Abstract: During the last decade, multimedia databases have become increasingly important in many application areas such as medicine, CAD, geography, and molecular biology. An important research topic in multimedia databases is similarity search in large data sets. Most current approaches that address similarity search use the feature approach, which transforms important properties of the stored objects into points of a high-dimensional space (feature vectors). Thus, similarity search is transformed into a neighborhood search in feature space. Multidimensional index structures are usually applied when managing feature vectors. Query processing can be improved substantially with optimization techniques such as blocksize optimization, data space quantization, and dimension reduction. To determine optimal parameters, an accurate estimate of index-based query processing performance is crucial. In this paper we develop a cost model for index structures for point databases such as the R*-tree and the X-tree. It provides accurate estimates of the number of data page accesses for range queries and nearest-neighbor queries under a Euclidean metric and a maximum metric and a maximum metric. The problems specific to high-dimensional data spaces, called boundary effects, are considered. The concept of the fractal dimension is used to take the effects of correlated data into account.

A stochastic process-based model for the positional error of line segments in GIS

Abstract: This paper presents a model for describing the positional error of line segments in geographical information systems (GIS). The model is based on stochastic process theory with the assumptions that the errors of the endpoints of a line segment follow two-dimensional normal distributions. The distribution and density functions of the line segments are derived statistically. The uncertainty information matrix of line segments is derived to indicate the error of an arbitrary point on the line segment. This model covers the cases where two-end points are correlated to each other and points on the line segment are stochastically continuous to each other. The model is a more generic error band model than those previously developed and is called the G-Band model.

Schauder's fixed-point theorem in nonlinear controllability problems

Abstract: This paper refers to application of t he Schauder's fixed point theorem together with linear co ntrollability results in get­ ting the sufficient controll ability conditions for various kinds of con­ trollability and for different types of nonlinea.r control systems. The following nonlinea.r control systems are considered: finite-dim eusiona.l systems, systems with delays in control or in the state variables, and infinite-dimensional systems. The paper presents the review of results existing in the literature which show how Scba.uder's fixed­ point theorem can be practically used to so lve several controllability problems for different types of nonlinea.r control systems.

Automatic Surface Reconstruction from Point Sets in Space

Abstract: In this paper an algorithm is proposed that takes as input a generic set of unorganized points, sampled on a real object, and returns a closed interpolating surface. Specifically, this method generates a closed 2-manifold surface made of triangular faces, without limitations on the shape or genus of the original solid. The reconstruction method is based on generation of the Delaunay tetrahedralization of the point set, followed by a sculpturing process constrained to particular criteria. The main applications of this tool are in medical analysis and in reverse engineering areas. It is possible, for example, to reconstruct anatomical parts starting from surveys based on TACs or magnetic resonance.

Stability of the blow-up profile of non-linear heat equations from the dynamical system point of view

Abstract: (see [Bal77] and [Lev73] for the existence of such solutions). Note that from the regularizing effect of the heat equation, the blow-up time does not depend on the space where the Cauchy problem is solved. The point a is a blow-up point if and only if there exists (an, tn) → (a, T ) as n → +∞ such that |u(an, tn)| → +∞. Note that in the case p < 3N+8 3N−4 or u(0) ≥ 0, we know from [MZ] that an equivalent definition could be a point a ∈ RN such that | u(x, t) | −→ (x,t)→(a,T ) +∞.

The two-point spectral Nevanlinna-Pick problem

Abstract: We present an analytic solution of certain special cases of the spectral Nevanlinna-Pick problem for two interpolation points and 2×2 matrices.

Generalized dual space indicator method for underwater imaging

Abstract: This paper presents a generalized dual space indicator method for imaging an obstacle in ocean environments. The method is based on the observation that the combination (weighted integration) of the measured scattered field can approximate the Green function very well when the Green function's source point is inside the obstacle, but not so well when the source is outside the obstacle. We set up an integral equation whose right-hand side is the Green function with a source point from a searching region. From our numerical experiments, we notice that the norm of the solution of the integral equation has local extrema that lie inside the unknown obstacle. Plotting the norm as a function of the source point in the searching region, and filtering out the region with no local extrema of the norm, we obtain a good image of the unknown obstacle. Imaging algorithms and numerical examples are presented.

Estimates for the principal spectrum point for certain time-dependent parabolic operators

Abstract: Non-autonomous parabolic equations are discussed. The periodic case is considered first and an estimate for the principal periodic-parabolic eigenvalue is obtained by relating the original problem to the elliptic one obtained by time-averaging. It is then shown that an analogous bound may be obtained for the principal spectrum point in the almost periodic case. These results have applications to the stability of nonlinear systems and hence, for example, to permanence for biological systems.

Point stabilization of mobile robots via state-space exact feedback linearization

Abstract: In this paper, we solve the point stabilization of mobile robots via state-space exact feedback linearization. The state-space exact feedback linearization has not been possible in the past for the point stabilization of mobile robots due to the restricted mobility caused by nonholonomic constraints. Under some proposed coordinates, however, the point stabilization problem can be exactly transformed into the problem of controlling a linear time-invariant system. Thus, using well-established linear control theory, the point stabilization of robots can be easily formulated.

Computer system and method for maintaining an audit record for data restoration

Abstract: A storage device for a computer, combining an audit trail storage with (1) a connector adapted for connecting the storage device to a connection point of the computer, (2) a primary storage having first data stored thereon, and adapted for sending the first data to the computer in response to a corresponding read command received at the connection point, and (3) secondary storage adapted for storing second data in response to a corresponding write command received at the connection point and further adapted for sending the second data to the computer in response to a corresponding read command received at the connection point. The audit trail storage is adapted for recording a log of communication activity occurring at the connection point. A storage device for a computer, comprising: (1) a connector connecting the storage device to a connection point of the computer; (2) a storage adapted for storing data in response to a corresponding write command received at the connection point and further adapted for sending the data to the computer in response to a corresponding read command received at the connection point, and (3) an audit trail storage adapted for recording a log of communication activity occurring at the connection point.

Spectral Localization by Gaussian Random Potentials in Multi-Dimensional Continuous Space

Abstract: A detailed mathematical proof is given that the energy spectrum of a non-relativistic quantum particle in multi-dimensional Euclidean space under the influence of suitable random potentials has almost surely a pure-point component. The result applies in particular to a certain class of zero-mean Gaussian random potentials, which are homogeneous with respect to Euclidean translations. More precisely, for these Gaussian random potentials the spectrum is almost surely only pure point at sufficiently negative energies or, at negative energies, for sufficiently weak disorder. The proof is based on a fixed-energy multi-scale analysis which allows for different random potentials on different length scales.

Bias-dependent linear, scalable millimeter-wave FET model

Abstract: This paper describes a measurement-based, bias-dependent, linear equivalent circuit FET/HEMT model that is accurate to at least 100 GHz and scalable up to 12 parallel gate fingers and from 100-1000 /spl mu/m total gate width. The equivalent circuit element values are determined at each bias point in V/sub gs/-V/sub ds/ space.

SOME PROPERTIES OF NONLINEAR σ-MODELS IN NONCOMMUTATIVE GEOMETRY

Abstract: We introduce nonlinear σ-models in the framework of noncommutative geometry with special emphasis on models defined on the noncommutative torus. We choose as target spaces the two point space and the circle and illustrate some characteristic features of the corresponding σ-models. In particular we construct a σ-model instanton with topological charge equal to 1. We also define and investigate some properties of a noncommutative analogue of the Wess–Zumino–Witten model.

e-weak minimal solutions of vector optimization problems with set-valued maps

Abstract: In this paper, we consider cone-subconvexlike vector optimization problems with set-valued maps in general spaces and derive scalarization results, ∈-saddle point theorems, and ∈-duality assertions using ∈-Lagrangian multipliers.

A Multiple View 3D Registration Algorithm with Statistical Error Modeling

Abstract: The contribution of the paper is two-fold: Firstly, a review of the point set registration literature is given, and secondly, a novel covariance weighted least squares formulation of the multiple view point set registration problem is presented. Point data for surface registration is commonly obtained by non-contact, 3D surface sensors such as scanning laser range finders or structured light systems. Our formulation allows the specification of anisotropic and heteroscedastic (point dependent) 3D noise distributions for each measured point. In contrast, previous algorithms have generally assumed an Isotropie sensor noise model, which cannot accurately describe the sensor noise characteristics. For cases where the point measurements are heteroscedastically and anisotropically distributed, registration results obtained with the proposed method show improved accuracy over those produced by an unweighted least squares formulation. Results are presented for both synthetic and real data sets to demonstrate the accuracy and effectiveness of the proposed technique.

Response surface model development for global/local optimization using radial basis functions*

Abstract: This paper considers the optimization of complex multi-parameter systems in which the objective function is not known explicitly, and can only be evaluated either through costly physical experiments or through computationally intensive numerical simulation. Furthermore, the objective function of interest may contain many local extrema. Given a data set consisting of the value of the objective function at a scattered set of parameter values, we are interested in developing a response surface model to reduce dramatically the required computation time for parameter optimization runs.To accomplish these tasks, a response surface model is developed using radial basis functions. Radial basis functions provide a way of creating a model whose objective function values match those of the original system at all sampled data points. Interpolation to any other point is easily accomplished and generates a model which represents the system over the entire parameter space. This paper presents the details of the use

Approximate congruence in nearly linear time

Abstract: The problem of geometric point set matching has been studied extensively in the domain of computational geometry, and has many applications in areas such as computer vision, computational chemistry, and pattern recognition One of the commonly used metrics is the bottleneck distance, which for two point sets P and Q is the minimum over all one-to-one mappings f : P → Q of maxp∈P d(p, f (p)) ,w hered is the Euclidean distance Much effort has gone into developing efficient algorithms for minimising the bottleneck distance between two point sets under groups of transformations However, the algorithms that have thus far been developed suffer from running times that are large polynomials in the size of the input, even for approximate formulations of the problem In this paper we define a point set similarity measure that includes both the bottleneck distance and the Hausdorff distance as special cases This measure relaxes the condition that the mapping must be one-to-one, but guarantees that only a few points are mapped to any point Using a novel application of Hall’s Theorem to reduce the geometric matching problem to a combinatorial matching problem, we present near-linear time approximation schemes for minimising this distance between two point sets in the plane under isometries; we note here that the best known algorithms for congruence under the bottleneck measure run in time O(n 25 ) We also obtain a combinatorial bound on the metric entropyof certain families of geometric objects This result yields improved algorithms for approximate congruence, and may be of independent interest  2002 Elsevier Science BV All rights reserved

Method and apparatus for detecting independent motion in three-dimensional scenes

Abstract: A system and method that detects independently moving objects in 3D scenes which are viewed under camera motion progressively applies constraints to the images to ensure the stability of the constraints. The system first calculates 2D view geometry constraints for a set of images. These constraints are tested to determine if the imaged scene exhibits significant 3D characteristics. If it does, then 3D shape constraints, are applied to the set of images. The 3D shape constraints are themselves constrained by the 2D view geometry constraints. The set of images is then tested to identify areas that are inconsistent with the 2D or 3D constraints. These areas correspond to the moving objects. The 2D view geometry constraints are calculated by computing a dominant image alignment for successive pairs of images and then computing constrained epipolar transformations for the two image pairs. This 2D view geometry is further refined based on a plurality of target point correspondences among the plurality of frames. The epipolar geometry for the point correspondence having a minimum median error is selected as the 2D view geometry of the scene. The 3D shape constraint is a parallax geometry that is calculated by iteratively minimizing errors in a parametric alignment of the images using an estimated parallax geometry.

A practical approach to creating precise and detailed 3d models from single and multiple views

Abstract: This paper describes a general system for creating geometrically correct and complete 3D models of objects and environments. The main process uses digital images and applies rigorous photogrammetric techniques. Once the images are registered using bundle adjustment, points in selected locations are measured in all the images where they appear. However, there are usually many parts of the scene that appear in only one image due to occlusions or lack of features. These parts can be reconstructed in the 3D space from the coordinates in a single image and the mathematical model of the surface determined by fitting a function to existing surface points. This produces a sampled geometry in the form of points in the three-dimensional space however the connectivity or the topology is not known and must be determined someway. The proposed approach relies on interactive point segmentation and automatic triangulation. Counting on images for modeling is limited because the features that can be extracted are usually fewer then the required level of details. To overcome this problem two options are implemented. First, large number of points can be automatically added to surfaces of known shape, such as spheres, cylinders and quadrics, using a polygon subdivision method. The second option integrates data from range sensors that can densely digitize the surface where filled out details are required. The presented approach will be assessed by several examples representing various types of objects and sites.

Problem-matched basis functions for moment method analysis-an application to reflection gratings

Abstract: In the evaluation of the frequency response of a scattering object by the integral equation technique, generally a large linear system of equations has to be solved for each frequency point. This paper deals with a technique that drastically reduces the size of the linear system without loss of accuracy, The key point is the definition of a set of problem-matched basis functions. These basis functions are extremely efficient in the representation of the unknown in the parameter range of interest. In this way, the central processing unit (CPU) time required in the response evaluation is drastically reduced. Examples of application concerning reflection gratings are reported.

Stereo Autocalibration from One Plane

Abstract: This paper describes a method for autocalibrating a stereo rig. A planar object performing general and unknown motions is observed by the stereo rig and, based on point correspondences only, the autocalibration of the stereo rig is computed. A stratified approach is used and the autocalibration is computed by estimating first the epipolar geometry of the rig, then the plane at infinity Π∞ (affine calibration) and finally the absolute conic Ω∞ (Euclidean calibration). We show that the affine and Euclidean calibrations involve quadratic constraints and we describe an algorithm to solve them based on a conic intersection technique. Experiments with both synthetic and real data are used to evaluate the performance of the method.

Control of erosion profile and process characteristics in magnetron sputtering by geometrical shaping of the sputtering target

Abstract: An apparatus and method for controlling and optimizing a non-planar target shape of a sputtering magnetron system are employed to minimize the redeposition of the sputtered material and optimize target erosion. The methodology is based on the integration of sputtered material from each point of the target according to its solid angle view of the rest of the target. The prospective target's geometry is optimized by analytically comparing and evaluating the methodology's results of one target geometry against that of another geometry, or by simply altering the first geometry and recalculating and comparing the results of the first geometry against the altered geometry. The target geometries may be of many different shapes including trapezoidal, cylindrical, parabolic, and elliptical, depending upon the optimum process parameters desired. A sputtering system is developed using this methodology, having a main magnet stack, a rotating magnet, a target having selected target shapes optimized for controlling erosion, downstream magnets, a substrate, and an electric field induced plasma stream.

On Weighting and Choosing Constraints for Optimally Reconstructing the Geometry of Image Triplets

Abstract: Optimally reconstructing the geometry of image triplets from point correspondences requires a proper weighting or selection of the used constraints between observed coordinates and unknown parameters. By analysing the ML-estimation process the paper solves a set of yet unsolved problems: (1) The minimal set of four linearily independent trilinearities (Shashua 1995, Hartley 1995) actually imposes only three constraints onto the geometry of the image triplet. The seeming contradiction between the number of used constraints, three vs. four, can be explained naturally using the normal equations. (2) Direct application of such an estimation suggests a pseudoinverse of a 4 × 4-matix having rank 3 which contains the covariance matrix of the homologeous image points to be the optimal weight matrix. (3) Insteadof using this singluar weight matrix one could select three linearily dependent constraints. This is discussed for the two classical cases of forward andlateral motion, and clarifies the algebraic analyis of dependencies between trilinear constraints by Faugeras 1995. Results of an image sequence with 800 images and an Euclidean parametrization of the trifocal tensor demonstrate the feasibility of the approach.

Method and system for measuring IP performance metrics

Abstract: A method and system is provided for measuring network performance. The method and system divides a stream of packets flowing through a first point into frames, the first point being any point in the network that supports a packet flow, creates packages corresponding to the frames, correlates each package with packets flowing through a second point, the second point being any point in the network that supports the packet flow, and calculates network performance information based on the correlated packages.

Infinitesimal geometry of quasiregular mappings

Abstract: We introduce the notion of the innitesimal space for a quasiregular mapping at a point. This can be used to study local topological and geometric properties of the mapping also at those points where the mapping is not dieren tiable.

System for sorting articles using a double carrying tray

Abstract: A system for sorting articles, the system having a track which defines a route starting at least one loading point, the route continuing on to a plurality of destination points and arriving back at the loading point. The system also has at least one tray for conveying an article from the loading point to a selected one of the destination points. The tray comprises a first and a second half pivotally coupled to each other. The track includes a first segment for momentarily tilting a leading end of the tray upward relative to a trailing end of the tray and possibly downward again, and a second segment for laterally tilting the first half and the second half of the tray at an angle. The first and second segments selectively maneuver an article loaded in the tray to a bottom corner thereof prior to the tray reaching the selected destination point in order to substantially reduce the jarring of the article during the discharge thereof at the selected destination point. A scanner is provided for scanning an identification-code disposed on the article. The scanner is coupled to a controller which determines the selected destination point using the information obtained by the scanner from the identification-code disposed on the article.

Measuring and reducing the Euclidean-space effects of robotic joint failures

Abstract: Robotic joint failures are directly characterized and measured in joint space. A locking failure, for example, is one for which a joint cannot move, and it gives an error equal to the desired value minus the locked value. This article extends the joint-space characterization to Euclidean space by measuring the failure effect. The approach is based on a rudimentary measure of point error that can be defined to be distance or path length. It is used to form comprehensive measures through weighted integration over Euclidean-space regions. For kinematically redundant manipulators, minimizing the measures using the redundancy is a method to induce failure tolerance. This can be applied both before a failure to reduce the likelihood of collision-induced damage and after a failure to reduce end-effector error. Examples for both cases are given.