Showing papers on "Point (geometry) published in 1996"

Fractals, random shapes and point fields : methods of geometrical statistics

Abstract: FRACTALS AND METHODS FOR THE DETERMINATION OF FRACTAL DIMENSIONS. Hausdorff Measure and Dimension. Deterministic Fractals. Random Fractals. Methods for the Empirical Determination of Fractal Dimension. THE STATISTICS OF SHAPES AND FORMS. Fundamental Concepts. Representation of Contours. Set Theoretic Analysis. Point Description of Figures. Examples. POINT FIELD STATISTICS. Fundamentals. Finite Point Fields. Poisson Point Fields. Fundamentals of the Theory of Point Fields. Statistics for Homogeneous Point Fields. Point Field Models. Appendices. References. Index.

Handbook of image processing operators

Abstract: Images, Windows and Operators. Methodical Fundamentals. Algorithmic Fundamentals. Coordinate Transformations and Geometrical Operators. Gray Scale Transformations and Point Operators. Window Functions and Local Operators. Global Operators. Glossary. Index.

On the nonexistence of bilipschitz parameterizations and geometric problems about $A_\infty$-weights

Abstract: How can one recognize when a metric space is bilipschitz equivalent to an Euclidean space? One should not take the abstraction of metric spaces too seriously here; subsets of Rn are already quite interesting. It is easy to generate geometric conditions which are necessary for bilipschitz equivalence, but it is not clear that such conditions should ever be sufficient. The main point of this paper is that the optimistic conjectures about the existence of bilipschitz parametrizations are wrong. In other words, there are spaces whose geometry is very similar to but still distinct from Euclidean geometry. Related questions of bilipschitz equivalence and embeddings are addressed for metric spaces obtained by deforming the Euclidean metric on Rn using an A8 weight.

Registration of multiple point sets

Abstract: Registering 3D point sets subject to rigid body motion is a common problem in computer vision. The optimal transformation is usually specified to be the minimum of a weighted least squares cost. The case of 2 point sets has been solved by several authors using analytic methods such as SVD. In this paper we present a numerical method for solving the problem when there are more than 2 point sets. Although of general applicability the new method is particularly aimed at the multiview surface registration problem. To date almost all authors have registered only two point sets at a time. This approach discards information and we show in quantitative terms the errors caused.

The modulus constraint: a new constraint self-calibration

Abstract: To obtain a Euclidean reconstruction from images the cameras have to be calibrated. In recent years different approaches have been proposed to avoid explicit calibration. The problem with these methods is that several parameters have to be retrieved at once. Because of the non-linearity of the equations this is not an easy task and the methods often fail to converge. In the's paper a stratified approach is proposed which allows to first retrieve the affine calibration of the camera using the modulus constraint. Having the affine calibration it is easy to upgrade to Euclidean. The important advantage of this method is that only three parameters have to be evaluated at first. From a practical point of view, the major gain is that an affine reconstruction is obtained from arbitrary sequences of views, whereas so far affine reconstruction has been based on pairs of views with a pure translation in between. A short illustration of another application is also given. Once the affine calibration is known, the constraint can be used to retrieve the Euclidean calibration in the presence of a variable focal length.

Approximating center points with iterative radon points

Abstract: We give a practical and provably good Monte Carlo algorithm for approximating center points. Let P be a set of n points in Rd. A point c∈Rd is a β-center point of P if every closed halfspace containing c contains at least βn points of P. Every point set has a 1/(d+1)-center point; our algorithm finds an Ω(1/d2)-center point with high probability. Our algorithm has a small constant factor and is the first approximate center point algorithm whose complexity is subexponential in d. Moreover, it can be optimally parallelized to require O(log2d log log n) time. Our algorithm has been used in mesh partitioning methods and can be used in the construction of high breakdown estimators for multivariate datasets in statistics. It has the potential to improve results in practice for constructing weak ∊-nets. We derive a variant of our algorithm whose time bound is fully polynomial in d and linear in n, and show how to combine our approach with previous techniques to compute high quality center points more quickly.

Computational Aspects of the LAMBDA Method for GPS Ambiguity Resolution

Abstract: Precise relative positioning based on a short observa- tion time span yields ambiguities that are heavily cor- related, together with position estimates of poor preci- sion. For an efficient estimation of the integer values of the GPS double difference ambiguities, the LAMBDA method has been developed and applied since 1993. In the context of the LAMBDA method, from a compu- tational point of view, there are various ways to arrive at the so-called ‘fixed solution’, in which the ambigui- ties are constrained to their integer values. Depending on the application at hand, it will be shown which way is most appropriate. This will be demonstrated with the help of a number of examples, both static and kinematic. The results show that efficient ambiguity resolution can be achieved very fast, on-the-fly (OTF), in a variety of cases, such as with roving receivers and in network sce- narios.

Computer-implemented method and apparatus for automatic curved labeling of point features

Abstract: A computer-implemented method and apparatus for automatically labeling maps in accordance with predefined label criteria provides automated labeling of any number of different types of maps with point, line and region features. For automatically labeling point features on a map, a horizontal placement step is first performed to determine whether the point feature name can be placed horizontally. If not, a curved placement step is executed in which the point feature name is placed along a curved arc to attempt to fit the name on the map without the name overlapping other names or other features. The curved placement step is performed by first calculating the length of the point feature name and then choosing a radius of curvature and angle of curvature to create a placement arc of a given length for placement of the point feature name. Once the placement arc is created and the point feature name place thereon, the curved point feature name is tested to see whether it satisfies predetermined criteria.

Working Capability Analysis of Stewart Platforms

Abstract: Working capability analysis of planar and spatial Stewart platforms with unilateral constraints on actuator length is carried out using numerical methods based on analytical criteria for the boundary of the accessible output set. Restrictions on achievable motion at singular configurations associated with points interior to the accessible output set are also analyzed. Since movement of the working point on a spatial Stewart platform occurs in three-dimensional space, the boundary of the accessible output set is a two-dimensional surface. Numerical methods used in this analysis map one-dimensional solution sets, permitting the boundary of the accessible output set to be characterized by a family of one dimensional generators. Motion control restrictions inside the accessible output set are similarly characterized by families of interior singular curves, and barriers to motion control across surfaces defined are analyzed.

Solving Real-World Linear Ordering Problems Using a Primal-Dual Interior Point Cutting Plane Method

Abstract: Cutting plane methods require the solution of a sequence of linear programs, where the solution to one provides a warm start to the next. A cutting plane algorithm for solving the linear ordering problem is described. This algorithm uses the primal-dual interior point method to solve the linear programming relaxations. A point which is a good warm start for a simplex-based cutting plane algorithm is generally not a good starting point for an interior point method. Techniques used to improve the warm start include attempting to identify cutting planes early and storing an old feasible point, which is used to help recenter when cutting planes are added. Computational results are described for some real-world problems; the algorithm appears to be competitive with a simplex-based cutting plane algorithm.

Robotic wafer handler

Abstract: A robotic wafer handler has first and second arms pivotally connected at a swing point to operate in a plane. Each arm is independently drivable through greater than 360° of rotation in the plane. The wafer handler may also include mechanisms for adjusting the plane of rotation, i.e., for providing lift and tilt.

Multi-view-point picture encoder

Abstract: PROBLEM TO BE SOLVED: To provide view point number scalability while keeping high encoding efficiency by limiting a reference screen to the same view point picture in the encoding of a reference view point picture and limiting the reference screen to the same view point picture and an adjacent view point picture in the picture encoding of a view point other than a reference view point. SOLUTION: At the time of encoding the picture of the reference view point V2, only motion compensation is performed and the pictures of the other view points are not referred to. On the other hand, at the time of encoding the view point V1 on a left side, an already encoded screen at the view point V1 or V2 is turned to the reference screen and the encoding is performed. It is similar for the view point V3 on a right side as well. In such a manner, by using only the picture strings of the view points V1 and V2 or the view points V2 and V3, reproduction for only the two view points can be performed. That is, no matter which of 1, 2 and 3 the view point number of the pictures to be reproduced is, by using the picture strings for the same number as the view point number, the reproduction is made possible and the view point number scalability is realized. COPYRIGHT: (C)1997,JPO

A new potential field-based algorithm for path planning

Abstract: In this paper, the path-planning problem is considered. We introduce a new potential function for path planning that has the remarkable feature that it is free from any local minima in the free space irrespective of the number of obstacles in the configuration space. The only global minimum is the goal configuration whose region of attraction extends over the whole free space. We also propose a new method for path optimization using an expanding sphere that can be used with any potential or penalty function. Simulations using a point mobile robot and smooth obstacles are presented to demonstrate the qualities of the new potential function. Finally, practical considerations are also discussed for nonpoint robots

Why bother about gas-sensitive field-effect devices?

Abstract: Gas-sensitive field-effect devices have been studied for more than 20 years. Commercial uses of such devices exist, but in special applications and in small volumes. The purpose of the present contribution is to point out several ongoing and possible developments, which make the prospects for gas-sensitive field-effect devices quite good. These are related to the fabrication of large sensing surfaces and sensor arrays, the combination of sensors and catalytic combustion and the use of semiconductor substrates other than silicon to allow operation at temperatures above 200–250 °C. More specifically, we discuss combustion monitoring with field-effect devices, sensors operating with time constants close to fundamental limits, distributed chemical sensing, and combinatorial chemistry for sensor arrays. Some of the remaining more fundamental research problems regarding gas-sensitive field-effect devices are also touched upon.

Zonoid Data Depth: Theory and Computation

Abstract: A new notion of data depth in d-space is presented, called the zonoid data depth. It is affine equivariant and has useful continuity and monotonicity properties. An efficient algorithm is developed that calculates the depth of a given point with respect to a d-variate empirical distribution.

Normal frames and the validity of the equivalence principle. I. Cases in a neighborhood and at a point

Abstract: A treatment in a neighborhood and at a point of the equivalence principle on the basis of derivations of the tensor algebra over a manifold is given. Necessary and sufficient conditions are given for the existence of local bases, called normal frames, in which the components of derivations vanish in a neighborhood or at a point. These frames (bases), if any, are explicitly described and the problem of their holonomicity is considered. In particular, the obtained results concern symmetric as well as nonsymmetric linear connections.

System and method for rapidly generating an optimal mesh model of a 3D object or surface

Abstract: A system and method for the rapid creation of a mesh model depicting a real world object, terrain or other three-dimensional surface. The system inserts points into the mesh incrementally, building the mesh point by point. Before incremental building, the system orders the points so that each next point is a near neighbor to the previously inserted point. This ordering procedure optimizes mesh construction by guaranteeing a minimal time for locating the area on the mesh into which the next point will be inserted. The present invention also provides a system and method to ensure an optimal quality of mesh at any level of insertion or deletion, following systematized checking function to maintain quality such as that required in Delaunay triangulation. The system and method can also incorporate a history file to store data concerning the results of the checking to substantially reduce processing time in mesh regeneration applications.

Large-Eddy Simulation of Flow Around a NACA 4412 Airfoil Using Unstructured Grids

Abstract: Large-eddy simulation (LES) has matured to the point where application to complex flows is described. The extension to higher Reynolds numbers leads to an impractical number of grid points with existing structured-grid methods. Furthermore, most real world flows are rather difficult to represent geometrically with structured grids. Unstructured-grid methods offer a release from both of these constraints. However, just as it took many years for structured-grid methods to be well understood and reliable tools for LES, unstructured-grid methods must be carefully studied before we can expect them to attain their full potential.

Display method of three-dimensional shape

Abstract: A presentation method of a three dimensional (3D) shape comprising: a view point and a display screen setting step including setting a view point and a display screen in space; a direction of sight, that is a view direction, setting step including setting a view line, that is a line-of-sight, from the view point; a target shape composing point detecting step including detecting a shape composing point near the set view line; an image of the target shape on a display screen constructing step including constructing an image of the target shape as a point of display screen as projecting points of the target shape.

Precise calibration procedure for sensor-based view point control system

Abstract: In a graphics processing and display system wherein the view point is controlled according to position and orientation of a view point reference with respect to a representation of the displayed graphics data determined by a view point reference coordinate sensing system comprising a source and a sensor, wherein the sensor has a fixed position and orientation with respect to said view point reference and the source has a fixed position and orientation with respect to the schematic representation, calibration of the system requires two ordered steps: view point reference-sensor calibration and source-representation calibration. View point reference-sensor calibration is performed by registering and processing four configurations of the sensor housing. Source-representation calibration is performed by storing and processing three positions of the sensor housing.

Partial surface matching by using directed footprints

Abstract: In this paper we present a new technique for partial surface and volume matching of images in three dimensions. In this problem, we are given two objects in 3-space, each represented as a set of points, scattered uniformly along its boundary or inside its volume. The goal is to find a rigid motion of one object which makes a sufficiently large portion of its boundary lying sufficiently close to a corresponding portion of the boundary of the second object. This is an important problem in pattern recognition and in computer vision, with many industrial, medical, and chemical applications. Our algorithm is based on assigning a directed footprint to every point of the two sets, and locating all the pairs of points (one of each set) whose undirected components of the footprints are sufficiently similar. The algorithm then computes for each such pair of points all the rigid transformations that map the first point to the second, while making the respective direction components of their footprints coincide. A voting scheme is employed for computing transformations which map significantly large number of points of the first set to points of the second set. Experimental results on various examples are presented and show the accurate and robust performance of our algorithm.

Return point route searching for vehicle navigation

Abstract: A vehicle navigation system copes with the situation when the vehicle deviates from a guided route (is off-route) and it is desired to reach the destination efficiently, i.e. with the least travel distance. The system determines the most efficient route to return to the guided route by analyzing the shortest distance between the current vehicle position and an unpassed road intersection on the original guided route, by searching for unpassed intersections on the original guided route within a particular radius of the current off-route vehicle position. The vehicle speed and heading angle are also used to determine the search radius, to find the shortest return route to the original guided route.