Showing papers on "Point (geometry) published in 1999"

The Art of Frame Theory

Abstract: Thye theory of frames for a Hilbert space plays a fundamental role in signal processing, image processing, data compression, sampling theory and much more, as well as being a fruitful area of research in abstract mathematics. In this ``tutorial'' on abstract frame theory, we will try to point out the major directions of research in abstract frame theory and give some sample techniques from each of the areas. We will also bring out some of the important open questions, discuss some of the limitations of the existing theory, and point to some new directions for research.

Method and apparatus for displaying a synthesized image viewed from a virtual point of view

Abstract: An image generating apparatus comprising: a camera or a plurality of cameras; space reconstructing means for mapping the input image from said camera, into a predetermined space model of a predetermined three-dimensional space; point-of-view converting means of synthesizing an image viewed from an arbitrary virtual point of view in said predetermined three-dimensional space by referencing to said space data mapped by said space reconstructing means; and displaying means of displaying the image converted by said point-of-view converting means.

One, Two and Three Times log n / n for Paths in a Complete Graph with Random Weights

Abstract: Consider the minimal weights of paths between two points in a complete graph Kn with random weights on the edges, the weights being, for instance, uniformly distributed. It is shown that, asymptotically, this is log n/n for two given points, that the maximum if one point is fixed and the other varies is 2 log n/n, and that the maximum over all pairs of points is 3 log n/n.Some further related results are given as well, including results on asymptotic distributions and moments, and on the number of edges in the minimal weight paths.

Image forming device

Abstract: PROBLEM TO BE SOLVED: To speedily reset required image-forming-operation-conditions, in all the cases an auto-clearing function operates SOLUTION: After an image forming operation or any key operation, the auto-clearing function is initialized (steps 222 and 224) Thereafter, in the case no operations are carried out until auto-clearing time elapses, the contents of image-forming-operation conditions at the point in time are stored in a RAM (step 214), and the image-forming-operation conditions are altered to standard conditions determined in advance (step 216) When an instruction is then given to cancel the auto-clearing, the set contents of the image-forming-operation conditions before the execution of the auto-clearing function are read from the RAM, and set again as new image-forming-operation-conditions Thus, the image-forming-operation conditions can speedily be set back to the conditions used before the execution of the auto-clearing function

A fast maximum power point tracker for photovoltaic power systems

Abstract: In this paper, the authors proposed a novel maximum power point controller, which not only can track the maximum power of an array quickly without perturbation and observation process but also can be implemented easily. The main idea is based on the graphical interpretation of the maximum power point as the intersecting point of two curves on the phase plane corresponding to the solution of two algebraic equations. In other words, the operating point is the intersecting point of the PV-array characteristic curve and the maximum power line. A circuit is constructed based on a boost circuit and a three phase full bridge inverter.

Statistics of closest returns for some non-uniformly hyperbolic systems

Abstract: For non uniformly hyperbolic maps of the interval with exponential decay of correlations we prove that the law of closest return to a given point when suitably normalized is almost surely asymptotically exponential. A similar result holds when the reference point is the initial point of the trajectory. We use the framework for non uniformly hyperbolic dynamical systems developed by L.S.Young.

Testing for parameter changes in ARCH models

Abstract: The paper develops the asymptotic theory for CUSUM-type tests for a change point in parameters of an ARCH(∞) model. Special attention is given to asymptotics under local alternatives.

CAD-based path planning for 3-D line laser scanning

Abstract: The problem of path planning for 3-D line laser scanning is addressed in this article. The path under study is for a line, as opposed to a point in conventional CNC and CMM toolpath planning. While the objective of the latter case is to drive a point along a curve, that of the former case is to drive a line across a surface. To solve this problem, a path planning method is developed. First, a slicing approach is put forward to divide a part CAD model into a number of sections, since the laser scanning line is limited by the scanning width and a single scanning pass cannot cover the whole surface. Second, for each section, a scanning pass is generated to cover the section surface. To ensure a maximum coverage for each section, the surface profile is determined, and the top of the scanning window is set along the upper boundary of the surface profile. Third, combination of scanning all the sections forms a complete scan of a surface. It is shown that with the proposed method a 3-D line laser scanning process can be effectively automated.

System and method of finding near neighbors in large metric space databases

Abstract: The present invention comprises a computer-implemented method of searching large metric space databases. It allows fast near neighbor searches in databases where the data elements in the database are high dimensional and each data element represents a point in a large metric space. Given a query item, which also represents a point in the large metric space, one or more data items in the database which are approximately nearest neighbors of the query item are found. A set of data items is first preprocessed by computing distances between pairs of items and storing links between pairs which are near one another. A search of the database proceeds by following links from item to item, usually by following links to items which are nearest the query Q. In one embodiment, the search terminates upon reaching an item R which is closer to Q than are all the items to which R links.

Algorithms for the on-line travelling salesman

Abstract: In this paper the problem of efficiently serving a sequence of requests presented in an on-line fashion located at points of a metric space is considered. We call this problem the On-Line Travelling Salesman Problem (OLTSP). It has a variety of relevant applications in logistics and robotics. We consider two versions of the problem. In the first one the server is not required to return to the departure point after all presented requests have been served. For this problem we derive a lower bound on the competitive ratio of 2 on the real line. Besides, a 2.5-competitive algorithm for a wide class of metric spaces, and a 7/3-competitive algorithm for the real line are provided. For the other version of the problem, in which returning to the departure point is required, we present an optimal 2-competitive algorithm for the above mentioned general class of metric spaces. If in this case the metric space is the real line we present a 1.75-competitive algorithm that compares with a \approx 1.64 lower bound.

Quermass-interaction processes: conditions for stability

Abstract: We consider a class of random point and germ-grain processes, obtained using a rather natural weighting procedure. Given a Poisson point process, on each point one places a grain, a (possibly random) compact convex set. Let Ξ be the union of all grains. One can now construct new processes whose density is derived from an exponential of a linear combination of quermass functionals of Ξ. If only the area functional is used, then the area-interaction point process is recovered. New point processes arise if we include the perimeter length functional, or the Euler functional (number of components minus number of holes). The main question addressed by the paper is that of when the resulting point process is well-defined: geometric arguments are used to establish conditions for the point process to be stable in the sense of Ruelle.

Experimental study of the ground motion on a large scale topographic hill at Kitherion (Greece)

Abstract: We present the results of an experiment about the effects on the seismic ground motion of a hill of large dimensions (6km long, 3km large and 700m high) near Corinth (Greece). We installed 7 seismometers across the hill, and analyzed the ground motion with different methods: the classical spectral ratios (CSR) and the horizontal to vertical spectral ratios calculated both on noise (HVNR) and earthquake data (RF). The amplification at the resonant frequency (around 0.7Hz) is low, as expected, but one of the two stations installed at the top exhibits large amplification (up to a factor of 10) at 3Hz. The comparison between the H/V results and the CSR ones suggests that the former method is able to point out the fundamental frequencies of a hill. Amplifications and spatial localization predicted by numerical 3D modeling are consistent with the experimental data only at frequencies lower than 1Hz.

Sketch-based editing of curves

Abstract: A method and apparatus implementing a technique for editing an existing curve in a computer graphics system. In one aspect, a method includes receiving a sketch curve as input. The sketch curve has a first modification end point and a second modification end point. A target section of the existing curve is calculated by finding a first target end point and a second target end point in the existing curve. The first target end point is a point on the existing curve closest to the first modification end point and the second target end point is a point on the existing curve closest to the second modification end point. The target section is removed from the existing curve. A replacement curve is created and is inserted into the existing curve in place of the target section. The existing curve and the replacement curve are faired at their respective neighboring end points.

Interpolation in transform space for multiple rigid object registration

Abstract: A method of mapping a chosen point in real space to its corresponding location in image space includes obtaining a diagnostic medical image of a subject including multiple rigid objects, and individually computing separate transforms which register each of the rigid objects in real space with their corresponding locations in image space. After choosing a target point in real space, the target point is mapped to image space using a designated transform. A number of the rigid objects are selected which are closest to the target point in image space, and an interpolated transform is generated from the separate transforms which correspond to the selected rigid objects. The target point is re-mapped in image space using the interpolated transform, and the interpolated transform is set as the designated transform for subsequent mappings.

Level-Set Surface Segmentation and Fast Cortical Range Image Tracking for Computing Intrasurgical Deformations

Abstract: We propose a method for estimating intrasurgical brain shift for image-guided surgery. This method consists of five stages: the identification of relevant anatomical surfaces within the MRI/CT volume, range-sensing of the skin and cortex in the OR, rigid registration of the skin range image with its MRI/CT homologue, non-rigid motion tracking over time of cortical range images, and lastly, interpolation of this surface displacement information over the whole brain volume via a realistically valued finite element model of the head. This papers focuses on the anatomical surface identification and cortical range surface tracking problems. The surface identification scheme implements a recent algorithm which imbeds 3D surface segmentation as the level-set of a 4D moving front. A by-product of this stage is a Euclidean distance and closest point map which is later exploited to speed up the rigid and non-rigid surface registration. The range-sensor uses both laser-based triangulation and defocusing techniques to produce a 2D range profile, and is linearly swept across the skin or cortical surface to produce a 3D range image. The surface registration technique is of the iterative closest point type, where each iteration benefits from looking up, rather than searching for, explicit closest point pairs. These explicit point pairs in turn are used in conjunction with a closed-form SVD-based rigid transformation computation and with fast recursive splines to make each rigid and non-rigid registration iteration essentially instantaneous. Our method is validated with a novel deformable brain-shaped phantom, made of Polyvinyl Alcohol Cryogel.

Cellular instabilities, sublimit structures and edge-flames in premixed counterflows

Abstract: We examine twin premixed flames in a plane counterflow and uncover, in the parameter space, a hitherto unknown domain of cellular instability. This leads us to hypothesize that for small Lewis numbers a two-dimensional (2D) steady solution branch bifurcates from the one-dimensional (1D) solution branch at a neutral stability point located near the strain-induced quenching point. Solutions on this 2D branch are constructed indirectly by solving an initial-value problem in the edge-flame context defined by the multiple-valued bistable 1D solution. Three kinds of solution are found: a periodic array of flame-strings, a single isolated flame-string and a pair of interacting flame-strings. These structures can exist for values of strain greater than the 1D quenching value, corresponding to sublimit solutions.

Other method for adjustment of multiple testing exists

Abstract: EDITOR—Perneger's paper on Bonferroni adjustments consists almost entirely of errors.1 He states that the Bonferroni adjustments are concerned with the wrong hypothesis and that the two groups are identical on all 20variables (the universal null hypothesis). This misses the main point of multiple test adjustments. Similarly he says, “If one or more of the 20P values is less than 0.00256…we can say that the two groups are not equal for all 20variables, but …

Device and method for processing information

Abstract: PROBLEM TO BE SOLVED: To provide an image without the feeling of incompatibility that a real space and a virtual space are merged SOLUTION: Relating to this information processor, the position in a three- dimensional space of an optical see-through type display part 1 is calculated in a three-dimensional position direction calculation part 3, the view point of a user is calculated in a view point position direction calculation part 5 and the coordinate of a virtual image is transformed on the basis of the position of the optical see-through type display part 1 and the view point of the user in a virtual object coordinate transformation part 8 Then, the virtual image after coordinate transformation is supplied to the optical see-through type display part 1 and displayed together with the image of the real space

A simple procedure for the design of classical displaced-axis dual-reflector antennas using a set of geometric parameters

Abstract: A simple procedure for the design of classical displaced-axis dual-reflector antennas is given. Using four geometric input parameters, a set of equations is derived to find the remaining geometric parameters, fully defining the systems. This initial geometry provides a good starting point for any optimization process.

The dual of sweep

Abstract: As an infinite union operation, sweep of a moving object through space is a powerful and natural addition to the Boolean set operations that incorporates motion-related information for the purposes of shaping, collision detection, and simulation of moving objects. Use of sweep has been hindered by limited computational support and by the fact that it is a ‘material growing’ operation, whereas many applications, such as interference elimination and mechanism design, appear to be better modeled by a ‘material removal’ operation. This article formally defines a new geometric modeling operation of unsweep . Given an arbitrary subset E of Euclidean space and a general motion M , unsweep ( E , M ) returns the largest subset of E that remains inside the original E under M . When M is a translation, unsweep ( E , M ) naturally reduces to the standard Minkowski difference of E and the trajectory generated by the inverted motion M . In this sense, the operation of unsweep is a generalization of Minkowski difference that corresponds to a ‘material removal’ operation, it can be also defined as an infinite intersection operation, and is the dual of sweep in a precise set-theoretic sense. We show that unsweep has attractive theoretical and computational properties, including a practical point membership test for arbitrary general motions. Using duality, the established properties of unsweep is extended to the general sweep operation, and can be used to improve the computational support for general sweeps.

Experimental comparisons of space vector neutral point balancing strategies for three-level topology

Abstract: Three-level neutral point clamp topology has attracted applications in medium-voltage high-power drive systems. Since the topology utilizes the neutral point voltage to achieve half bus voltage withstand of power devices and three-level output voltage delivery, it is critical to balance the neutral point voltage in occasions of disturbed or even continuous unbalance load conditions. This paper proposes a couple of balancing techniques based on space vector modulation principle and experimentally compares their effectiveness against the existing method.

Local Mirror Symmetry: Calculations and Interpretations

Abstract: We describe local mirror symmetry from a mathematical point of view and make several A-model calculations using the mirror principle (localization). Our results agree with B-model computations from solutions of Picard-Fuchs differential equations constructed form the local geometry near a Fano surface within a Calabi-Yau manifold. We interpret the Gromov-Witten-type numbers from an enumerative point of view. We also describe the geometry of singular surfaces and show how the local invariants of singular surfaces agree with the smooth cases when they occur as complete intersections.

A Note on the Number of Distinct Distances

Abstract: We refine a method introduced in [1] and [2] for studying the number of distinct values taken by certain polynomials of two real variables on Cartesian products. We apply it to prove a "gap theorem", improving a recent lower bound on the number of distinct distances between two collinear point sets in the Euclidean space.

Feature Point Tracking for Incomplete Trajectories

Abstract: A new algorithm is presented for feature point based motion tracking in long image sequences. Dynamic scenes with multiple, independently moving objects are considered in which feature points may t...

Matching for Shape Defect Detection

Abstract: The problem of defect detection in 2D and 3D shapes is analyzed. A shape is represented by a set of its contour, or surface, points. Mathematically, the problem is formulated as a specific matching of two sets of points, a reference one and a measured one. Modified Hausdorff distance between these two point sets is used to induce the matching. Based on a distance transform, a 2D algorithm is proposed that implements the matching in a computationally efficient way. The method is applied to visual inspection and dimensional measurement of ferrite cores. Alternative approaches to the problem are also discussed.1

Deviation-Function Based Pitch Curve Modification for Conjugate Pair Design

Abstract: In this paper a method for generating new conjugate kinematic pairs is developed. This method, called the “Deviation-Function ” method, is to use deviation functions to reshape the original pitch pairs so that the desired profiles of generated pairs can be obtained. A deviation function is defined as the distance between contacts and their corresponding instant centers of two conjugate pairs. In other words, a deviation function measures the amount of deviation of a point on the generated profile from its corresponding point on the original pitch profile. As demonstrated, this new method is applicable to any type of pitch pairs including circular or noncircular and identical or nonidentical. In addition, by using this method, it is relatively easier to realize desired geometrical and mechanical properties into the design.

Existence of the spectral gap for elliptic operators

Abstract: LetM be a connected, noncompact, complete Riemannian manifold, consider the operatorL=Δ+∇V for someV∈C2(M) with exp[V] integrable with respect to the Riemannian volume element. This paper studies the existence of the spectral gap ofL. As a consequence of the main result, let ϱ be the distance function from a point o, then the spectral gap exists provided limϱ→∞ supLϱ<0 while the spectral gap does not exist if o is a pole and limϱ→∞ infLϱ≥0. Moreover, the elliptic operators onRd are also studied.

Trajectory triangulation over conic section

Abstract: We consider the problem of reconstructing the 3D coordinates of a moving point seen from a monocular moving camera, ie, to reconstruct moving objects from line-of-sight measurements only The task is feasible only when same constraints are placed on the shape of the trajectory of the moving point We coin the family of such tasks as "trajectory triangulation" In this paper we focus on trajectories whose shape is a conic-section and show that generally 9 views are sufficient for a unique reconstruction of the moving point and fewer views when the conic is a known type (like a circle in 3D Euclidean space for which 7 views are sufficient) Experiments demonstrate that our solutions are practical The paradigm of Trajectory Triangulation in general pushes the envelope of processing dynamic scenes forward Thus static scenes become a particular case of a more general task of reconstructing scenes rich with moving objects (where an object could be a single point)