Showing papers on "Point (geometry) published in 1993"

Nonparametric methods in change-point problems

Abstract: Preface. Introduction: Goals and problems of change point detection. 1. Preliminary considerations. 2. State-of-the-art review. 3. A posteriori change point problems. 4. Sequential change point detection problems. 5. Disorder detection of random fields. 6. Applications of nonparametric change point detection methods. 7. Proofs, new results and technical details. References.

A multi-resolution technique for comparing images using the Hausdorff distance

Abstract: The Hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa. An efficient method of computing this distance is developed, based on a multi-resolution tessellation of the space is possible transformations of the model set. One of the key ideas is that entire cells in this tessellation can be ruled out quickly, without actually computing the Hausdorff distance for many of them. Emphasis is placed on the case in which the model is allowed to translate and scale (independently in x and y) with respect to the image. This four-dimensional transformation space is searched rapidly while guaranteeing that no match will be missed. Some examples of identifying an object in a cluttered scene are presented, including cases where the object is partially hidden from view. >

Method for segmenting features in an image

Abstract: A dual echo magnetic resonance imaging system produces two registered images of a patient in which the images have different contrast relationships between different tissue types. A two dimensional feature space histogram of the two images is produced and a separate centroid is located in the feature space histogram for each one of a pair of tissue types. A Cartesian coordinate system is defined in the feature space so that one axis of the system passes through the two centroids. Vector decomposition is employed to project each image element data point in the feature space onto a point on the one axis. The fractional quantity of each tissue type present in the image element is determined based upon the Euclidean distances from that axis point to the respective centroids. The fractional quantity is calculated for each element in the original images to form a pair of tissue images. The elements of a tissue image are processed to measure the amount of that tissue type in the imaged portion of the patient.

The slab dividing approach to solve the euclidean p-center problem

Abstract: Givenn demand points on the plane, the EuclideanP-Center problem is to findP supply points, such that the longest distance between each demand point and its closest supply point is minimized. The time complexity of the most efficient algorithm, up to now, isO(n 2 p−1· logn). In this paper, we present an algorithm with time complexityO(n 0(√P)).

Parameterized point pattern matching and its application to recognition of object families

Abstract: The problem of recognizing and localizing objects that can vary in parameterized ways is considered. To achieve this goal, a concept of parameterized point pattern is introduced to model parameterized families of such objects, and a parameterized point pattern matching algorithm is proposed. A parameterized point pattern is a very flexible concept that can be used to model a large class of parameterized objects, such as a pair of scissors with rotating blades. The proposed matching algorithm is formulated as a tree search procedure, and it generates all maximum matchings satisfying a condition called delta -boundedness. Several pruning methods based on the condition of delta -boundedness and their efficient computing techniques are given. The proposed matching algorithm is applied to a real shape matching problem in order to check the validity of the approach. >

Finding an interior point in the optimal face of linear programs

Abstract: We study the problem of finding a point in the relative interior of the optimal face of a linear program. We prove that in the worst case such a point can be obtained in O(n3L) arithmetic operations. This complexity is the same as the complexity for solving a linear program. We also show how to find such a point in practice. We report and discuss computational results obtained for the linear programming problems in the NETLIB test set.

Computation of stationary points of distance functions

Abstract: This paper presents an algorithm for computation of the stationary points of the squared distance functions between two point sets. One point set consists of a single space point, a rational B-spline curve, or a rational B-spline surface. The problem is reformulated in terms of solution of n polynomial equations with n variables expressed in the tensor product Bernstein basis. The solution method is based on subdivision relying on the convex hull property of the n-dimensional Bernstein basis and minimization techniques. We also cover classification of the stationary points of these distance functions, and include a method for tracing curves of stationary points in case the solution set is not zerodimensional. The distance computation problem is shown to be equivalent to the geometrically intuitive problem of computing collinear normal points. Finally, examples illustrate the applicability of the method

Signal recovery by best feasible approximation

Abstract: The objective of set theoretical signal recovery is to find a feasible signal in the form of a point in the intersection of S of sets modeling the information available about the problem. For problems in which the true signal is known to lie near a reference signal r, the solution should not be any feasible point but one which best approximates r, i.e., a projection of r onto S. Such a solution cannot be obtained by the feasibility algorithms currently in use, e.g., the method of projections onto convex sets (POCS) and its offsprings. Methods for projecting a point onto the intersection of closed and convex sets in a Hilbert space are introduced and applied to signal recovery by best feasible approximation of a reference signal. These algorithms are closely related to the above projection methods, to which they add little computational complexity. >

An incremental algorithm for constructing shortest watchman routes

Abstract: The problem of finding the shortest watchman route in a simple polygon P through a point s on its boundary is considered. A route is a watchman route if every point inside P can be seen from at least one point along the route. We present an incremental algorithm that constructs the shortest watchman route in O(n3) time for a simple polygon with n edges. This improves the previous O(n4) bound.

CHAPTER 5.2 – Stochastic Geometry

Abstract: Publisher Summary This chapter discusses stochastic geometry. Random points are the simplest random objects in geometry. They can be used in different ways, to generate a great variety of random geometrical objects, and they have applications in several domains—for instance, in statistics, computer geometry, and pattern analysis. A natural generalization of the notion of a random point in a convex body is the notion of a random flat meeting a convex body. An important property of Poisson point processes is that the different points are independent. The intensity measure of the Poisson process is not concentrated on the set of hyperplanes parallel to a line. For almost all realizations of the process, all cells are bounded. A nondegenerate stationary Poisson hyperplane network X is uniquely determined by the intensity measure of the generating Poisson process of hyperplanes. Stereological problems are the main field of applications of stochastic geometry. Stereology deals with the determination of characteristic geometric properties of objects by investigations of sections, projections, intersections with test sets, or other transformed images.

Image object recognition system and method

Abstract: A pseudo-inverse derived model-point-to-image-point transformation hypothesis generator as could be used in a computer vision system. Preferred embodiments include generation of n-point transformations directly from n point pair sets and generation of n-point transformations from sets of n point pairs defined by a preliminary three-point transformation plus sets of (n−3) points having minimal error with respect to the three-point trnasformation. Systems include salient corner extraction and hypothesis transformation verification by further sets of point pairs.

Computing the discrepancy

Abstract: We develop algorithms for computing the discrepancy of point sets in various Euclidean range spaces.

Preferred Point Geometry and Statistical Manifolds

Abstract: A new mathematical object called a preferred point geometry is introduced in order to (a) provide a natural geometric framework in which to do statistical inference and (b) reflect the distinction between homogeneous aspects (e.g., any point $\theta$ may be the true parameter) and preferred point ones (e.g., when $\theta_0$ is the true parameter). Although preferred point geometry is applicable generally in statistics, we focus here on its relationship to statistical manifolds, in particular to Amari's expected geometry. A symmetry condition characterises when a preferred point geometry both subsumes a statistical manifold and, simultaneously, generalises it to arbitrary order. There are corresponding links with Barndorff-Nielsen's strings. The rather unnatural mixing of metric and nonmetric connections in statistical manifolds is avoided since all connections used are shown to be metric. An interpretation of duality of statistical manifolds is given in terms of the relation between the score vector and the maximum likelihood estimate.

Helical micro-drill point design and grinding

Abstract: A new drill point geometry, termed the helical drill point, specifically intended for micro-drills, is developed in order to alleviate the disadvantages of existing planar micro-drill points. A mathematical model for this new drill point has been established. It is shown that this model is more general than existing drill point models. The commonly used conical, cylindrical and planar drill point models are only special cases of the helical model. For uniquely determining the grinding parameters of the new drill point as well as guiding the grinder design, the characteristics, the controllability and the sensitivity of the grinding parameters have been analyzed. Finally the geometric characteristics of this new drill point are investigated.

Method and apparatus for convex interpolation for color calibration

Abstract: A convex interpolation apparatus and method to map source color signals in a n-dimensional color space to target color signals in a m-dimensional color space includes finding a set of sample signals in the source color space whose convex hull encloses the given signal; determining the coefficients needed to express the given signal as a convex combination of the set of sample signals; and interpolating the source signal to obtain a target signal in the target color space by using the coefficients and the sample signals is the target color space that correspond to the sample signals selected in the source color space. The sample signals in both color spaces can be lattice points or non-lattice points. A method and apparatus are also provided which can not only determine if a point is enclosed by a convex hull of a set of points in a n-dimensional space, but also simultaneously derive the coefficients needed to express the given point as a convex combination of the set of points.

System and method for simplifying a computer-generated path

Abstract: The present invention is for a system and process for simplifying complex graphical paths. The process first analyzes individual curve and straight line segments of the path, possibly splitting curved segments at local extrema points. Next, the process creates a list of points which includes the endpoints of all the original curve and straight line segments, as well as generating intermediate points along the curve and straight line segments. The process also flags each point in the list indicating what kind of point it is, or what the original path looks like at each point. Thereafter, the process flags any and all extrema points of the types the user specified. Then, the process uses a curve fitting routine for refitting each section of the path with new curves. The process tries to find a minimum set of curves which will reproduce the original path into a simplified version within the tolerances the user has specified.

Grid modeling of robot cells: A memory-efficient approach

Abstract: This article introduces a new approach to modeling robot workspace in two dimensions (and its extension to 21/2 dimensions and to mobile objects). The scheme proves to be attractive because it requires less memory space and is execution-efficient. It is very useful for real-time applications. The grid modeling consists in dividing the space into horizontal and vertical strips whose intersection will form elementary cells. A function giving the access conditions (either a binary one allowing access or nonallowed access, or a more elaborate one including other elements (task, geometries)) is associated to each cell. The size of the adaptive grid will depend on the criterion of the obstacle minimal approach by the robot. Then a method for path planning is developed. The Lee and A* algorithms being the starting point, the method has been conceived by executing mask operations. So the method requires less memory space and allows an admissible trajectory to be quickly found.

Color image processing method and apparatus for generating device-dependent color signals

Abstract: A method and apparatus for finding the stored device independent coordinate triplet (CIEL*a*b*triplet) which is closest to the device-independent target color triplet and then looking up the coordinates in device-dependent ABC space which correspond to this best fit among the color patches. A set of new points is defined in ABC space about the best fit point. The raster for the selection of these points in ABC space is independent of the stored color patch points. The magnitude of the increments away from the best fit color patch can therefore be made as small or large as desired. Using this new set of points about the best fit color match, each point of this set is converted back into CIEL*a*b* space points by interpolation and each of these points is compared with the target color in CIEL*a*b* space and the point determined with the smallest difference thereto, ΔE.

Comprehensive three-dimensional rotary tool point compensation

Abstract: The present invention provides a system and method to accurately provide three-dimensional rotary tool point compensation by evaluating a CNC machining center's geometric condition with respect to a trunnioned spindle mechanism of the machining center as it applies to the degrees of freedom of motion that affect the rotary tool point positioning of a cutting tool mounted in a tool holder of the spindle mechanism. The present invention evaluates the geometric condition of the trunnioned spindle mechanism by positioning the tool point in contact with a reference point or datum and recording a first coordinate position, then rotating the spindle mechanism 90° about a trunnion axis and positioning the tool point in contact with the same reference point a second time. A second coordinate location is recorded when the tool point contacts the reference point the second time. The rotary tool point offsets are then determined from the two recorded coordinate locations and the coordinates of the tool point may be appropriately automatically compensated for the offsets during a machining operation.

An upper bound for the minimum diameter of integral point sets

Abstract: For alln>d there existn points in the Euclidean spaceEd such that not all points are in a hyperplane and all mutual distances are integral. It is proved that the minimum diameter of such integral point sets has an upper bound of 2c logn log logn.

Wakes and waves in N dimensions

Abstract: An impulsive point excitation in a linear, nondispersive wave medium can produce an after‐signal, which has been called a ‘‘wake’’ in the mathematical physics literature Relations are derived between such wakes and the dimensionality of the space by regarding a point source in space of dimensionality N−2 as a line source in N−1 dimensions and as a plane source in N dimensions The ‘‘magic’’ of one and three dimensions is discussed from a new point of view

An interior point algorithm for large scale portfolio optimization

Abstract: The minimum-norm point problem which arises in portfolio selections is discussed and an interior point algorithm to solve the problem is proposed in this paper. Three kinds of problems, the mean-variance, the index matching and the multiple factor models are viewed as variants of the minimum-norm point problem. Results of the computational experiments are attached to show the proposed algorithm as a very powerful tool for large scale portfolio optimization.

System for positioning a work point in three dimensional space

Abstract: A system for positioning a work point in three dimensional space has at least three reeving systems spaced apart from one another, with each reeving system having a adjustable support element connected to it. These support elements are also connected to the work point, with the length of the support elements between the work point and the reeving determining the work point's location. Associated with each reeving system is an actuator adapted for releasing and taking up the support element. A control system controls the actuators to release and take up each of the support elements to move the work point with respective to at least three spatial coordinate axes while controlling at least one motion parameter of the work point in a predetermined manner.

Probability and Problems in Euclidean Combinatorial Optimization

Abstract: This article summarizes the current status of several streams of research that deal with the probability theory of problems of combina- torial optimization. There is a particular emphasis on functionals of finite point sets. The most famous example of such functionals is the length associated with the Euclidean traveling salesman problem (TSP), but closely related problems include the minimal spanning tree problem, minimal matching problems and others. Progress is also surveyed on (1) the approximation and determination of constants whose existence is known by subadditive methods, (2) the central limit problems for several functionals closely related to Eucidean functionals, and (3) analogies in the asymptotic behavior between worst-case and expected-case behavior of Euclidean problems. No attempt has been made in this survey to cover the many important applications of probability to linear programming, arrangement search- ing or other problems that focus on lines or planes.