Showing papers on "Euclidean distance published in 1984"

Distance transformations in arbitrary dimensions

Abstract: In many applications of digital picture processing, distances from certain feature elements to the nonfeature elements must be computed. In two dimensions at least four different families of distance transformations have been suggested, the most popular one being the city block/chessboard distance family. The purpose of this paper is twofold: To generalize these transformations to higher dimensions and to compare the computed distances with the Euclidean distance. All of the four distance transformation families are presented in three dimensions, and the two fastest ones are presented in four and arbitrary dimensions. The comparison with Euclidean distance is given as upper limits for the difference between the Euclidean distance and the computed distances.

The mental representation of knowledge acquired from maps.

Abstract: The experiments reported here, tested how knowledge acquired from simple maps is mentally represented and processed. These experiments also tested a new methodology for examining spatial representations. The main question addressed in this research was how route and distance information are represented in cognitive maps. In particular, the experiments examined the relative contributions of route and Euclidean distance on a map to determining the psychological distance between locations in the mental representation of that map. For example, in Figure 1, the cities Sedona and Emmet are equidistant from Nesmith in terms of Euclidean distance. However, Sedona is much closer to Nesmith than is Emmet in terms of route distance. In Experiments 1 and 2, we attempted to determine if the psychological distance between cities in a cognitive map would be primarily dependent on the route distance or the Euclidean distance between those cities on the real map. The second goal of this research was to test a new methodology for examining the

The p -Centre Problem Heuristic and Optimal Algorithms

Abstract: The p-centre problem, or minimax location-allocation problem in location theory terminology, is the following: given n demand points on the plane and a weight associated with each demand point, find p new facilities on the plane that minimize the maximum weighted Euclidean distance between each demand point and its closest new facility. We present two heuristics and an optimal algorithm that solves the problem for a given p in time polynomial in n. Computational results are presented.

An Optimal Global Nearest Neighbor Metric

Abstract: A quadratic metric dAO (X, Y) =[(X - Y)T AO(X - Y)]? is proposed which minimizes the mean-squared error between the nearest neighbor asymptotic risk and the finite sample risk. Under linearity assumptions, a heuristic argument is given which indicates that this metric produces lower mean-squared error than the Euclidean metric. A nonparametric estimate of Ao is developed. If samples appear to come from a Gaussian mixture, an alternative, parametrically directed distance measure is suggested for nearness decisions within a limited region of space. Examples of some two-class Gaussian mixture distributions are included.

Configural processing of faces in the left and the right cerebral hemispheres.

Abstract: This study investigates the rules by which the component features of faces are combined when presented in the left or the right visual field, and it examines the validity of the analytic-holistic processing dichotomy, using concepts elaborated by Garner (1978, 1981) to specify stimulus properties and models of similarity relations as performance criteria. Latency measures of dissimilarity, obtained for the two visual fields, among a set of eight faces varying on three dimensions of two levels each, were fitted to the dominance metric model, the feature-matching model, the city-block distance metric model, and the Euclidean distance metric model. In addition to a right-visual-field superiority in different responses, a maximum likelihood estimation procedure showed that, for each subject and each visual field, the Euclidean model provided the best fit of the data, suggesting that the faces were compared in terms of their overall similarity. Moreover, the spatial representations of the results revealed interactions among the component facial features in the processing of faces. Taken together, these two findings indicate that faces initially projected to the right or to the left hemisphere were not processed analytically but in terms of their gestalt. Human information-processing capacities are the product of a highly adaptive and versatile nervous system that provides individuals with a large number of alternative means for achieving successful performance on any particular task. This versatility is partly attributed to the functional specialization of the two cerebral hemispheres whereby specific skills are alleged to be unilaterally represented, thus doubling the brain processing capacity while avoiding potential conflicts that would result from promiscuity. This specialization was initially characterized in terms of information that each hemisphere was better equipped to operate on (e.g., Milner, 1971). However, the diversity and heterogeneity of the type of information that each hemisphere could be shown to process, initially in experiments with commissurotomized patients, prompted researchers to inquire about the processes un

Minimum Euclidean distance for combinations of short rate 1/2 convolutional codes and CPFSK modulation

Abstract: Continuous phase frequency shift keying (CPFSK) is a constant amplitude modulation method with good spectral sidelobe properties. Good error probability properties can be obtained with coherent maximum-likelihood detection. In this paper we study the Euclidean distance properties of signals formed by a conventional rate 1/2 convolutional encoder followed by a binary or 4 -level CPFSK modulator. The minimum Euclidean distance is calculated for these signal sets as a function of the modulation index and the observation interval length. The optimum detector is discussed for rational modulation index values. The best obtainable codes are found for the case of short rate 1/2 codes with binary or 4 -level CPFSK modulation. Lists of the best codes are given. Among the results are that the noncatastrophic rate 1/2 convolutional codes with optimum free Hamming distance do not in general give the best Euclidean distance with CPFSK.

A New Upper Bound for The Cardinality of 2-Distance Sets in Euclidean Space

Abstract: It is proved that the cardinality of a 2-distance set S in Euclidean d -dimensional space satisfies cards( S )≤½( d +1)( d +2).

The lattices of six-dimensional Euclidean space

Abstract: The lattices of full rank of the six-dimensional Euclidean space are classified according to their automorphism groups (Bravais classification). We find 826 types of such lattices.

An optimal algorithm for computing the minimum vertex distance between two crossing convex polygons

Abstract: LetP={p 1 ,p 2 , ...,p m } andQ={q 1 ,q 2 , ...,q n } be two intersecting convex polygons whose vertices are specified by their cartesian coordinates in order. An optimalO(m+n) algorithm is presented for computing the minimum euclidean distance betweena vertexp i inP and a vertexq j inQ.

Spherically symmetric systems of fields and black holes. III. Positivity of energy and of a new type Euclidean action

Abstract: Within the scope of the two-dimensional model of gravity which was defined and studied in the two preceding papers, we investigate the three famous positivity problems of general relativity: (1) energy, (2) Euclidean action, and (3) divergence identities. We show that the energy can be split in a unique way into a black-hole mass and a field energy. If there are no fields in the model which could discharge the hole, then the field energy itself is non-negative and has a zero minimum for the vacuum value of the fields. In the opposite case, the greatest lower bound for the total energy is the irreducible mass of the hole. We define a new type of Euclidean action for gravity theories, which is different from the action used currently in Euclidean quantum gravity. The new Euclidean action is obtained by a true analytical continuation of a reduced Lorentzian action so that the relation between the Euclidean and Lorentzian regimes is well defined. We prove that the new Euclidean action is positive definite without any additional ''complexification.'' We show that the possibility of gravitational collapse leads to an unusual, saturation-curve-like form, of the Hamiltonian and of the new Euclidean action.

Darboux's problem of quadratic integrals

Abstract: The problem of determining all standard classical Hamiltonians in two dimensions with Euclidean metric which admit constants of motion quadratic in the momenta is resolved. Several general results are given which make it obvious that the systems found do possess such integrals.

Multidimensional scaling models with inequality and equality constraints

Abstract: Recently, a lot of attention has been brought to constrained estimation theory in multidimensional scaling models. So far, only equality constraints have been thoroughly studied. In this paper, the optimization theory is extended to general multidi-mensional scaling models with both inequality and equality constraints. A Newton-Raphson based algorithm is developed to produce the constrained least squares estimate. To illustrate the theory, some classical color data are reanalyzed in the context of the linear Euclidean distance model.

On simultaneous diophantine approximation

Abstract: This paper provides a lower bound for the approximation constant in IR s with respect to the Euclidean norm.

Application of the ellipsoid method in an interactive procedure for multicriteria linear programming

Abstract: The research reported in this paper is concerned with an application of the ellipsoid algorithm in the interactive multicriteria linear programming step method (STEM) byBenayoun et al. [1971]. Due to this application we eliminate some drawbacks of the original version of STEM and, moreover, we avoid extra computations connected with sensitivity analysis in every iteration. Specifically, we use the ellipsoid algorithm to minimize the Euclidean norm in the criterion space instead of the Chebyshev norm, which ensures that every solution submitted to the decision maker is efficient. As follows from a computational experiment, in comparison with the application of the simplex method, the proposed modification of STEM shows a smaller increase of the computational effort when the number of criteria increases. However, the absolute computation time becomes worse for problems of larger size.

Coincidence index for fiber-preserving maps an approach to stable cohomotopy

Abstract: A Coincidence index in any generalized (multiplicative) cohomology theory is defined for certain pairs of maps between euclidean neighborhood retracts over a metric space B.

On combinatorial properties of spheres in euclidean spaces

Abstract: For λ>√2 there exists a triangle-free graphG such that for nod canG be imbedded into thed-dimensional unit sphere with two points joined if and only if their distance is >λ.

A stable method for the calculation of the force fields of polyatomic molecules in dependent coordinates

Abstract: The problem of constructing a stable algorithm for the solution of the inverse vibrational problem in the case of polyatomic molecules (with the use of data on Isotopically substituted compounds) in a complete system of dependent natural coordinates was presented to us. Our formulation of the problem has been presented in [2]. Let Z be the linear space of real symmetric matrices of dimensionality n x n, in which the closeness of the matrices is characterized by the Euclidean norm for vectors of dimensionality n(n + 1)/2 which are composed of the elements lying on or above the principal diagonals of the matrices. Let T-I~Z be the prescribed positive definite symmetric matrix of the kinematic coefficients and let A be an operator which correlates to each matrix U~Z, an ordered (in order of increasing size, for example) set (a vector from the Euclidean space R n) of eigenvalues of the matrix T-*U, i.e., the vector of the squares of the frequencies of the normal vibrations A~R =. The operator A is defined and continuous everywhere on Z. The problem of determin

Evaluating method of degradation condition of equipment

Abstract: PURPOSE:To rationalize handling of data, by quantifying the degree of dissociation between parameters of a numerical formula model for system identification, which are obtained by giving condition information values of an equipment, and plural parameter groups at the normal time to evaluate the degradation. CONSTITUTION:Condition information of an evaluation object equipment, for example, oscillation or the like is detected secularly and is sampled at a certain period, and sampling values are given to a preliminarily determined numerical formula for system identification to calculate parameters of the numerical formula, and the degree of dissociation between this calculated rsult and plural parameter groups at the normal time is quantified as a Euclidean distance which is weighted with reverse matrixes of variation and covariation matrixes of parameter groups at the normal time, namely, Maharanobis generalized distance D 0, and a considerable degradiation of the equipment is detected at the time when the distance D 0 is increased rapidly.

Möbius Equivalence and Euclidean Symmetry

Abstract: (1984). Mobius Equivalence and Euclidean Symmetry. The American Mathematical Monthly: Vol. 91, No. 4, pp. 225-247.

Euclidean Yang-Mills flows in the orbit space

Abstract: We establish a global setting for the canonical formalism of the Euclidean Yang-Mills theory in the orbit space M. In this setting it is shown that the Euclidean Yang-Mills equations lead to an ordinary second order differential system of M and the (anti) self-dual solutions are in the flow of a densely defined vector field ±H of M. We also prove that, for the particular case of having T3 as space manifold the flows ±H are homotopic complete, i.e., in each class of π1(M) there exists a closed integral curve of ±H.