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Showing papers on "Metric (mathematics) published in 1993"


Journal ArticleDOI
TL;DR: A twin-comparison approach has been developed to solve the problem of detecting transitions implemented by special effects, and a motion analysis algorithm is applied to determine whether an actual transition has occurred.
Abstract: Partitioning a video source into meaningful segments is an important step for video indexing. We present a comprehensive study of a partitioning system that detects segment boundaries. The system is based on a set of difference metrics and it measures the content changes between video frames. A twin-comparison approach has been developed to solve the problem of detecting transitions implemented by special effects. To eliminate the false interpretation of camera movements as transitions, a motion analysis algorithm is applied to determine whether an actual transition has occurred. A technique for determining the threshold for a difference metric and a multi-pass approach to improve the computation speed and accuracy have also been developed.

1,360 citations


Journal ArticleDOI
TL;DR: A hierarchical model of animal spatial cognitive maps is provided and it is suggested that the hippocampal formation and the posterior parietal cortex would act differently by handling topological and metric information, respectively.
Abstract: This article provides a hierarchical model of animal spatial cognitive maps. Such maps include both topological information, which affords loose, yet operational, representations of the connectivity of space and its overall arrangement, and metric information, which provides information about angles and distances. The model holds that maps can be initially described as a set of location-dependent reference frameworks providing directional information about other locations. The addition of an overall directional reference allows for the buildup of more complete (allocentric) representations. A survey of recent neurobiological data provides some hints about the brain structures involved in these processes and suggests that the hippocampal formation and the posterior parietal cortex would act differently by handling topological and metric information, respectively.

492 citations


Journal ArticleDOI
TL;DR: A new metric on linear, time-invariant systems is defined that is no greater than the gap metric, and is in fact the smallest metric for which a certain robust stabilization result holds.
Abstract: A new metric on linear, time-invariant systems is defined. This metric is no greater than the gap metric, and is in fact the smallest metric for which a certain robust stabilization result holds. Unlike other known metrics which induce the graph topology, it has a clear frequency response interpretation. This allows questions regarding robustness in the face of parametric uncertainty to be considered in terms of this metric. >

482 citations


Journal ArticleDOI
TL;DR: In this article, the authors consider some basic properties of nonsmooth and set-valued mappings (multifunctions) connected with open and inverse mapping principles, distance estimates to the level sets (metric regularity), and a locally Lipschitzian behavior.
Abstract: We consider some basic properties of nonsmooth and set-valued mappings (multifunctions) connected with open and inverse mapping principles, distance estimates to the level sets (metric regularity), and a locally Lipschitzian behavior. These properties have many important applications to various problems in nonlinear analysis, optimization, control theory, etc., especially for studying sensitivity and stability questions with respect to perturbations of initial data and parameters. We establish interrelations between these properties and prove effective criteria for their fulfillment stated in terms of robust generalized derivatives for multifunctions and nonsmooth mappings

345 citations


Proceedings Article
29 Nov 1993
TL;DR: This paper shows that minimizing the disagreement between the outputs of networks processing patterns from these different modalities is a sensible approximation to minimizing the number of misclassifications in each modality, and leads to similar results.
Abstract: One of the advantages of supervised learning is that the final error metric is available during training. For classifiers, the algorithm can directly reduce the number of misclassifications on the training set. Unfortunately, when modeling human learning or constructing classifiers for autonomous robots, supervisory labels are often not available or too expensive. In this paper we show that we can substitute for the labels by making use of structure between the pattern distributions to different sensory modalities. We show that minimizing the disagreement between the outputs of networks processing patterns from these different modalities is a sensible approximation to minimizing the number of misclassifications in each modality, and leads to similar results. Using the Peterson-Barney vowel dataset we show that the algorithm performs well in finding appropriate placement for the codebook vectors particularly when the confuseable classes are different for the two modalities.

245 citations


Book
04 Oct 1993
TL;DR: This critique demonstrates that McCabe's cyclomatic complexity metric is based upon poor theoretical foundations and an inadequate model of software development, and for a large class of software it is no more than a proxy for, and in many cases is outperformed by, lines of code.
Abstract: McCabe's cyclomatic complexity metric (1976) is widely cited as a useful predictor of various software attributes such as reliability and development effort This critique demonstrates that it is based upon poor theoretical foundations and an inadequate model of software development The argument that the metric provides the developer with a useful engineering approximation is not borne out by the empirical evidence Furthermore, it would appear that for a large class of software it is no more than a proxy for, and in many cases is outperformed by, lines of code< >

212 citations


Journal ArticleDOI
TL;DR: In this article, the integrability of equations of topological-antitopological fusion describing the ground state metric on a given 2D topological field theory (TFT) model, is proved.
Abstract: Integrability of equations of topological-antitopological fusion (being proposed by Cecotti and Vafa) describing the ground state metric on a given 2D topological field theory (TFT) model, is proved. For massive TFT models these equations are reduced to a universal form (being independent on the given TFT model) by gauge transformations. For massive perturbations of topological conformal field theory models the separatrix solutions of the equations bounded at infinity are found by the isomonodromy deformations method. Also it is shown that the ground state metric together with some part of the underlined TFT structure can be parametrized by pluriharmonic maps of the coupling space to the symmetric space of real positive definite quadratic forms.

184 citations


Journal ArticleDOI
TL;DR: The appropriateness of a given layout is computed by weighting the cost of each sequence of actions by how frequently the sequence is performed, which emphasizes frequent methods of accomplishing tasks while incorporating less frequent methods in the design.
Abstract: Numerous methods for evaluating user interfaces have been investigated to develop a metric that incorporates simple task descriptions which can assist designers in organizing their user interface. The metric, Layout Appropriateness (LA), requires a description of the sequences of actions users perform and how frequently each sequence is used. This task description can either be from observations of an existing system or from a simplified task analysis. The appropriateness of a given layout is computed by weighting the cost of each sequence of actions by how frequently the sequence is performed, which emphasizes frequent methods of accomplishing tasks while incorporating less frequent methods in the design. In addition to providing a comparison of proposed or existing layouts, an LA-optimal layout can be presented to the designer. The designer can compare the LA-optimal and existing layouts or start with the LA-optimal layout and modify it to take additional factors into consideration. >

157 citations


Journal ArticleDOI
01 Jul 1993
TL;DR: In this paper, it was shown that for suitable decompositions of a metric space there are Mayer-Vietoris sequences both in coarse cohomology and in the K-theory of the C*-algebra associated to a metric cone.
Abstract: In [1], [4], and [6] the authors have studied index problems associated with the ‘coarse geometry’ of a metric space, which typically might be a complete noncompact Riemannian manifold or a group equipped with a word metric. The second author has introduced a cohomology theory, coarse cohomology, which is functorial on the category of metric spaces and coarse maps, and which can be computed in many examples. Associated to such a metric space there is also a C*-algebra generated by locally compact operators with finite propagation. In this note we will show that for suitable decompositions of a metric space there are Mayer–Vietoris sequences both in coarse cohomology and in the K-theory of the C*-algebra. As an application we shall calculate the K-theory of the C*-algebra associated to a metric cone. The result is consistent with the calculation of the coarse cohomology of the cone, and with a ‘coarse’ version of the Baum–Connes conjecture.

152 citations


Journal ArticleDOI
TL;DR: A mesh smoothing technique that uses optimization principles to minimize a distortion metric throughout a mesh is presented and comparison is made with laplacian and isoparametric smoothing techniques.

132 citations


Journal ArticleDOI
TL;DR: The fuzzy distance of two C NF sets can be defined, and by this distance, closeness and similarity of CNF sets, as well.

Journal ArticleDOI
TL;DR: Two algorithms for computing the extent of regular equivalence among pairs of nodes in a network are presented, with CATREGE being significantly faster and its output similarity coefficients have better metric properties.

Journal ArticleDOI
TL;DR: In this article, the relevance of the theory of size functions to visual perception is investigated, and an algorithm for the computation of the size functions is presented, and many theoretical properties of size function theory are demonstrated on real images.
Abstract: According to a recent mathematical theory a shape can be represented by size functions, which convey information on both the topological and metric properties of the viewed shape. In this paper the relevance of the theory of size functions to visual perception is investigated. An algorithm for the computation of the size functions is presented, and many theoretical properties of the theory are demonstrated on real images. It is shown that the representation of shape in terms of size functions (1) can be tailored to suit the invariance of the problem at hand and (2) is stable against small qualitative and quantitative changes of the viewed shape. A distance between size functions is used as a measure of similarity between the representations of two different shapes. The results obtained indicate that size functions are likely to be very useful for object recognition. In particular, they seem to be well suited for the recognition of natural and articulated objects.

Patent
24 Jun 1993
TL;DR: The dual-maxima metric generation (DMD) as mentioned in this paper is a method for decoding an orthogonally encoded data signal in a non-coherent receiver system, which comprises the steps of sequentially searching for a maximum energy level in each of two subsets of a given set of symbol indexes and associated energy levels and calculating a difference of the two values to form a soft decision output value.
Abstract: A method and apparatus for decoding an orthogonally encoded data signal in a noncoherent receiver system. The method is referred to as dual-maxima metric generation. It comprises the steps of sequentially searching for a maximum energy level in each of two subsets of a given set of symbol indexes and associated energy levels and calculating a difference of the two values to form a soft decision output value. The two subsets are identified by the binary value (either "0" or "1") of a given digit of the binary equivalent of the symbol index. The soft decision output value reflects a measure of confidence of the value of the corresponding digit of the original signal. The dual-maxima generator sequences through the steps one time for each binary digit of the original signal. The method allows the correlated energy from multiple receivers to be combined before the decoding of the signals, thus further reducing the complexity of the circuitry and improving the performance of the decoder.

Journal ArticleDOI
TL;DR: It is shown that most vacuum Weyl solutions can arise as the metrics of counter-rotating relativistic disks and how the Curzon, Schwarzschild, Zipoy-Vorhees, and Israel-Kahn metrics can be generated by the disks.
Abstract: Among known finite-mass nonspherical solutions of Einstein's equations few have physical sources. We show that most vacuum Weyl solutions can arise as the metrics of counter-rotating relativistic disks. We give the metric for the general counter-rotating relativistic disk and show how the Curzon, Schwarzschild, Zipoy-Vorhees, and Israel-Kahn metrics can be generated by the disks. The physical properties of the disks are discussed and illustrated. The central gravitational redshift can become arbitrarily large. The disks with new metrics are discussed elsewhere.

Journal ArticleDOI
TL;DR: In this article, a geometric framework for robust stabilization of infinite-dimensional time-varying linear systems is presented, where the uncertainty of a system is described by perturbations of its graph and is measured in the gap metric.
Abstract: A geometric framework for robust stabilization of infinite-dimensional time-varying linear systems is presented. The uncertainty of a system is described by perturbations of its graph and is measured in the gap metric. Necessary and sufficient conditions for robust stability are generalized from the time-invariant case. An example is given to highlight an important difference between the obstructions, which limit the size of a stabilizable gap ball, in the time-varying and time-invariant cases. Several results on the gap metric and the gap topology are established that are central in a geometric treatment of the robust stabilizability problem in the gap. In particular, the concept of a “graphable” subspace is introduced in the paper. Subspaces that fail to be graphable are characterized by an index condition on a certain semi-Fredholm operator.

Journal ArticleDOI
TL;DR: Verifiable conditions ensuring the important notion of metric regularity for general nondifferentiable programming problems in Banach spaces are established and used to obtain Lagrange-Kuhn-Tucker multipliers for minimization problems with infinitely many inequality and equality constraints.
Abstract: This paper establishes verifiable conditions ensuring the important notion of metric regularity for general nondifferentiable programming problems in Banach spaces. These conditions are used to obtain Lagrange-Kuhn-Tucker multipliers for minimization problems with infinitely many inequality and equality constraints.

Journal ArticleDOI
TL;DR: In this article, the authors define families of nonempty closed subsets of a metric space with uniformities defined by semimetrics, which are sufficient to define almost all convergences known up to now.
Abstract: We endow families of nonempty closed subsets of a metric space with uniformities defined by semimetrics. Such structure is completely deter- mined by a class (which is a family of closed sets) and a type (which is a semi- metric). Two types are sufficient to define (and classify) almost all convergences known till now. These two types offer the possibility of defining other set con- vergences.

Book ChapterDOI
23 Jun 1993
TL;DR: This study aims to model an appropriate set of 2-dimensional spatial objects embedded in R2 with the usual metric and topology and aims to capture explicitly some important topological properties of the spatial objects, e.g. connectedness and region inclusion.
Abstract: This study aims to model an appropriate set of 2-dimensional spatial objects (i.e. areas) embedded in R2 with the usual metric and topology. The set of objects to be modelled is an extension of the set of 2-dimensional objects which can be represented within the vector-based data model. The model aims to capture explicitly some important topological properties of the spatial objects, e.g. connectedness and region inclusion. The construction discussed in this paper is capable of representing a large class of areal objects, including objects with holes which have islands (to any finite level). It has the virtue of being canonical, in the sense that any appropriate areal object has a unique representation in this model. The paper describes the model by specifying the areal objects under consideration and providing their representation. It also defines a set of operations and discusses algorithms for their implementation.


Journal ArticleDOI
TL;DR: This work considers the (massless) scalar field on a two-dimensional manifold with metric that changes signature from Lorentzian to Euclidean and gives a variational approach, obtaining the same results from a natural Lagrangian.
Abstract: We consider the (massless) scalar field on a two-dimensional manifold with metric that changes signature from Lorentzian to Euclidean. Requiring a conserved momentum in the spatially homogeneous case leads to a particular choice of propagation rule. The resulting mix of positive and negative frequencies depends only on the total (conformal) size of the spacelike regions and not on the detailed form of the metric. Reformulating the problem using junction conditions, we then show that the solutions obtained above are the unique ones which satisfy the natural distributional wave equation everywhere. We also give a variational approach, obtaining the same results from a natural Lagrangian.

Journal ArticleDOI
TL;DR: It is shown that the partial derivative of the output nodes with respect to a given input feature yields a sensitivity measure for the probability of error.

Book ChapterDOI
01 Jan 1993
TL;DR: The average hamming distance of a population is used as a syntactic metric to obtain probabilistic bounds on the time convergence of genetic algorithms and employs linearly computable syntactic information to provide upper limits on thetime beyond which progress is unlikely on an arbitrary function.
Abstract: We use the average hamming distance of a population as a syntactic metric to obtain probabilistic bounds on the time convergence of genetic algorithms. Analysis of a flat function provides worst case time complexity for static functions and gives a theoretical basis to the problem of premature convergence. We suggest simple changes that mitigate this problem and help fight deception. Further, employing linearly computable syntactic information, we can provide upper limits on the time beyond which progress is unlikely on an arbitrary function. Preliminary results support our analysis.

Journal ArticleDOI
TL;DR: In this article, the theory of mono-and multifractal sets is presented and a geometric and thermodynamic description of the multifractal set is developed. But the focus is mainly on the application of the fractal concept for a thermodynamic system with partial memory loss, turbulent fluid flow, hierarchically coordinated set of statistical ensembles, Anderson's transition, and incommensurable and quasicrystalline structures.
Abstract: Basic information about the theory of mono- and multifractal sets is presented. Geometric and thermodynamic descriptions are developed. The geometric picture is presented on the basis of the simplest examples of the Koch and Cantor fractal sets. An ultrametric space, representing the metric of a fractal set, is introduced on the basis of Cayley's hierarchical tree. The spectral characteristics of a multifractal formation are described. Attention is focused mainly on the application of the fractal concept for a thermodynamic system with partial memory loss, turbulent fluid flow, hierarchically coordinated set of statistical ensembles, Anderson's transition, and incommensurable and quasicrystalline structures.

Journal ArticleDOI
TL;DR: A statistical model is added to the conventional physical model underlying factor analysis of medical image sequences that allows a derivation of the optimal metric to be used for the orthogonal decomposition involved in FAMIS.
Abstract: A statistical model is added to the conventional physical model underlying factor analysis of medical image sequences (FAMIS). It allows a derivation of the optimal metric to be used for the orthogonal decomposition involved in FAMIS. The oblique analysis of FAMIS is extended to take this optimal metric into account. The case of scintigraphic image sequences is used. The authors derive in this case that the optimal decomposition is obtained by correspondence analysis. A scintigraphic dynamic study illustrates the practical consequences of the use of the optimal metric in FAMIS.

Journal ArticleDOI
TL;DR: In this paper, the authors consider the prediction of stationary max-stable processes, i.e., spaces of extreme value distributed random variables that are closed under scalar multiplication and the taking of finite maxima.
Abstract: We consider prediction of stationary max-stable processes. The usual metric between max-stable variables can be defined in terms of the $L_1$ distance between spectral functions and in terms of this metric a kind of projection can be defined. It is convenient to project onto max-stable spaces; that is, spaces of extreme value distributed random variables that are closed under scalar multiplication and the taking of finite maxima. Some explicit calculations of max-stable spaces generated by processes of interest are given. The concepts of deterministic and purely nondeterministic stationary max-stable processes are defined and illustrated. Differences between linear and nonlinear prediction are highlighted and some characterizations of max-moving averages and max-permutation processes are given.

Patent
26 May 1993
TL;DR: An error control decoder for decoding signals encoded with an M-ary convolutional code and a method for decoding such a code was presented in this paper. But decoding such codes is computationally intensive.
Abstract: An error control decoder (44) for use in decoding signals encoded with an M-ary convolutional code and a method for decoding such a code. The error control decoder includes a branch metrics module (46) that determines differences between the correlation values of each of eight possible symbols used to represent data encoded and the largest of these correlation values. An add-compare-select module (50) determines path metric values for each of 64 states by adding selected branch metric values to prior state metrics for the two possible paths that lead to a current state metric. The minimum path metric of the two is then assigned as a new state metric, and a logic level identifying the selected path metric is stored in a path history module (62). This procedure is repeated for each of the 64 states. A minimum state metric from the prior symbol period is determined and used to normalize the current state metrics to avoid overflow. After processing data for 36 symbol periods to form the initial path history, the data are decoded by tracing back through the path history to identify a state that most likely represents the binary data originally encoded. The error control decoder is disclosed in use in a spread spectrum communication system (20).

Journal ArticleDOI
TL;DR: In this article, a probabilistic multiple source solution for the bioelectromagnetic inverse problem is described, which assumes a finite number of discrete primary sources at fixed locations within a bounded conductor.
Abstract: A probabilistic multiple source solution for the bioelectromagnetic inverse problem is described The model-dependent solution assumes a finite number of discrete primary sources at fixed locations within a bounded conductor Covariance statistics derived from a set of detectors outside the conducting region are used to determine a metric on the space of possible sources This metric function is used to construct a weighted pseudo-inverse matrix, which, in turn, may be used to estimate the spatio-temporal distribution of source activity The results are embodied in the form of the PROMS (probabilistic reconstruction of (multiple sources) algorithm Computer simulations using the algorithm are described These methods are compared with other algorithms, including minimum norm estimation, and the MUSIC and spatial filtering algorithms

Journal ArticleDOI
TL;DR: New conditions are derived for when the distance between two linear systems in the gap metric is less than one by including a coprimeness assumption in the coprime factor uncertainty description and it is shown that an open ball in thegap metric is equivalent to anopen ball phrased in terms of coprIME factor perturbations.

Journal ArticleDOI
TL;DR: This study shows that the new metric measures a source of variation not accounted for in the set of metric primitives, which provides additional resolution on the description of differences among data structures among program elements.