Showing papers on "Euclidean distance published in 1990"

Pseudo-Gray coding

Abstract: A pseudo-Gray code is an assignment of n-bit binary indexes to 2" points in a Euclidean space so that the Hamming distance between two points corresponds closely to the Euclidean distance. Pseudo-Gray coding provides a redundancy-free error protection scheme for vector quantization (VQ) of analog signals when the binary indexes are used as channel symbols on a discrete memoryless channel and the points are signal codevectors. Binary indexes are assigned to codevectors in a way that reduces the average quantization distortion introduced in the reproduced source vectors when a transmitted index is corrupted by channel noise. A globally optimal solution to this problem is generally intractable due to an inherently large computational complexity. A locally optimal solution, the binary switching algorithm, is introduced, based on the objective of minimizing a useful upper bound on the average system distortion. The algorithm yields a significant reduction in average distortion, and converges in reasonable running times. The sue of pseudo-Gray coding is motivated by the increasing need for low-bit-rate VQ-based encoding systems that operate on noisy channels, such as in mobile radio speech communications. >

A distance measure for classifying arima models

Abstract: . In a number of practical problems where clustering or choosing from a set of dynamic structures is needed, the introduction of a distance between the data is an early step in the application of multivariate statistical methods. In this paper a parametric approach is proposed in order to introduce a well-defined metric on the class of autoregressive integrated moving-average (ARIMA) invertible models as the Euclidean distance between their autoregressive expansions. Two case studies for clustering economic time series and for assessing the consistency of seasonal adjustment procedures are discussed. Finally, some related proposals are surveyed and some suggestions for further research are made.

A distance for similarity classes of submanifolds of a Euclidean space

Abstract: A distance is defined on the quotient of the set of submanifolds of a Euclidean space, with respect to similarity. It is then related to a previously defined function which captures the metric behaviour of paths.

An alternating projection algorithm for computing the nearest euclidean distance matrix

Abstract: Recent extensions of von Neumann’s alternating projection algorithm permit an effective numerical approach to certain least squares problems subject to side conditions. This paper treats the problem of minimizing the distance from a given symmetric matrix to the class of Euclidean distance matrices; in dimension $n = 3$ we obtain the solution in closed form.

Contour tracing by piecewise linear approximations

Abstract: We present a method for tracing a curve that is represented as the contour of a function in Euclidean space of any dimension. The method proceeds locally by following the intersections of the contour with the facets of a triangulation of space. The algorithm does not fail in the presence of high curvature of the contour; it accumulates essentially no round-off error and has a well-defined integer test for detecting a loop. In developing the algorithm, we explore the nature of a particular class of triangulations of Euclidean space, namely, those generated by reflections.

Computational Complexity of Norm-Maximization

Abstract: This paper discusses the problem of maximizing a quasiconvex functionφ over a convex polytopeP inn-space that is presented as the intersection of a finite number of halfspaces. The problem is known to beNP-hard (for variablen) whenφ is thepth power of the classicalp-norm. The present reexamination of the problem establishesNP-hardness for a wider class of functions, and for thep-norm it proves theNP-hardness of maximization overn-dimensionalparallelotopes that are centered at the origin or have a vertex there. This in turn implies theNP-hardness of {−1, 1}-maximization and {0, 1}-maximization of a positive definite quadratic form. On the “good” side, there is an efficient algorithm for maximizing the Euclidean norm over an arbitraryrectangular parallelotope.

Euclidean continuation of the Dirac fermion

Abstract: We have found a one-complex-parameter family of Dirac actions which interpolates between the Minkowski and a Euclidean Dirac action The interpolating action is invariant under the ‘‘interpolating Lorentz transformations’’ The resultant Euclidean action is Hermitian and SO(4) invariant There is no doubling of degrees of freedom of the Dirac fermion and no contradiction between the SO(4) invariance and the Hermiticity property of the Euclidean propagator The Euclidean theory so obtained also satisfies the Osterwalder-Schrader positivity condition

Collision-free motion planning for two articulated robot arms using minimum distance functions

Abstract: This paper presents a collision-free motion planning method of two articulated robot arms in a three dimensional common work space Each link of a robot arm is modeled by a cylinder ended by two hemispheres, and the remaining wrist and hand is modeled by a sphere To describe the danger of collision between two modeled objects, minimum distance functions, which are defined by the Euclidean norm, are used These minimum distance functions are used to describe the constraints that guarantee no collision between two robot arms The collision-free motion planning problem is formulated as a pointwise constrained nonlinear minimization problem, and solved by a conjugate gradient method with barrier functions To improve the minimization process, a simple grid technique is incorporated Finally, a simulation study is presented to show the significance of the proposed method

Tracking and Describing Deformable Objects Using Active Contour Models

Abstract: Technical Report TR-CIM-90-9 In this thesis we consider a number of issues in developing techniques and algorithms to automate the visual tracking of deformable objects in the plane. We have applied these techniques in cell locomotion and tracking studies. We examine two classes of computer vision problems. First, we consider the segmentation of a noisy intensity image and the tracking of a nonrigid object. Second, we consider the shape analysis of an amorphous object. In evaluating these problems, we explore a new technique based on an active contour model commonly called a "snake." The snake permits us to simultaneously solve, in constrained cases, both the segmentation and tracking problems. We present a detailed analysis of the snake model, emphasizing its limitations and shortcomings, and propose various improvements to the original description of the model. Then, we study the two complementary types of shape descriptors: boundary- and region-based. We propose to combine these within the context of the grassfire transform. Two new algorithms are described. First, we present a contour segmentation technique using mathematical morphology on the curvature function, we call curvature morphology. Accurate localization for different scales of curvature features is achieved, leading to a Morphological Curvature Scale-space or MCS. Second, the snake model is used to simulate the grassfire transform using the previously extracted contour features. This permits us to produce a multiscale skeleton representation of shape which is based on the Euclidean distance metric. New significance criteria for our shape descriptors, such as the ``region-support'' of curvature extrema and the ``ridge-support'' of skeleton branches are also proposed. Finally, numerous implementation details are discussed; for example, the description of an efficient sequential Euclidean distance transform.

Metric transforms and Euclidean embeddings

Abstract: It is proved that if 0 < c < 0.72/« then for any «-point met- ric space (X, d), the metric space (X,dc) is isometrically embeddable into a Euclidean space. For 6-point metric space, c = j log2 | is the largest exponent that guarantees the existence of isometric embeddings into a Euclidean space. Such largest exponent is also determined for all «-point graphs with "truncated distance".

Generating skeletons and centerlines from the medial axis transform

Abstract: An algorithm for generating connected skeletons of objects in binary images is described. Three main properties of the algorithm are that: (1) it is noniterative, taking a fixed number of passes through the image to produce the skeleton regardless of the width of the objects; (2) it is based on a distance transform that uses a good approximation to the Euclidean distance, giving skeletons that are well centered and robust with respect to rotation; and (3) the skeletons it produces are connected. In addition, the skeletons are thin and allow the objects to be nearly reconstructed. The algorithm can also be run in a mode to produce centerlines, a connected approximation to the skeleton that is less sensitive to border noise and that is useful in image analysis applications. >

Better than Uniform Approximation on Closed Sets by Harmonic Functions with Singularities

Abstract: We work in the Euclidean space R N , where, unless the contrary is stated, N≥2. The Euclidean norm of a point x∈R N is denoted by ∥x∥. If r>0, the, we denote the open ball of centre x and radius r by B(x, r) and we write B 0 (x, r)=B(x, r)\{x}

The smallest point of a polytope

Abstract: This note suggests new ways for calculating the point of smallest Euclidean norm in the convex hull of a given set of points inR n . It is shown that the problem can be formulated as a linear least-square problem with nonnegative variables or as a least-distance problem. Numerical experiments illustrate that the least-square problem is solved efficiently by the active set method. The advantage of the new approach lies in the solution of large sparse problems. In this case, the new formulation permits the use of row relaxation methods. In particular, the least-distance problem can be solved by Hildreth's method.

Oriented Non-Radial Basis Functions for Image Coding and Analysis

Abstract: We introduce oriented non-radial basis function networks (ONRBF) as a generalization of Radial Basis Function networks (RBF)- wherein the Euclidean distance metric in the exponent of the Gaussian is replaced by a more general polynomial. This permits the definition of more general regions and in particular- hyper-ellipses with orientations. In the case of hyper-surface estimation this scheme requires a smaller number of hidden units and alleviates the "curse of dimensionality" associated kernel type approximators. In the case of an image, the hidden units correspond to features in the image and the parameters associated with each unit correspond to the rotation, scaling and translation properties of that particular "feature". In the context of the ONBF scheme, this means that an image can be represented by a small number of features. Since, transformation of an image by rotation, scaling and translation correspond to identical transformations of the individual features, the ONBF scheme can be used to considerable advantage for the purposes of image recognition and analysis.

Medial axis transformation with single-pixel and connectivity preservation using Euclidean distance computation

Abstract: A novel medial axis transformation (MAT) algorithm extracted from the Euclidean distance transform of a binary image is presented. The extracted MAT satisfies the following properties: reconstructivity, rotation-invariance, connectivity, and single-pixel width. The preservation of properties is proved, and some experimental results are shown. The skeleton is trimmed by removing short branches to make it simpler and useful for object recognition. >

Combined coded/multi-h CPFSK signaling

Abstract: A continuous-phase frequency-shift-keying (CPFSK) signaling technique is suggested that combines convolutional encoding and multi-h signaling. In contrast to regular multi-h signaling, this technique changes the modulation index in a preselected pattern in order to maximize the minimum Euclidean distance. A rate-1/2 convolutional encoder along with a 2-h quaternary CPFSK modulator which uses two fixed modulation indexes is considered. Minimum Euclidean distances are calculated corresponding to the best encoder/mapper combinations for different modulation index patterns at attractive pairs of modulation indexes. Numerical results obtained for encoder memory lengths of one and two are used to illustrate that the minimum Euclidean distance of coded CPFSK signals can be significantly increased by combining with multi-h signaling. Modulation index patterns which perform significantly better than regular multi-h signals are determined. An error event analysis over the additive-white-Gaussian noise channel is carried out to investigate the actual error rate performance and to verify the theoretical results. >

Knowledge-based interpretation of road maps based on symmetrical skeletons

Abstract: f' scanner raw.dataS ' 5 The objective of our research reported here is to show the various processing steps on all levels of a computer vision system required to interpret and describe road maps. First, the foundation for the recognition process is laid by computing two sets of distance skeletons. They are termed endoand exo-skeleton and are symmetrical with respect to the boundary between foreground and background of a binary raster image. The skeletons are derived from a novel implementation of Blum's concept of the MAT in the semicontinuum which preserves important features such as Euclidean metric and correct topology. To eliminate noise and quantization effects a new regularization method has been devised based on which the MAT is pruned to its stable inner branches. After the removal of artefacts and further simplifiration of the skeleton the recognition of meaningful complex structures is accomplished in several steps with the aid of a growing amount of domain-specific knowledge. Scene knowledge helps to verify (local) hypotheses in a larger context and to arrive at a consistent interpretation throughout thr scenr. The selection of the object-oriented programming paradigm proved to be very effective.

Bayesian Inference in Models with Euclidean Structures

Abstract: When a parameter space is endowed with a Euclidean structure, there is a Euclidean measure, called the structural (or geometric) prior, which is an obvious candidate to represent ignorance concerning an unknown parameter. The rationale for using this prior is strengthened when the unknown parameter is the canonical parameter of an exponential family. Then the structural prior is the uniform prior for the canonical parameter. It is shown also that Euclidean structures can be combined in different ways with group structures. The structural (or geometric) prior is then the product of the invariant prior for the group structure and the structural (or geometric) prior for the Euclidean structure.

On the chromatic number of rational five-space

Abstract: The chromatic number of rational five-space is the chromatic number of the infinite graph whose vertex set is the set of all those five-dimensional vectors with all the coordinates being rational numbers and with two vertices forming an edge iff the Euclidean distance is exactly one. In this paper it is shown that the chromatic number of rational five-space is at least six.