Showing papers on "Affine transformation published in 1978"
TL;DR: An analytical representation for m -dimensional piecewise-linear functions which are affine over convex polyhedral regions bounded by linear partitions is introduced in this paper, where explicit formulas are presented to compute the coefficients associated with this representation along with an example.
Abstract: An analytical representation is introduced for m -dimensional piecewise-linear functions which are affine over convex polyhedral regions bounded by linear partitions. Explicit formulas are presented to compute the coefficients associated with this representation along with an example.
118 citations
60 citations
TL;DR: In this paper, the scattering function S(k) for neutrons off a randomly cross-linked phantom network is calculated, where the mean position of the chain deforms affinely and fluctuations about this mean are random.
Abstract: The scattering function S(k) for neutrons off a randomly cross-linked phantom network is calculated. Adopting the results of Deam and Edwards (1976) in which the mean position of the chain deforms affinely and fluctuations about this mean are random (i.e. non-affine) gives very different results from Benoit (1975) and co-workers who assume affine deformation of the chain shape. Some of the results obtained are similar to those of Pearson (1977) who calculates S(k) using Flory's theory (1976) of non-affine fluctuations. However, the predictions for networks more densely cross-linked are different from those of Flory's theory.
59 citations
TL;DR: The degradation in acquisition probability that occurs when cross correlation is used to determine the offset of two images of the same scene that differ by a relative geometric distortion is presented.
Abstract: The degradation in acquisition probability that occurs when cross correlation is used to determine the offset of two images of the same scene that differ by a relative geometric distortion is presented. The geometric distortions considered can be represented by a general affine transformation of image coordinates. The analysis shows that for a given geometric distortion there is an image size and shape that minimizes the probability of false acquisition. The results are derived for images modeled as random patterns with arbitrary auto-correlation functions. The results are illustrated for images with Gaussian autocorrelation functions.
56 citations
46 citations
TL;DR: In this paper, the effect of geometric distortion on the local accuracy of the image registration algorithms using cross correlation is presented using a probabilistic model describing images as homogeneous random patterns, expressions for the mean and covariance of the local error vector in terms of image and noise autocorrelation functions, geometric distortion, and reference image area are derived.
Abstract: The effect of geometric distortion on the local accuracy of the image registration algorithms using cross correlation is presented. Using a probabilistic model describing images as homogeneous random patterns, expressions for the mean and covariance of the local error vector in terms of image and noise autocorrelation functions, geometric distortion, and reference image area are derived. The geometric distortions considered are those represented by an affine transformation of image coordinates. It is shown that for a fixed geometric distortion there is an image size (integration area) that minimizes the local error. The optimum area decreases with increasing geometric distortion.
43 citations
01 Jan 1978
TL;DR: The microprogrammable local parallel pattern processor (PPPPPP) as discussed by the authors is a hardware architecture for image processing that includes seven special purpose modules for two-dimensional convolution, point mapping, linear coordinate transformation, logical filtering, histogram generation, region labeling, and pixel operations.
Abstract: This chapter presents an approach called microprogrammable local parallel pattern processor (PPP) which has several basic image processing functions in a simple hardware. It discusses major concepts considered for the design of the PPP. The chapter describes the details of the implementation of the basic image processing functions. It shows some simple examples of programming the PPP. By using dynamically rewritable microprogram architecture, powerful and flexible programs of image processing were designed and demonstrated in the interactive image processing system. Two-dimensional linear coordinate transformation (affine transformation) is performed by the address control module. The PPP includes seven special purpose modules for two-dimensional convolution, point mapping, linear coordinate transformation, logical filtering, histogram generation, region labeling, and pixel operations. These functions can be combined for more global and complex functions such as texture analysis, shape identification, region separation, and so on. The scratch-pad memory is used for histogram counting registers for image data.
43 citations
TL;DR: In this article, the authors give a rule Q which generalizes the Weyl correspondence to systems whose configuration space is equipped with an affine connection, and show that [Q (f, Q (g)]=iQ ({f, g}) for arbitrary f provided g has the form Xipi, where Xi is an affines vector field.
Abstract: We give a rule Q which generalizes the Weyl correspondence to systems whose configuration space is equipped with an affine connection. We show that [Q (f), Q (g)]=iQ ({f, g}) for arbitrary f provided g has the form Xipi, where Xi is an affine vector field.
42 citations
27 citations
TL;DR: In this article, the authors extend the theory of identifiability of linear dynamic models with autocorrelated errors to the case of cross-equation restrictions, and consider global identificability and local identificaiton for affine and continuously differentiable crossequation constraints.
26 citations
TL;DR: In this paper, the authors used the generating function notion to give a representation of the inhomogeneous symplectic group as group of affine canonical transformations, and the classical action for linear mechanical systems, the Hamiltonians of which belong to the algebrah sp(2n,R), is deduced; the Maslov index is explicitly constructed for the quantum corresponding sets of Hamiltonians considered in the classical case.
Abstract: The generating function notion is used to give a representation of the inhomogeneous symplectic group as group of affine canonical transformations. Then the classical action for linear mechanical systems, the Hamiltonians of which belong to the algebrah sp(2n,R), is deduced; it is explicitely constructed for all the Hamiltonians belonging to some particular subalgebras ofh sp(2n,R). The metaplectic representation ofW Sp(2n,R) onL2(R) and the solutions of the Schrodinger equation for linear systems are also obtained in terms of generating functions. The Maslov index is explicitly constructed for the quantum corresponding sets of Hamiltonians considered in the classical case.
TL;DR: In this article, the Palatini method of variation is compared with the Hilbert method for symmetric metrics and affine connections, and it is found that the two methods are in general inequivalent.
Abstract: The Palatini method of variation is compared with the Hilbert method for symmetric metrics and affine connections. It is found that the two methods are in general inequivalent. The Hilbert method is recommended as being more general.
01 Jan 1978
TL;DR: This article showed that only the Dynamically - Restricted Anholonomized General Coordinate Transformation Group reproduces Einstein's theory of Gravitation directly when gauged, which amounts to a Modified Poincare group where translations are replaced by parallel transport.
Abstract: We prove that only the Dynamically - Restricted Anholonomized General Coordinate Transformation Group reproduces Einstein's theory of Gravitation directly when gauged This amounts to a Modified Poincare group where translations are replaced by Parallel transport We also explain the role of GL(4R) and explore the Modified Affine Group Using the Ogievetsky theorem, we present several No-Go theorems restricting the joint application of Conformal and Affine Symmetries
01 Jan 1978
TL;DR: In this article, the state space of finite-dimensional, discrete-time, internally biaffine systems is constructed via Nerode equivalance relations, and an algorithm which amounts to choosing a frame for the affine space is presented.
Abstract: New results on the realization of finite-dimensional, discrete-time, internally biaffine systems are presented in this paper. The external behavior of such systems is described by multiaffine functions and the state space is constructed via Nerode equivalance relations. We prove that the state space is an affine space. An algorithm which amounts to choosing a frame for the affine space is presented. Our algorithm reduces in the linear and bilinear case to a generalization of algorithms existing in the literature. Explicit existence criteria for span-canonical realizations as well as an affine isomorphism theorem are given.
Journal Article•
TL;DR: In this article, the existence of bivalued linear representations of the Group of General Coordinate Transformations (G. G. T. ) was shown for n = 2, 3, 4.
Abstract: 2014 We demonstrate the existence of bivalued linear (infinite) spinorial representations of the Group of General Coordinate Transformations. We discuss the topology of the G. G. C. T. and its subgroups GA(nR), GL(n, R), SL(nR) for n = 2, 3, 4, and the existence of a double covering. We demonstrate the construction of the half-integer spin representations in terms of Harish-Chandra modules. We give D. W. Joseph’s explicit matrices for = -, c = 0 in SL(3R), which will act as little group in GA(4R). 2
TL;DR: In this article, the authors consider the problem of steering a point in Rn to an affine target set with the autonomous control system x = Ax + Bu, and derive geometric properties of subspace cores and apply these to the controllability problem.
Journal Article•
TL;DR: In this article, necessary and sufficient conditions for the existence of metric in two-dimensional affine manifolds are found, where Rβγδδτ and Rβδ are respectively the Riemann tensor and Ricci tensor of the manifold.
TL;DR: In this article, the authors present a precise definition of the limiting processes involved and prove analytically that the clock readings coincide with an affine parameter of the Weyl connection.
Abstract: In a Weyl space it is possible to construct geometrical clocks along timelike geodesics using projective and conformal techniques. We present a precise definition of the limiting processes involved and prove analytically that the clock readings coincide with an affine parameter of the Weyl connection.
TL;DR: In this paper, it was shown that a Desarguesian affine Hjelmslev plane is ordered if and only if its A.H. ring is ordered.
Abstract: A Desarguesian affine Hjelmslev plane (D.A.H. plane) may be coordinatized by an affine Hjelmslev ring (A.H. ring), which is a local ring whose radical is equal to the set of two-sided zero divisors and whose principal right ideals are totally ordered (cf. [3]). In his paper on ordered geometries [4], P. Scherk discussed the equivalence of an ordering of a Desarguesian affine plane with an ordering of its coordinatizing division ring. We shall define an ordered D.A.H. plane and follow Scherk's methods to extend his results to D.A.H. planes and their A.H. rings i.e., we shall show that a D.A.H. plane is ordered if and only if its A.H. ring is ordered. We shall also give an example of an ordered A.H. ring. Finally, we shall discuss some infinitesimal aspects of the radical of an ordered A.H. ring.
01 Jan 1978
TL;DR: In this article, the authors present a two-part work on structured sequential decision processes with affine structure, which allows the decision-maker to restrict attention to (invariant) policies that select the same decision for all states.
Abstract: This is a precis of the authors' two-part work [2,3] on structured sequential decision processes having (affine) structure, which lets the decision-maker restrict attention to (invariant) policies that select the same decision for all states. When the planning horizon is n epochs, a sequence of n invariant policies is optimal. When the planning horizon is infinite, a stationary invariant policy is optimal, providing the affine structure is supplemented in either of two ways. Two examples are included for illustration.
TL;DR: In this article, it was shown that an ergodic affine transformation of a compact abelian group is loosely Bernoulli, that is, it can be induced from a Beroulli shift.
Abstract: We prove that an ergodic affine transformation of a compact abelian group is loosely Bernoulli, that is, it can be induced from a Bernoulli shift.
TL;DR: Some distribution-free tests for affine symmetry of a continuous bivariate distribution are proposed and studied in this article, where rank order tests and tests of the Kolmogorov-Smirnov and Cramer-von Mises type (based on the empirical distribution) are considered.
Abstract: Some distribution-free tests for affine symmetry of a continuous bivariate distribution are proposed and studied here. Both rank order tests and tests of the Kolmogorov-Smirnov and Cramer-von Mises type (based on the empirical distribution) are considered and their asymptotic relative efficiency results are studied.