A probabilistic artificial neural network is presented. It is of a one-layer, feedback-coupled type with graded units. The learning rule is derived from Bayes's rule. Learning is regarded as collecting statistics ...
A probabilistic artificial neural network is presented. It is of a one-layer, feedback-coupled type with graded units. The learning rule is derived from Bayes's rule. Learning is regarded as collecting statistics and recall as a statistical inference process. Units correspond to events and connections come out as compatibility coefficients in a logarithmic combination rule. The input to a unit via connections from other active units affects the a posteriori belief in the event in question. The new model is compared to an earlier binary model with respect to storage capacity, noise tolerance, etc. in a content addressable memory (CAM) task. The new model is a real time network and some results on the reaction time for associative recall are given. The scaling of learning and relaxation operations is considered together with issues related to representation of information in one-layer artificial neural networks. An extension with complex units is discussed.
The cylindrical algebraic decomposition method decomposes E r into regions over which a given polynomial has constant sign by extension of one complicated decomposition of E r-1 . We investigate a method which decompo...
The cylindrical algebraic decomposition method decomposes E r into regions over which a given polynomial has constant sign by extension of one complicated decomposition of E r-1 . We investigate a method which decomposes E r into sign-invariant region by combining several but simpler decompositions of E r-1 . We can obtain a sign-invariaat decomposition of E 2 defined by a bivariate polynomial of total degree n and coefficient size d in time O(n 12 (d + log n) 2 log n) . Preliminary experiments suggest that the method is useful in practice.
The edge focusing method produces a series of edge images ranging from coarser to finer scale resolution. The displacements of these extracted edges in this series are discussed. A three-step method of labelling the e...
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The edge focusing method produces a series of edge images ranging from coarser to finer scale resolution. The displacements of these extracted edges in this series are discussed. A three-step method of labelling the extracted edges as coming from objects or as coming from shadows and other illumination phenomena using this series is tried. More precisely, we show that it seems possible to label edges into the categories ‘diffuse’ and ‘non-diffuse’ from a binary multi-scale representation, i.e. without using the image intensities directly.
A method is developed for the measurement of short-range visual motion in image sequences, making use of the motion of image features such as edges and points. Each feature generates a Gaussian activation profile in a...
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A method is developed for the measurement of short-range visual motion in image sequences, making use of the motion of image features such as edges and points. Each feature generates a Gaussian activation profile in a spatiotemporal neighborhood of specified scale around the feature itself; this profile is then convected with motion of the feature. The authors show that image velocity estimates can be obtained from such dynamic activation profiles using a modification of familiar gradient techniques. The resulting estimators can be formulated in terms of simple ratios of spatiotemporal filters (i.e. receptive fields) convolved with image feature maps. A family of activation profiles of varying scale must be utilized to cover a range of possible image velocities. They suggest a characteristic speed normalization of the estimate obtained from each filter in order to decide which estimate is to be accepted. They formulate the velocity estimators for dynamic edges in 1-D and 2-D image sequences, as well as that for dynamic feature points in 2-D image sequences.< >
We consider Lipschitz-continuous nonlinear maps in finite-dimensional Banach and Hilbert spaces. Boundedness and monotonicity of the operator are characterized quantitatively in terms of certain functionals. These fun...
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We consider Lipschitz-continuous nonlinear maps in finite-dimensional Banach and Hilbert spaces. Boundedness and monotonicity of the operator are characterized quantitatively in terms of certain functionals. These functionals are used to assess qualitative properties such as invertibility, and also enable a generalization of some well-known matrix results directly to nonlinear operators. Closely related to the numerical range of a matrix, the Gerschgorin domain is introduced for nonlinear operators. This point set in the complex plane is always convex and contains the spectrum of the operator's Jacobian matrices. Finally, we focus on nonlinear operators in Hilbert space and hint at some generalizations of the von Neumann spectral theory.
In this paper the relations between semi-infinite programs and optimisation problems with finitely many variables and constraints are reviewed. Two classes of convex semi-infinite programs are defined, one based on th...
In this paper the relations between semi-infinite programs and optimisation problems with finitely many variables and constraints are reviewed. Two classes of convex semi-infinite programs are defined, one based on the fact that a convex set may be represented as the intersection of closed halfspaces, while the other class is defined using the representation of the elements of a convex set as convex combinations of points and directions. Extension to nonconvex problems is given. A common technique of solving a semi-infinite program computationally is to derive necessary conditions for optimality in the form of a nonlinear system of equations with finitely many equations and unknowns. In the three-phase algorithm, this system is constructed from the optimal solution of a discretised version of the given semi-infinite program. i.e. a problem with finitely many variables and constraints. The system is solved numerically, often by means of some linearisation method. One option is to use a direct analog of the familiar SOLVER method.
Computer graphics and computer vision deal with converse problems. In graphics the goal is to synthesize the image(s) of a scene from a given description in terms of a model or some observed data. In vision, on the ot...
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Computer graphics and computer vision deal with converse problems. In graphics the goal is to synthesize the image(s) of a scene from a given description in terms of a model or some observed data. In vision, on the other hand, the aim is to create a description of the world (the scene), given the image(s). Due to this difference of the goals the two fields have developed separately. Nevertheless, they often deal with aspects of the same physical reality. Therefore, many fundamental concepts and problems are shared by the two areas, even though the context may differ. In this paper we discuss some of the issues which unify and discriminate the fields. The purpose is not to present a self-contained presentation of the relevant notions and techniques. We refer to the existing literature for such details. Instead we try to elucidate aspects in which the two fields may benefit from each other and aspects in which this may be difficult.
We consider the general class of power series where the terms may be expressed as the Laplace transforms of known functions. The sum of the series can then be evaluated efficiently and accurately by means of quadratur...
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We consider the general class of power series where the terms may be expressed as the Laplace transforms of known functions. The sum of the series can then be evaluated efficiently and accurately by means of quadrature schemes, recently published by Frank Stenger. The method works also far outside the region of convergence as will be illustrated by numerical examples.
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