Showing papers on "Kernel (image processing) published in 1982"
01 Dec 1982-Graphical Models \/graphical Models and Image Processing \/computer Vision, Graphics, and Image Processing
TL;DR: A parametric implementation of cubic convolution image reconstruction is presented which is generally superior to the standard algorithm and which can be optimized to the frequency content of the image.
Abstract: Cubic convolution, which has been discussed by Rifman and McKinnon (1974), was originally developed for the reconstruction of Landsat digital images. In the present investigation, the reconstruction properties of the one-parameter family of cubic convolution interpolation functions are considered and thee image degradation associated with reasonable choices of this parameter is analyzed. With the aid of an analysis in the frequency domain it is demonstrated that in an image-independent sense there is an optimal value for this parameter. The optimal value is not the standard value commonly referenced in the literature. It is also demonstrated that in an image-dependent sense, cubic convolution can be adapted to any class of images characterized by a common energy spectrum.
349 citations
TL;DR: In this article, the Backus-Gilbert inverse theory was applied to the Wiener shaping filter for source wavelet deconvolution in exploration seismology, and the results provided novel insights into the performance.
Abstract: Seismic source wavelet deconvolution can be treated within the framework of the Backus‐Gilbert (BG) inverse theory. A time shift‐invariant version of this theory leads to the Wiener shaping filter, which has enjoyed widespread use for source wavelet deconvolution in exploration seismology. The model of the BG theory is the ground impulse response, the BG mapping kernel is the source wavelet, and the BG resolving kernel is the convolution between the source wavelet and the Wiener shaping filter. BG inversion involves the minimization of an optimality criterion under a set of constraints. The application of the BG “filter energy” or “noise output power” constraint to Wiener filter design leads to the familiar prewhitening parameter that stabilizes the filter on the one hand, but degrades resolution on the other. The BG “unimodular” constraint produces an unbiased estimate of the model, or ground impulse response. These constraints provide novel insights into the performance of deconvolution filters.
66 citations
TL;DR: The versatility of degenerate four-wave mixing has made possible its application to two major areas of spatial information processing: distortion correction and mathematical operations.
Abstract: The versatility of degenerate four-wave mixing (D4WM) has made possible its application to two major areas of spatial information processing: distortion correction and mathematical operations. The first area can be divided into predetection and postdetection processing. Distortions can be compensated for before the imaging. process by exploiting the phase-conjugating capability of D4WM. Phase-conjugate mirrors (PCM's) may also find use in optical processors designed to remove distortions after the imaging process is complete and the object is no longer available. Examples of linear operations that can be implemented using the nonlinear optics of D4WM are image convolution and correlation. An example of a nonlinear mathematical operation that can be implemented using D4WM is edge detection of two-dimensional images.
30 citations
01 Jan 1982
TL;DR: This paper contains a new method to solve Wiener-Hopf integral equations, which employs explicitly connections with linear systems based on a special exponential operator representation of the kernel of the integral equation whose Fourier transform is analytic on the real line and at infinity.
Abstract: This paper contains a new method to solve Wiener-Hopf integral equations, which employs explicitly connections with linear systems. These connections are based on a special exponential operator representation of the kernel of the integral equation whose Fourier transform is analytic on the real line and at infinity. With this approach explicit formulas for solutions, Fredholm characteristics, asymptotics etc. are derived. Analogous results are obtained for the inversion of Toeplitz matrices. The method does not use factorization, and it can also be applied to convolution equations on a finite interval. This application will be made in a forthcoming publication.
30 citations
Proceedings Article•
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01 Jan 1982
TL;DR: Quadratic filters are the simplest non linear time-invariant systems and correspond to the second term of the Volterra expansion and their kernel is a symmetric finite or infinite square matrix.
Abstract: Quadratic filters are the simplest non linear time-invariant systems and correspond to the second term of the Volterra expansion. Such filters are completely defined by their kernel which is a symmetric finite or infinite square matrix. Some examples are presented. The harmonic representation of such filters is discussed and also the calculation of the statistical properties of the output in the case of a Gaussian input. Finally some problems of implementation of such filters are discussed.
26 citations
TL;DR: In this article, various classes of two-dimensional finite impulse response (FIR) filters that can be implemented with such techniques are studied and design procedures are presented for each of the classes.
Abstract: Sequentially convolving images with small size operators is a promising idea for performing image filtering. Various classes of two-dimensional finite impulse response (FIR) filters that can be implemented with such techniques are studied. Design procedures are presented for each of the classes. They are based upon minimizing L2and L∞criteria. Results are assessed in an image processing context.
24 citations
TL;DR: In this article, the use of the An approximate method in solving the monokinetic neutron transport equation has been studied and it has been shown that the system of space second-order differential equations which constitute the method may be cast into a form perfectly equivalent to the PN model, for any geometry.
21 citations
TL;DR: In this paper, a generalization of the Wiener-Hopf method is obtained for convolution equations on the finite interval where is the convolution operator,, for, is the CNN operation, is a kernel belonging to, is operator of restriction of a generalized function to the interval, and.
Abstract: A generalization of the Wiener-Hopf method is obtained for convolution equations on the finite interval where is the convolution operator , , for , is the convolution operation, is a kernel belonging to , is the operator of restriction of a generalized function to the interval , and . Here and are the Schwartz spaces of rapidly decreasing test functions and generalized functions of slow growth on , respectively.Bibliography: 19 titles.
18 citations
16 citations
01 Jan 1982
TL;DR: The main objective of as mentioned in this paper is to focus attention on fast algorithms for the summation of lagged products, which are very common in physics and are usually related to the computation of digital filtering processes, convolutions, and correlations.
Abstract: The main objective of this chapter is to focus attention on fast algorithms for the summation of lagged products. Such problems are very common in physics and are usually related to the computation of digital filtering processes, convolutions, and correlations. Correlations differ from convolutions only by virtue of a simple inversion of one of the input sequences. Thus, although the developments in this chapter refer to convolutions, they apply equally well to correlations.
10 citations
TL;DR: A pipelined tree machine architecture composed of modular FPT, FFT, and Chinese Remainder Theorem computational units is developed to efficiently compute a 2-D cyclic convolution and the extension of this tree Machine architecture to efficiently computed a multidimensional cyclic Convolution is discussed.
Abstract: In this paper, a technique is proposed to decompose a two-dimensional (2-D) cyclic convolution of two d_{1} \times d_{2} arrays, where d_{2} = 2^{m} with m > 1 , into many identical and independent 2-D cyclic convolutions of smaller size. Using this technique and the fact that fast polynomial transform (FFT) exists when d_{1}=2^{m-r+1} for 1 \leq r \leq m , a pipelined tree machine architecture composed of modular FPT, FFT, and Chinese Remainder Theorem (CRT) computational units is then developed to efficiently compute a 2-D cyclic convolution. Finally, the extension of this tree machine architecture to efficiently compute a multidimensional cyclic convolution is discussed in this paper.
TL;DR: In this paper, the off-shell t matrix is expressed as a sum of one nonseparable and one separable terms, which is useful for applications to more than two body problems.
Abstract: The off-shell t matrix is expressed as a sum of one nonseparable and one separable terms so that it is useful for applications to more-than-two body problems. All poles are involved in this one separable term. Both the nonseparable and the separable terms of the kernel G/sub 0/t are regular at the origin. The nonseparable term of this kernel vanishes at large distances, while the separable term behaves asymptotically as the spherical Hankel function. These properties make our expression free from defects inherent in the Jost or the K-matrix expressions, and many applications are anticipated. As the application, a compact expression of the many-level formula is presented. Also the application is suggested to the breakup threebody problem based on the Faddeev equation. It is demonstrated that the breakup amplitude is expressed in a simple and physically interesting form and we can calculate it in coordinate space.
TL;DR: An optical processor design is proposed and its processing capacity is calculated and it is proposed that this 4D convolution can be performed coherent-optically by means of sequence convolution in the case of “variation bandlimited” point spread functions.
TL;DR: On the basis of Collins' diffraction in tegral theory, a diffraction integral formula for misaligned optical systems has been devived employing a kernel expressed in terms of augmented 4×4 transfer matrix elements as discussed by the authors.
Abstract: On the basis of Collins' diffraction in tegral theory, a diffraction integral formula for misaligned optical systems has been devived employing a kernel expressed in terms of augmented 4×4 transfer matrix elements.
Proceedings Article•
01 Jan 1982
DOI•
01 Jan 1982
TL;DR: This thesis describes an experiment in the design of a multiprocessor operating system based on the distribution of kernel functionality among the processors, named Distributed Verex, which is an extension of VereX which is a descendant of Thoth.
Abstract: The possibilities of increased responsiveness, throughput, availability, reliability and cost-effectiveness invite investigation of the hardware and software design of multiprocessor computing systems. This thesis describes an experiment in the design of a multiprocessor operating system based on the distribution of kernel functionality among the processors. One of the design objectives was to build a system capable of supporting real-time applications and a general-purpose, multi-user environment concurrently. The hardware base is a simple, closely-coupled, star network of autonomous computers constructed from "off-the-shelf" boards. The operating system developed, named Distributed Verex, is an extension of Verex which is a descendant of Thoth. The Verex kernel provides an environment of processes and inter-process communication via message-passing on a uniprocessor computer. Distributed Verex provides the same environment uniformly and transparently throughout the multiprocessor system. Distributed Verex has been implemented and is undergoing continuing development. Initial performance measurements are given.
TL;DR: In this paper, a linear Fredholm integral equation of the first kind with only approximately known and near-singular kernel is solved by approximation of the solution by a cubic spline function.
Abstract: Revelation of details which are hidden in a backscattering spectrum due to finite apparatus resolution demands the numerical solution of a linear Fredholm integral equation of the first kind with only approximately known and near-singular kernel. Unphysical oscillations of the solution are largely avoided by properly chosen smoothness conditions. Adequate algebraization of the problem is achieved by approximation of the solution by a cubic spline function. Reliability of the approach is studied by mathematical experiments with realistic kernels.
01 May 1982
TL;DR: The design of an image convolver suitable for the convolution of a (256 × 256) image with large filter impulse responses in under 1/30 of a second is described.
Abstract: This paper describes the design of an image convolver suitable for the convolution of a (256 × 256) image with large filter impulse responses in under 1/30 of a second. The memory architecture of the convolver is based on the structures associated with parallel and pipelined FFT/NTT processors that use ROM oriented implementation of the Residue Number System and a 2 D radix-r Ordered-input, Ordered-output FFT algorithm. The 2 D convolution operation is performed by the use of overlap-save technique of sectioned convolutions.
01 Oct 1982
TL;DR: YALE as mentioned in this paper is a layout editor which runs on SUN workstations, and deals with cells expressed in the SILT language, providing graphical hooks into many features describable in SILT.
Abstract: YALE is a layout editor which runs on SUN workstations, and deals with cells expressed in the SILT language. It provides graphical hooks into many features describable in SILT. YALE runs under the V kernel, and makes use of a window manager than provides a multiple viewpoint capability.
TL;DR: In this paper, the Hilbert boundary value problem corresponding to a convolution equation on a finite interval, with kernel belonging to a class singled out earlier by the author, is reduced to a system of integral equations.
Abstract: The Hilbert boundary value problem corresponding to a convolution equation on a finite interval, with kernel belonging to a class singled out earlier by the author, is reduced to a system of integral equations. The solvability of this system in appropriate weighted spaces is studied and an algorithm for constructing a canonical matrix of solutions of the Hilbert problem from certain solutions of the system. Estimates of partial indices are given. Bibliography: 15 titles.
01 Jan 1982
TL;DR: In the point kernel technique, the fundamental assumption is made that nuclear reactors and other extended sources of radiation can be regarded as consisting of differential isotropic point sources and that the effect of the radiation from the whole source, at the point of interest, can be obtained by the summation of the contributions from individual differential sources that comprise the entire source region as mentioned in this paper.
Abstract: In the point kernel technique, the fundamental assumption is made that nuclear reactors, and other extended sources of radiation, can be regarded as consisting of differential isotropic point sources and that the effect of the radiation from the whole source, at the point of interest, can be obtained by the summation of the contributions from the individual differential sources that comprise the entire source region. The effect of the radiation at a particular point is usually identified with the response of an idealized detector situated there. There are two different approaches for solving the spatial integration problem. The analytic approach can be achieved at the cost of considerable simplification of the actual source-shield configuration. The great merit of this approach is that it produces formulae for basic source-shield configurations, which provide the quickest means of obtaining approximate answers to many practical shielding problems. The direct numerical integration approach implemented on a computer by means of computer programs is often of fairly sophisticated form. The advantage of this approach is that there is no longer the necessity to contrive the kernel to have special mathematical properties that are conducive to an analytical solution.
01 Oct 1982
TL;DR: A coherent numerical approach to solve the problems of the solution of a two-dimensional singular integral equation of electric type and to calculate the current distribution in microstrip antennas of arbitrary shape is presented.
Abstract: The accurate determination of surface currents in microstrip planar antennas requires the solution of a two-dimensional singular integral equation of electric type (EFIE). The first problem encountered when solving this equation numerically, is the obtention of a fast and accurate algorithm for evaluating its kernel. This kernel is given by a combination of Sommerfeld-like integrals where the surface wave phenomena are automatically included, and standard computer integration routines are unable to evaluate it. A second problem is the implementation of an efficient moment method. This task is very delicate because the kernel is singular. In particular, the self (diagonal) terms of the moment matrix must be carefully evaluated. Also, the modelling of the coaxial feed probe offers considerable difficulties which have been overcame by using Richmond's reaction method. This paper presents a coherent numerical approach to solve these problems and to calculate the current distribution in microstrip antennas of arbitrary shape.
TL;DR: The two-dimensional case is examined in greatest detail to demonstrate these performance advantages over the telephotographic procedures operating on a direct pixel-by-pixel basis.
01 May 1982
TL;DR: This work describes a multifactor algorithm for two-dimensional, noncyclic, convolution of two finite sequences that occurs in such applications as image enhancement and in the processing of data from radar and sonar arrays.
Abstract: This work describes a multifactor algorithm for two-dimensional, noncyclic, convolution of two finite sequences. This type of processing occurs in such applications as image enhancement and in the processing of data from radar and sonar arrays.