Showing papers on "Bicubic interpolation published in 1981"
TL;DR: It can be shown that the order of accuracy of the cubic convolution method is between that of linear interpolation and that of cubic splines.
Abstract: Cubic convolution interpolation is a new technique for resampling discrete data. It has a number of desirable features which make it useful for image processing. The technique can be performed efficiently on a digital computer. The cubic convolution interpolation function converges uniformly to the function being interpolated as the sampling increment approaches zero. With the appropriate boundary conditions and constraints on the interpolation kernel, it can be shown that the order of accuracy of the cubic convolution method is between that of linear interpolation and that of cubic splines. A one-dimensional interpolation function is derived in this paper. A separable extension of this algorithm to two dimensions is applied to image data.
3,280 citations
TL;DR: Generation and recursion formulas for these interpolation functions necessary for direct evaluation of a signal's derivatives, integrals, and fractional derivatives directly from the sample values are presented.
Abstract: The Whittaker-Shannon cardinal series dictates that any L 2 bandlimited signal is defined everywhere by its (sufficiently closely spaced) sample values. This paper derives those interpolation functions necessary for direct evaluation of such a signal's derivatives, integrals, and fractional derivatives directly from the sample values. Generation and recursion formulas for these interpolation functions are presented.
88 citations
TL;DR: The application of the method of three-point bilinear interpolation is shown to generate a smoothly interpolated image, free from erroneous substructure generated by the interpolation scheme itself.
75 citations
01 Jan 1981
TL;DR: In this article, a new ordering scheme for the Hermite bicubic collocation equations is presented, where the unknowns and equations of the collocation equation are usually numbered so as to give a coefficient matrix of the linear system which is somewhat bi-diagonal.
Abstract: Publisher Summary This chapter explains a new ordering scheme for the Hermite bicubic collocation equations. A Hermite cubic is a C1 piecewise cubic polynomial and a Hermite bicubic is the tensor product of Hermite cubics in x and in y. The unknowns and equations of the collocation equation are usually numbered so as to give a coefficient matrix of the linear system which is somewhat bi-diagonal. The chapter presents the pattern of nonzero elements with n = 3 and a Poisson problem with Dirichlet boundary conditions. The pattern illustrated in the chapter is not the expected somewhat tridiagonal pattern of nonzeros and, potentially more serious, any of the standard iteration methods cannot be used on the equations because of the large number of zero elements on the diagonal. Thus, it leads to search for a new ordering that has nonzeros on the diagonals and which is more natural. Such an ordering is called collorder.
19 citations
TL;DR: Bicubic splines with variable knots are employed in an attempt to answer the question as to what extent images are finitely representable in the context of digital sensors and computers.
Abstract: This paper presents a degree of freedom or information content analysis of images in the context of digital image processing. As such it represents an attempt to quantify the number of truly independent samples one gathers with imaging devices. The degrees of freedom of a sampled image itself are developed as an approximation problem. Here, bicubic splines with variable knots are employed in an attempt to answer the question as to what extent images are finitely representable in the context of digital sensors and computers. Relatively simple algorithms for good knot placement are given and result in spline approximations that achieve significant parameter reductions at acceptable error levels. The knots themselves are shown to be useful as an indicator of image activity and have potential as an image segmentation device, as well as easy implementation in CCD signal processing and focal plane smart sensor arrays. Both mathematical and experimental results are presented.
19 citations
16 citations
10 citations
8 citations
TL;DR: In this article, the authors consider interpolation by piecewise polynomials, where the interpolation conditions are on certain derivatives of the function at certain points, specified by a finite incidence matrix E.
Abstract: We consider interpolation by piecewise polynomials, where the interpolation conditions are on certain derivatives of the function at certain points, specified by a finite incidence matrix E . Similarly the allowable discontinuities of the piecewise polynomials are specified by a finite incidence matrix F . We first find necessary conditions on ( E , F ) for the problem to be poised, that is to have a unique solution for any given data. The main result gives sufficient conditions on ( E , F ) for the problem to be poised, generalising a well-known result of Atkinson and Sharma. To this end we prove some results involving estimates of the numbers of zeros of the relevant piecewise polynomials.
7 citations
Patent•
10 Aug 1981
TL;DR: In this article, a means of interpolating scanning lines by a cubic convolution method, a bilinear method of a nearest neighbor method and the calculations for interpolation are performed with logic circuits according to the quality of respective images, whereby the effective interpolation method can be selected freely.
Abstract: PURPOSE:To select an adequate interpolation method according to an image and to permit satisfactory photoengraving of a video image by making selection of any cubic convolution method possible, a bilinear method and a nearest neighbor method according to the contents of the images. CONSTITUTION:Means of interpolating scanning lines by a cubic convolution method, a bilinear method of a nearest neighbor method are provided and the calculations for interpolation are performed with logic circuits according to the quality of respective images, whereby the effective interpolation method can be selected freely. Any of ROMs 16a-16d is selected by switching an address selecting circuit 14 with a switch 13 for selecting interpolation methods. The ROMs 16a-16d are segmented to the kinds of the interpolation methods, the positions of interpolation ranges and the interpolation positions within the respective interpolation ranges, and are further discriminated to four regions including ''through''.
TL;DR: This paper describes a new interpolation method for surfaces with tension, which are completely defined without specifying tangent-and twist-vectors, which produces fair surfaces and is fast and simple from a computational point of view.
TL;DR: In this paper, the effects of the differences in the effective cross sections given by the various interpolation methods on nuclear characteristics of fast reactors are calculated by using the JAERI-Fast Set Version II.
Abstract: Accuracies of various interpolation methods used for the “table look-up” method of resonance shielding factors are studied. The cubic spline interpolation is shown to produce the most excellent and stable accuracies with short computing time. The effects of the differences in the effective cross sections given by the various interpolation methods on nuclear characteristics of fast reactors are calculated by using the JAERI-Fast Set Version II. The maximum deviations of the effects are summarized as follows: 0.2% for the effective multiplication factor, 1.5% for the control rod reactivity worth, 6% for Doppler effect, 2.5% for the reaction rate distribution in the blanket region and negligible small for the sodium void effect, respectively, in typical fast reactor.
30 Jun 1981
TL;DR: The TIBRO code as discussed by the authors has been modified extensively to improve the interpolation methods used and to allow use of vector potential fields in the simulation of charged particle orbits on a 3D domain.
Abstract: The single particle orbit code, TIBRO, has been modified extensively to improve the interpolation methods used and to allow use of vector potential fields in the simulation of charged particle orbits on a 3D domain. A 3D cubic B-spline algorithm is used to generate spline coefficients used in the interpolation. Smooth and accurate field representations are obtained. When vector potential fields are used, the 3D cubic spline interpolation formula analytically generates the magnetic field used to push the particles. This field has del.BETA = 0 to computer roundoff. When magnetic induction is used the interpolation allows del.BETA does not equal 0, which can lead to significant nonphysical results. Presently the code assumes quadrupole symmetry, but this is not an essential feature of the code and could be easily removed for other applications. Many details pertaining to this code are given on microfiche accompanying this report.
TL;DR: Four interpolation schemes using small sample sets are considered for real-time D/A conversion applications based on a mean-square-error criterion, and hardware suitability is considered with respect to the number of operations per interpolation and degree of parallelism.
Abstract: Four interpolation schemes using small sample sets are considered for real-time D/A conversion applications. Evaluation, for sampling rates near the Nyquist limit, is based on a mean-square-error criterion. Hardware suitability is considered with respect to the number of operations per interpolation and degree of parallelism.
01 Jan 1981
TL;DR: A derivation of quarter-plane filtering algorithms which obtain smoothed estimates of function values and their derivatives by fitting two-dimensional smoothing splines in a recursive manner is presented.
Abstract: In the past, smoothing splines originated from approximation theory have been successfully applied to data filtering and image smoothing problems. Even though the nonrecursive technique of smoothing splines provides an optimal solution, the amount of computation increases rapidly with the size of the two-dimensional data. Here, we present a derivation of quarter-plane filtering algorithms which obtain smoothed estimates of function values and their derivatives by fitting two-dimensional smoothing splines in a recursive manner. The derivation procedure will highlight specific problems encountered in two-dimensional filtering problem. Also, the amount of computation for this recursive processor increases only linearly with the size of the two-dimensional data. Due to some approximations introduced in its derivation, this recursive processor becomes suboptimal.
TL;DR: In this paper, spectral properties of linear least-squares interpolation are discussed with main emphasis on its linear least squares version, which is shown to be a close approximation to the interpolation with a low-pass filtering effect.
TL;DR: A pre-compensative interpolation coding method is proposed such that given the interpolation method at the receiving end, the transmission point values at the sending end are determined so that the sum of the squared error between the transmitted points and interpolated points is minimized.
Abstract: In the interpolative coding method, the pixels constituting the image are divided into “transmitted points” and “interpolated points,” and the former only are transmitted to the receiving end from the sending end. The latter are reconstructed by interpolation at the receiving end. Commonly, the original image values have been used for the transmitted point values as they are, or, the original image values have been properly lowpass filtered for the transmitted point values. However, judging from the entire image transmission system, the problem of how to determine the transmission point values at the sending end is closely related to the interpolation method at the receiving end.
In this paper, we propose a pre-compensative interpolation coding method such that given the interpolation method at the receiving end, the transmission point values at the sending end are determined so that the sum of the squared error between the transmitted points and interpolated points is minimized. We introduce two kinds of pre-compensative interpolation coding methods for the case where the interpolation at the receiving end is linear, that is, a locally pre-compensative interpolation coding method and a globally pre-compensative interpolation coding method. According to a simulation using a standard image, the following effects have been recognized: the improvement of the SN ratio in comparison with existing simple linear interpolation which uses the original image values as the transmitted point values, and the decrease of the image quality degradation which seems to be caused by noise.