Showing papers on "Bicubic interpolation published in 1983"
TL;DR: In this paper, the authors compared the performance of linear and cubic B-spline interpolation, linear interpolation and high-resolution cubic spline with edge enhancement with respect to the initial coordinate system.
Abstract: When resampling an image to a new set of coordinates (for example, when rotating an image), there is often a noticeable loss in image quality. To preserve image quality, the interpolating function used for the resampling should be an ideal low-pass filter. To determine which limited extent convolving functions would provide the best interpolation, five functions were compared: A) nearest neighbor, B) linear, C) cubic B-spline, D) high-resolution cubic spline with edge enhancement (a = -1), and E) high-resolution cubic spline (a = -0.5). The functions which extend over four picture elements (C, D, E) were shown to have a better frequency response than those which extend over one (A) or two (B) pixels. The nearest neighbor function shifted the image up to one-half a pixel. Linear and cubic B-spline interpolation tended to smooth the image. The best response was obtained with the high-resolution cubic spline functions. The location of the resampled points with respect to the initial coordinate system has a dramatic effect on the response of the sampled interpolating function?the data are exactly reproduced when the points are aligned, and the response has the most smoothing when the resampled points are equidistant from the original coordinate points. Thus, at the expense of some increase in computing time, image quality can be improved by resampled using the high-resolution cubic spline function as compared to the nearest neighbor, linear, or cubic B-spline functions.
844 citations
01 Jan 1983
TL;DR: Two forms of spatial interpolation, the interpolation of point and areal data, are distinguished in this article, where point interpolation is applied to isarithmic, that is, contour mapping and the areal int
Abstract: Two forms of spatial interpolation, the interpolation of point and areal data, are distinguished Traditionally, point interpolation is applied to isarithmic, that is, contour mapping and areal int
816 citations
TL;DR: In this article, it was shown that interpolation at the midpoint of a data record yields the minimum interpolation error for an autoregressive process and infinite length interpolators are simply derived.
Abstract: Using a well-known form for the inverse of a symmetric Toeplitz matrix, some results in linear interpolation theory are derived. For an autoregressive process it is shown that interpolation at the mid-point of a data record yields the minimum interpolation error. Also, some results for infinite length interpolators are simply derived.
56 citations
TL;DR: This paper describes a method for moving datapoints in a curve net to new ‘smoother’ positions and different techniques to analyse the result of the smoothing are discussed.
Abstract: Bicubic parametric surfaces are often used to represent complex shapes in systems for computer-aided design and manufacture. Such as surface can be defined by a topologically rectangular mesh of cubic parametric splines, a curve which is an approximate mathematical model of the linear elastic beam. Smoothing a bicubic parametric surface can be done by smoothing the curve net that defines it. This paper describes a method for moving datapoints in a curve net to new ‘smoother’ positions. Different techniques to analyse the result of the smoothing are also discussed.
47 citations
TL;DR: This technique for smooth surface interpolation over grid data reduces the number of extraneous local optima and inflection points of the surface.
Abstract: Compared with other methods, this technique for smooth surface interpolation over grid data reduces the number of extraneous local optima and inflection points of the surface.
39 citations
TL;DR: In this article, the authors studied the duality of Banach pairs (A0, A1) for which all interpolation is described by Peetre's K- method of interpolation.
Abstract: In this paper we study those Banach pairs (A0, A1) for which all interpolation is described by Peetre's K- method of interpolation. Special emphasis is given to duality and to the case when (A0, A1) is a pair of K-spaces.
25 citations
20 citations
TL;DR: In this paper, a method to construct convex cubic C1-splines which interpolate a given convex data set is presented, which is reduced to the solution of a system of linear inequalities.
18 citations
TL;DR: The authors present a modified bicubic spline interpolation function, which gives better forward projections at all angles than the simpler nearest neighbour and bilinear interpolation schemes.
Abstract: Describes a simple formulation for computing forward projections directly from 3D data that is independent of any special geometries. Two-dimensional interpolation functions are used to weight the contribution of voxels in the 3D reconstruction to pixels in the 2D projection. The authors present a modified bicubic spline interpolation function, which gives better forward projections at all angles than the simpler nearest neighbour and bilinear interpolation schemes. In the authors' application, electron microscopy, a 3D image of a macromolecule or macromolecular complex can be reconstructed from a set of 2D projected images of different, individual macromolecules lying in different orientations with respect to one another. In particular, the 3D orientation of an individual nucleoprotein complex with respect to a set of reference axes can be determined by selective imaging of the nucleic acid component.
15 citations
TL;DR: The program will either produce the rational interpolation of the data (xj,fj),j=0,...,L+M by a (generalized) continued fraction or state that the interpolation is not feasible because there are unattainable points.
Abstract: This note contains a program for rational interpolation with degree of numerator equal toL and of denominator equal toM (forL≥M). The program will either produce the rational interpolation of the data (x
j,f
j),j=0,...,L+M by a (generalized) continued fraction or state that the interpolation is not feasible because there are unattainable points. We use the algorithm given in [2] and incorporate the reordering of data for numerical stabilisation due to Graves-Morris [1]. The reordering may be suppressed. The performance of the program is illustrated by several examples.
13 citations
01 Apr 1983
TL;DR: A two-dimensional extension of earlier work in one dimension of image interpolators is presented and may be compared with the more common ones, such as nearest-neighbor, bilinear and cubic convolution.
Abstract: Interpolation methods in image processing are necessary in various applications. In this work the problem of image interpolation is approached from the viewpoint of digital signal processing. This paper presents a two-dimensional extension of earlier work in one dimension. A class of image interpolators is thus obtained and may be compared with the more common ones, such as nearest-neighbor, bilinear and cubic convolution.
TL;DR: In this article, it was shown that the sum of the squares of the Lagrangian splines in cubic periodic spline interpolation with period N on the grid Z is bounded by one.
TL;DR: In this paper, it was shown that higher order cardinal splines can be written as convolutions of lower order ones, using a new notion of convolution due to Jones (1982).
Abstract: Duchon (1978) considered interpolation in ℝn by “Dm-splines”, which are interpolating functions having, in a sense, minimum energy. The purpose of this paper is to consider the analogous interpolation at the lattice of points in ℝn with integer co-ordinates, generalising aspects of Schoenberg's (1973) theory of cardinal spline interpolation. Following Schoenberg, we prove that higher order “basic” splines can be written as convolutions of lower order ones, using a new notion of convolution due to Jones (1982).