Showing papers on "Bicubic interpolation published in 1990"

Direction finding using an interpolated array

Abstract: A direction-finding technique is developed which uses the outputs of a virtual array computed from the real array using a linear interpolation procedure. The geometry of the virtual array is under the control of the designer. Using a linear virtual array, an extension of the root-MUSIC algorithm to arbitrary array geometries is developed. >

Digital image interpolator with multiple interpolation algorithms

Abstract: An interpolator for enlarging or reducing a digital image includes an interpolation coefficient memory containing interpolation coefficients representing several different one dimensional interpolation kernels. A row interpolator receives image pixel values, retrieves interpolation coefficients from the memory, and produces interpolated pixel values by interpolating in a row direction. A column interpolator receives multiple rows of interpolated pixel values from the row interpolator, retrieves interpolation coefficients from the memory, and produces rows of interpolated pixel values by interpolating in a column direction. A logic and control unit monitors the content of the input data and switches between interpolation kernels to provide optimum interpolation for each type of content.

Smooth mesh interpolation with cubic patches

Abstract: An algorithm for the local interpolation of a mesh of cubic curves with 3- and 4-sided facets by a piecewise cubic C 1 surface is stated and illustrated by an implementation. Precise necessary and sufficient conditions for oriented tangent-plane continuity between adjacent patches are derived, and the explicit constructions are characterized by the degree of the three scalar weight functions that relate the versal to the two transversal derivatives. The algorithm fully exploits the possibility of reparametrization by choosing all three weight functions nonconstant and not just degree-raising polynomials. The construction is local and consists mainly of averaging. The only systems to be solved are linear and of size 2 × 2. The algorithm guarantees interpolating surfaces without cusps and has a simple, implemented extension to n -sided facets.

Improvement on dynamic elastic interpolation technique for reconstructing 3-D objects from serial cross sections (biomedical application)

Abstract: An improved method for automatically reconstructing a three-dimensional object from serial cross sections is presented. The method improves the dynamic elastic contour interpolation technique. There are two major improvements: (1) in the case of branching that involves concave contours, instead of pairwise interpolation between the start contour and each goal contour, the goal image is considered globally and local constraints are imposed on the forces exerting upon the vertices; and (2) it takes the continuity of high-order derivatives into consideration and incorporates the schemes of spline theory, quadratic-variation-based surface interpolation, and finite-element-based multilevel surface interpolation to create smoother surfaces of the reconstructed object. Based on the output from the preliminary processing, two alternatives, a quadratic-variation-based surface interpolation algorithm and a finite-element-based multilevel surface interpolation algorithm, can be adopted to obtain the final surface representation. >

Analysis and Synthesis of Tones by Spectral Interpolation

Abstract: A technique is presented for the analysis and digital resynthesis of instrumental sounds. The technique is based on a model that uses interpolation of amplitude spectra to reproduce short-time spectral variations. The main focus of this work is the analysis algorithm. Starting from a digital recording the authors were able to compute automatically the parameters of this model. Two analysis/synthesis methods are studied based on spectral interpolation. The first uses only spectral interpolation. The second method is a hybrid in which a sampled attack is spliced onto a sustain synthesized via spectral interpolation

Adaptive rational splines

Abstract: The classical interpolation problems for cubic and rational splines are merged to get an “adaptive” rational interpolating spline which automatically uses cubic pieces to model unavoidable inflection points and retain convexity/concavity elsewhere. An existence proof, a numerical method, and a series of examples are presented. Furthermore, the two-dimensional case is discussed.

A Family of Highly Accurate Interpolation Functions for Magnitude-Mode Fourier Transform Spectroscopy

Abstract: A new family of highly efficient interpolating functions, the KCe functions, KCe(ω) = (aω2 + b ω + c)e, where e is the exponent, is developed for three-point frequency interpolation of discrete, magnitude-mode, apodized Fourier transform spectra. The family is characterized by high interpolation accuracy and ease of implementation. Various members of the family can be generated by varying the exponent. Prior work from this laboratory indicated that the parabola is the interpolating function of choice for interpolation of discrete, apodized magnitude spectra. We show here that, compared to parabolic interpolation, KCe interpolation typically gives residual systematic errors which are lower by between one and two orders of magnitude. These systematic errors are analytically derived and the efficacy of interpolation is rigorously examined as a function of the KCe exponent, the number of zero-fillings, the amount of damping in the transient, and the window function used to apodize the spectrum. For Hanning-apodized spectra, the KC5.5 function gives the lowest residual systematic errors, which are typically 15 times less than those remaining after parabolic interpolation. Similarly, the KC6.6 function is optimal for Hamming-apodized spectra (22 times better than parabolic interpolation) and the KC9.5 function is optimal for Blackman-Harris-apodized spectra (80 times better than parabolic interpolation). By extrapolation from other optimal KCe functions, we estimate that the optimal KCe function for interpolation of Kaiser-Bessel-apodized spectra is KC12.5. Analytical formulae for propagation of random errors in spectral intensity into random errors in interpolated frequency are derived for parabolic interpolation and for KCe interpolation. These error propagation formulae give random errors which are inversely proportional to the SNR of the spectrum. These formulae are evaluated with the appropriate KCe exponent for each of the Hanning, the Hamming, and the Blackman-Harris windows. In all cases we find that the random error is essentially independent of both window type and interpolation scheme. While zero-filling prior to interpolation reduces the residual systematic frequency interpolation error, it increases the random frequency error. The increase in random error with higher levels of zero-filling is explained. Because the random errors are proportional to noise level, the optimal number of zero-fillings varies with SNR. If the apodizing window is chosen to match the dynamic range of the spectrum, as we have previously recommended, then the systematic error for KCe interpolation of non-zero-filled spectra is so low that the overall error is dominated by the random error. In this case, KCe interpolation is, for all intents and purposes, exact. Since the random error is minimized by no zero-filling, the lowest overall error will be achieved by a combination of no zero-filling and KCe interpolation. In constrast, the minimum total error for parabolic interpolation is achieved by interpolation of the once-zero-filled spectrum. A further advantage of KCe interpolation, over and above its lower total error, is that KCe interpolation obviates the need for zero-filling.

New shape-based interpolation technique for three-dimensional images

Abstract: The problem of interpolating a high-resolution binary-valued 3-D image given a lower-resolution grayscale 3-D image and a corresponding segmented 3-D image is addressed. Three algorithms for this problem are described. Algorithms 1 and 2 perform shape- and located-based binary interpolation. Algorithm 3, which subsumes algorithms 1 and 2, incorporates grayscale information as well as object shape and slice-to-slice object spatial relationships. Results show that algorithm 3 generates better interpolated objects than the segmented volumes arising from standard grayscale-based interpolation techniques. Algorithm 2, which subsumes algorithm 1, uses only the known presegmented volume to interpolate a new binary-valued volume. the methods show particular merit in cases where the objects to interpolate are thin tube-like structures, such as the coronary arteries. >

Application of Lagrangian Blending Functions for Grid Generation Around Airplane Geometries

Abstract: A simple procedure has been developed and applied for the grid generation around an airplane geometry. This approach is based on a transfinite interpolation with Lagrangian interpolation for the blending functions. A monotonic rational quadratic spline interpolation has been employed for the grid distributions.

Efficient sampling rate conversion with cubic splines

Abstract: An efficient implementation of a two-stage fractional sampling rate conversion for digital audio signals is presented, based on: local cubic spline interpolation. The first (up-converter) stage is computationally optimal, using polyphase networks. The second (down-converter) stage generally requires coefficient calculations for each sample, but is also efficient because of the local nature of the cubic spline interpolation. >

Shape Preserving Interpolation

Abstract: We examine numerical and theoretical questions related to constrained interpolation and smoothing. The prototype problem consists in finding the interpolating or approximating function preserving some convex constraints such as monotonicity or convexity of given data. Monovariate shape preserving interpolation schemes and related algorithms, in particular of the fit and modify type, are considered. A short survey of local methods to interpolate surfaces under some constraints, such as monotonicity and convexity, is presented. In particular we treat some extensions of univariate results to monotone and/or convex bivariate interpolation and the related algorithms. Graphic displays are given to illustrate some results obtained.

Interpolation Problems for Matrix Polynomials and Rational Matrix-Functions

Abstract: In this chapter we consider a few different interpolation problems for matrix polynomials and rational matrix valued functions. We have in mind the tangential Lagrange and Lagrange-Sylvester interpolation, contour integral interpolation and interpolation with a given set of divisions and remainders. Connections among all these problems are established and in each case a complete solution is suggested.

Comparison of interpolation methods in three-dimensional surface display

Abstract: The three-dimensional (3-D) object data obtained from a scanner usually have unequal sampling frequencies in the x y and z directions. Generally the 3-D data is first interpolated between slices to obtain isotropic resolution reconstructed then operated on by object extraction and display algorithms. Several interpolation methods are available. Here three interpolation algorithms: hnear polynomial and shape methods are used for comparison. The performances of these three algorithms are compared based on the image quality and accuracy in volume measurement of the 3-D object. 1.© (1990) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Discrete interpolation surface

Abstract: In this paper, a method to construct a surface with point interpolation and normal interpolation is presented. An algorithm to construct the discrete interpolation is also presented, which has the time complexityO (Nlog N), whereN in the number of scattered points.

A Parallel Method for Fast and Practical High-Order

Abstract: . We present parallel algorithms for the computation and evaluation of interpolating polynomials.Thealgorithmsuseparallelprefixtechniquesforthe calculationofdivideddifferencesintheNewtonrepresentationof the interpolating polynomial. For n+ 1 given input pairs, the proposed interpolation algorithm requires only2 d log (n+ 1 )e 2 parallel arithmetic steps and circuit size O 2 , reducing the best known circuit size forparallel interpolation by a factor of log n . The algorithm for the computation of the divided differences is shownto be numerically stable and does not require equidistant points, precomputation, or the fast Fourier transform.We report on numerical experiments comparing this with other serial and parallel algorithms. The experimentsindicate that the method can be very useful for very high-order interpolation, which is made possible for specialsets of interpolation nodes.AMS subject classifications.65D05, 65W05, 68C25 1. Introduction. Given a set of n+ 1 pairs of values,

Interpolation and Approximation by Splines on [0, ∞ )

Abstract: We investigate interpolation and approximation problems by splines, which possess a countable set of knots on the positive axis. In particular, we characterize those sets of points, which admit unique Lagrange interpolation and give some sufficient and some necessary conditions for best approximations. Moreover, we show that the classical results of spline-approximation theory are not available for splines with a countable set of knots.