Showing papers on "Bicubic interpolation published in 1979"

Linear interpolator for color correction

Abstract: A linear interpolating method and apparatus for color signals in a memory of a picture reproducing machine, wherein the stored signals are addressed in a three-dimensional fashion and a cubic interpolation unit in the memory is dissected into tetrahedra. It is determined which of these tetrahedra contains the interpolation point, and then the value at that point is interpolated from the known values at the vertices of the tetrahedron, using a certain method of linear interpolation. An apparatus is described for carrying out the method.

Design Problems for Optimal Surface Interpolation.

Abstract: : We consider the problem of interpolating a surface given its values at a finite number of points. We place a special emphasis on the question of choosing the location of the points where the function will be sampled. Using minimal norm interpolation in reproducing kernel Hilbert spaces, equivalently Bayesian interpolation, and N-widths, we provide lower bounds for interpolation error relative to certain error criteria. These lower bounds can be used when evaluating an existing design, or when attempting to obtain a good design by iterative procedures to decide whether further minimization is worthwhile. The bounds are given in terms of the eigenvalues of a relevant reproducing kernel and the asymptotic behavior of these eigenvalues for certain tensor product spaces in the unit d-dimensional cube is obtained.

A Comparative Study of the Use of Linear and Modified Cubic Spline Interpolation for Image Reconstruction

Abstract: Image reconstruction is the process of recovering a function of two variables from experimentally obtained estimates of its integrals alone certain lines. An important version in medicine is the recovery of the density distribution within a cross-section of the human body from a number of X-ray projections. A computationally efficient technique for image reconstruction is the so-called convolution method. It consists of two steps: (i) data obtained by each of the projections of the cross-section are separately (discrete) convolved with a fixed function; (ii) the density of the function at any point in the cross-section is estimated as the sum of values (one from each projection) of the convolved projection data. A difficulty is that part (ii) usually requires values of the convolved projection data at points other than where they have been calculated during part (i). This is usually resolved by interpolation between the calculated values. In this paper we report on a computer experimental study which compares the efficacy of two methods of interpolation (linear interpolation and a modified cubic spline interpolation) when used with the convolution reconstruction method. The two interpolation techniques are examined for their mathematical properties and are compared from the points of view of resolution of fine details, smoothness of the reconstructed cross-sections, sensitivity to noise in the data, the overall nearness of the original and reconstructed objects, and the cost of implementation. Both methods are illustrated on reconstructions of a mathematically described cross-section of the human head from computer simulated X-ray data.

Bicubic spline interpolation: a quantitative test of accuracy and efficiency*

Abstract: Two different methods for the construction of an approximation to bicubic splines for interpolating irregularly spaced two-dimensional data are described. These are referred to as the least squares line (LSL) and linear segment (LINSEG) construction procedures. A quantitative test is devised for investigating the absolute accuracy and efficiency of the two spline interpolation procedures. The test involves (i) laying of artificial flight lines on the analytically known field of a model, (ii) interpolation of field values along the flight lines and their subtraction from the original field values to compute the residuals. This test is applied on fields due to four models (three prism models and one dyke model) placed at different depths below the flight lines, and for each case the error estimates (the mean error, the maximum error and the standard deviation) are tabulated. An analysis of the error estimates shows in all cases the LSL interpolation to be more accurate than the LINSEG, although the latter is about 50% faster in computer time. The relative accuracy and efficiency of the LSL interpolation is also tested against a recent method based on harmonization procedure, which shows the latter to be more precise, though much slower in speed.

Data compression of Linear Prediction (LP) analyzed speech by interpolation and quantization of pseudo‐formant parameters

Abstract: Pseudoformants and bandwidths, derived from LP coefficients, prove highly susceptible to data compression techniques such as interpolation and quantization because of their low entropy and smooth sequential nature. We have developed a heuristic to label initially unordered pseudoformants in a way that reveals their sequential smoothness, so that linear interpolation can be successfully applied to each pseudoformant separately. A linear least‐squares fit is made over several points; the number of points is limited by a bound on the allowed mean‐squared fractional difference between the data and the interpolating line, and another bound on the maximum‐squared fractional difference. Quantization of the resulting parameters is constrained not to introduce more error than was allowed in the interpolation procedure. All parameters need not be interpolated using the same bound; if the relative importance of the parameters is chosen in an acoustically reasonable way, interpolation can produce very high quality sound at considerably reduced bit rates. [Work supported by NSF.]

Modal Interpolation Program, L 215 (INTERP)

Abstract: The design, structure, and usage of the modal interpolation program L215 are presented. The program uses modal data sets of arrays containing interpolation coefficients. The interpolation arrays are used to determine displacements at various aerodynamic control points. The displacements consist of translations normal to the aerodynamic surface and surface slopes that are parallel and perpendicular to the free stream direction. Five different interpolation methods are available.

Experimental comparison of parameter interpolation in LPC vocoders

Abstract: LPC parameter interpolation is effective in smoothing synthesized speech roughness. To choose an appropriate interpolation parameter, LPC parameter interpolation properties were compared experimentally, using: (1) spectral distortion between interpolated spectrum and actual spectrum, and (2) spectral distance relationships among interpolated spectrum and two boundary spectra. Both k parameter and LAR (log area ratio), which are used as transmission parameters because of their good quantization properties, sometimes provide an undesired speech spectrum interpolation. These two parameters cannot interpolate formants correctly, in particular, when the formant bandwidth shows a big change between the two boundary spectra. On the other hand, α parameter provides better speech spectrum interpolation than the former two. Listening tests show that unnatural formant transition due to the k‐parameter interpolation can be perceived as slurring and gliding, which are hardly perceived in the α‐parameter interpolation.