Showing papers on "Bicubic interpolation published in 1982"

Image reconstruction by parametric cubic convolution

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.

Visually C2 cubic splines

Abstract: Generalized C 2 conditions are used to define a class of cubic splines. A B spline-like design scheme is provide for these curves.

Industrial articulated robot linear interpolation control device

Abstract: In a control device for an industrial articulated robot, in the linear interpolation between two specified points, the distance between the two points is divided into segments, and the interpolation increments of the articulation drive axes for each interpolation internal, which correspond to the segments, are calculated for interpolation so that the interpolation increments are distributed uniformly with time.

Two-dimensional digital linear interpolation system

Abstract: A two-dimensional interpolation of image data is pro­ vided for a video display system, in which a one-dimensional interpolator performs the interpolation in both dimensions with data flow control so that images can be transmitted, scaled and displayed in real time.

Application of the Bézier curve to data interpolation

Abstract: A method of using Bernstein—Bezier curves for data interpolation is proposed. The curves obtained satisfy the required conditions for ‘visual content’. A numerical example is executed not only on data points in a plane but also on the data points of a 3D object. The proposed curves are assessed for stereoscopic effect. Comparisons of the new interpolating curves with cubic splines demonstrate their merits.

Scanline rendering of parametric surfaces

Abstract: A scanline algorithm is described which renders bicubic patches directly from the parametric description without producing a polygonal approximation. The algorithm is partially based on earlier work by Whitted. A primitive object, called a “curved-edge polygon”, is defined, and an algorithm for breaking down a bicubic patch into the primitive objects is described. A general surface intersection method is employed to provide a robust silhouette edge detector. Shades are computed by calculating a cubic approximation to the normal surface and performing either a cubic or a linear interpolation of the bounding edge normals across the scanline. Subdivision of parametric surfaces is used to reduce the complexity of the surfaces being rendered, providing dramatic improvement in the results of both the silhouette detector and the shading methods.

Discrete cubic spline interpolation

Abstract: In the present paper we study the existence, uniqueness and convergence of discrete cubic spline which interpolate to a given function at one interior point of each mesh interval. Our result in particular, includes the interpolation problems concerning continuous periodic cubic splines and discrete cubic splines with boundary conditions considered respectively in Meir and Sharma (1968) and Lyche (1976) for the case of equidistant knots.

Analysis of linear interpolation schemes for bi-level image applications

Abstract: In the office, it is often necessary to scan a picture at a certain resolution and then reproduce it at a different (usually higher) resolution This conversion can be achieved by interpolating the

Techniques for the generation of three-dimensional data for use in complex image synthesis

Abstract: An integrated system for the creation and modification of three dimensional data for use in image synthesis using a digital computer is studied. Techniques for efficiently accomplishing this goal are presented. An algorithm is described which finds the space curve which is the intersection of two bicubic patches. Associated data structures are discussed, including a quadtree structure which incorporates the curve of intersection in a way suitable for efficient reconstruction of the intersected object.

Some improvements to the design programs for equiripple FIR filters

Abstract: Some methods are proposed which try to improve the execution of FIR filter design programs based on the Remez algorithm. The number of evaluations of the Lagrange interpolation formula needed for finding the extrema of the error function can be reduced by searching for the zeros of the derivative. The derivative of the Lagrange interpolation polynomial can be computed together with the Lagrange interpolation itself with little additional effort. The precision of the evaluation of the Lagrange interpolation can be improved by utilizing all the points resulting from the Remez algorithm. A couple of other minor improvements are given, too.

Interactive surface representation system using a B-spline formulation with interpolation capability

Abstract: An interactive surface representation system is described which uses a parametric uniform bicubic B-spline formulation which can describe a surface initially defined to interpolate a specified network of points.

On the use of splines in hierarchical image transmission

Abstract: A quick identification of the received image is a desirable feature in low bandwith transmission systems. A gross quality approximation of the image is obtained at early stages when it is hierarchically encoded. This allows faster recognition than raster scanning methods, without transmission overhead. Spline interpolation facilitates this process, greatly improving the efficiency of hierarchical approaches. The same subjective impression is obtained with half of the information. Cubic convolution interpolation has all the advantages of the former, and can be more easily calculated. Recognition with less amount of received bits can be achieved with a non uniform development of the hierarchy. In order to automatize this procedure, two algorithms are presented with their advantages and drawbacks. In all the considered cases, transmission can be ended when the receiver decides. So, compression can be achieved at the cost of an approximation errors.

Piecewise Cubic Hermite Interpolation Package. Final specifications

Abstract: This document contains the specifications for PCHIP, a new Fortran package for piecewise cubic Hermite interpolation of data. It features software to produce a monotone and visually pleasing interpolant to monotone data. Such an interpolant may be more reasonable than a cubic spline if the data contains both steep and flat sections. Interpolation of cumulative probability distribution functions is another application.

Piecewise Cubic Interpolation Package

Abstract: PCHIP (Piecewise Cubic Interpolation Package) is a set of subroutines for piecewise cubic Hermite interpolation of data. It features software to produce a monotone and "visually pleasing" interpolant to monotone data. Such an interpolant may be more reasonable than a cubic spline if the data contain both 'steep' and 'flat' sections. Interpolation of cumulative probability distribution functions is another application. In PCHIP, all piecewise cubic functions are represented in cubic Hermite form; that is, f(x) is determined by its values f(i) and derivatives d(i) at the breakpoints x(i), i=1(1)N. PCHIP contains three routines - PCHIM, PCHIC, and PCHSP to determine derivative values, six routines - CHFEV, PCHFE, CHFDV, PCHFD, PCHID, and PCHIA to evaluate, differentiate, or integrate the resulting cubic Hermite function, and one routine to check for monotonicity. A FORTRAN 77 version and SLATEC version of PCHIP are included.

Optimal real-time interpolation for D/A conversion of sparsely sampled signals

Abstract: Interpolative cubic splines are considered for real-time D/A conversion applications. Four methods are examined that evaluate the derivatives at the end-points of the interval. The performance evaluation of these methods is based on both a mean-square-error criterion and a figure of merit which considers hardware complexity.

Splines Interpolation For Image Reconstruction

Abstract: In this paper, an interpolation method based on B-spline functions is used in image reconstruction. First, an elementary review of B-spline function interpolation theory is given. Next, the influence of the boundary conditions assumed here on the interpolation of filtered projections and also on the image reconstruction is discussed. It is shown that this boundary condition has almost no influence on the image in the central region of the image space, because the error of the interpolation decreases rapidly - indeed, by a factor of ten in shifting two pixels from the edge toward the center. The implementation results show that the computational cost for the interpolation using this algorithm is about one-tenth that of the same subjective and objective fidelity as the conventional algorithm.© (1982) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.