Showing papers on "Bicubic interpolation published in 1986"

Algorithms for subpixel registration

Abstract: This paper presents an analysis of four algorithms which are able to register images with subpixel accuracy; these are correlation interpolation, intensity interpolation, differential method, and phase correlation. The subpixel registration problem is described in detail and the resampling process for subpixel registration is analyzed theoretically. It is shown that the main factors affecting registration accuracy are the interpolation function, sampling frequency, number of bits per pixel, and frequency content of the image. An iterative version of the intensity interpolation algorithm, which achieves maximum computational efficiency, is also presented. Analyses, computer simulations, and experiments for measuring displacements of objects using their speckle images have shown that this algorithm is faster than a direct intensity interpolation algorithm by a factor of more than ten thousand. Using bilinear interpolation and representing pixels by 8-bit samples, a 0.01 to 0.05 pixel registration accuracy can be achieved.

An adaptive subdivision method for surface-fitting from sampled data

Abstract: A method is developed for surface-fitting from sampled data Surface-fitting is the process of constructing a compact representation to model the surface of an object based on a fairly large number of given data points In our case, the data is obtained from a real object using an automatic three-dimensional digitizing system The method is based on an adaptive subdivision approach, a technique previously used for the design and display of free-form curved surface objects Our approach begins with a rough approximating surface and progressively refines it in successive steps in regions where the data is poorly approximated The method has been implemented using a parametric piecewise bicubic Bernstein-Bezier surface possessing G1 geometric continuity An advantage of this approach is that the refinement is essentially local reducing the computational requirements which permits the processing of large databases Furthermore, the method is simple in concept, yet realizes efficient data compression Some experimental results are given which show that the representation constructed by this method is faithful to the original database

Convex interval interpolation with cubic splines, II

Abstract: A necessary and sufficient criterion is presented under which the problem of the convex interval interpolation with cubicC1-splines has at least one solution. The criterion is given as an algorithm which turns out to be effective.

A simple rational spline and its application to monotonic interpolation to monotonic data

Abstract: We shall consider a class of simple rational splines and their application to monotonic interpolation to monotonic data. Our method is situated between interpolation with the usual cubic splines and with monotone quadratic splines. A selection of numerical results is presented in Figs. 4–11.

Real-time interpolation with cubic splines and polyphase networks

Abstract: Deals with the development of a new approach to the problem of real-time interpolation of digital signals. Whereas the traditional methods of performing this operation make use of digital filters (FIR or IIR), this approach utilizes local cubic polynomial interpolative routines known as cubic spline functions. By using cubic splines, an algorithm has been obtained which can be implemented in a simple and economical way, yielding the desired real-time interpolator. The properties of this system include conceptual and structural simplicity, local control, speed of operation, and versatility.

Describing free-form 3D surfaces for animation.

Abstract: A system for interactively describing and modifying free-form surfaces is presented. The system is based on the use of bicubic patches. Although it is not a full-fledged mechanical CAD system, it has been used to construct complex surface descriptions. It is also useful as a testbed for further experimentation.

Fourier Domain Interpolation Techniques for Synthetic Aperture Radar

Abstract: : Spotlight-mode synthetic aperture radar (SAR) produces complex Fourier data points on a polar grid which is offset from dc in the frequency domain To produce an image in the spatial domain, it is necessary to invert this sampled Fourier data prior to extracting magnitude information However, the polar format of the data makes this difficult, since there is no known polar FFT An alternative is to interpolate the complex polar data to a Cartesian grid and then perform the two-dimensional FFT The magnitude of the resulting data array represents the magnitude of the complex ground reflectivity of the terrain under illumination The interpolation process can be very computationally intense, with an order two to fifty times that of the FFT Reducing the computation in the interpolation stage, while maintaining reconstruction quality is the focus of this work Several 2D interpolation techniques are examined, including nearest neighbor, bilinear, inverse-distance to the nth power, weighted sinc, chirp z-transform, and the newest interpolation algorithm proposed for this problem - the cubic spline It is found that separable interpolation schemes outperform the more commonly used nearest neighbor and inverse distance algorithms, and that the cubic spline is very competitive the weighted sinc interpolator in computation requirements and reconstruction quality The chirp z-transform is determined to be a good alternative to the classical interpolation-DFT approach

An Analysis of Elliptic Grid Generation Techniques Using an Implicit Euler Solver.

Abstract: : Several control function interpolation techniques in a general three-dimensional elliptic grid generation code and their effects on flow solutions using an implicit Euler algorithm are examined. These results will serve to guide the design of control function procedures and interpolation techniques in general grid generation codes. Three configurations and three grid types (O, C, and H grids) are examined. The results indicate that the selection of the control function interpolation techniques, which affect grid spacing, should be based on boundary curvature and spacing. The selection of the interpolation technique can then be made transparent to the user of general grid generation codes. (Author)

The Spectral Approximation of Bicubic Splines on the Sphere

Abstract: Formulas are given for the spherical harmonic coefficients of bicubic splines. These formulas are useful for determining a spectral approximation to a discrete function which may be defined on a latitude-longitude grid or at arbitrarily scattered points on the surface of the sphere.