Bicubic interpolation

About: Bicubic interpolation is a research topic. Over the lifetime, 3348 publications have been published within this topic receiving 73126 citations.

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.

Edge-enhanced image zooming

Abstract: A new adaptive algorithm for image interpolation with percep- tual edge enhancement is proposed. Here, perceptual means that edges are enhanced and interpolated in a visually pleasing way. Each pixel neighborhood is classified into one of three categories (constant, ori- ented, or irregular). In each case, an optimal interpolation technique finds the missing pixels without generating unpleasant artifacts such as aliasing or ringing effects. Furthermore, a quadratic Volterra filter is em- ployed to extract perceptually important details from the original image, which are then used to improve the overall sharpness and contrast. Both qualitative and quantitative simulation results clearly show the superiority of our method over standard low-pass interpolation algorithms such as bilinear, diamond-filter, or B-spline interpolation. © 1996 Society of Photo-Optical Instrumentation Engineers. Subject terms: image interpolation; zooming; quadratic Volterra filters; detail en- hancement; image enhancement; edge enhancement.

Interpolation with interval and point tension controls using cubic weighted v-splines

Abstract: Various methods have been developed to control the shape of an interpolating curve for computer-aided design applications. Some methods are better suited for controlling the tension of the curve on an interval, while others are better suited for controlling the tension at the individual interpolation points. The weighted v-spline is a C1 piecewise cubic polynomial interpolant that generalizes C2 cubic splines, weighted splines, and v-splines. Shape controls are available to “tighten” the weighted v-spline on intervals and/or at the interpolation points. The mathematical theory is presented together with short algorithms for parametric interpolation.

Molecular potential energy surfaces by interpolation in Cartesian coordinates

Abstract: We present a new method for expressing a molecular potential energy surface (PES) as an interpolation of local Taylor expansions. By using only Cartesian coordinates for the atomic positions, this method avoids redundancy problems associated with the use of internal coordinates. The correct translation, rotation, inversion, and permutation invariance are incorporated in the PES via the interpolation method itself. The method is most readily employed for bound molecules or clusters and is demonstrated by application to the vibrational motion of acetylene.

Smooth geometry images

Abstract: Previous parametric representations of smooth genus-zero surfaces require a collection of abutting patches (e.g. plines, NURBS, recursively subdivided polygons). We introduce a simple construction for these surfaces using a single uniform bi-cubic B-spline. Due to its tensor-product structure, the spline control points are conveniently stored as a geometry image with simple boundary symmetries. The bicubic surface is evaluated using subdivision, and the regular structure of the geometry image makes this computation ideally suited for graphics hardware. Specifically, we let the fragment shader pipeline perform subdivision by applying a sequence of masks (splitting, averaging, limit, and tangent) uniformly to the geometry image. We then extend this scheme to provide smooth level-of-detail transitions from a subsampled base octahedron all the way to a finely subdivided, smooth model. Finally, we show how the framework easily supports scalar displacement mapping.