Bicubic interpolation

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

Markov Random Field Model-Based Edge-Directed Image Interpolation

Abstract: This paper presents an edge-directed image interpolation algorithm. In the proposed algorithm, the edge directions are implicitly estimated with a statistical-based approach. Consequently, the local edge directions are represented by length-16 vectors, which are denoted as weight vectors. The weight vectors are used to formulate geometric regularity constraint, which is imposed on the interpolated image through the Markov Random Field (MRF) model. Furthermore, the interpolation problem is formulated as a Maximum A Posterior (MAP)-MRF problem and, under the MAP-MRF framework, the desired interpolated image corresponds to the minimal energy state of a two-dimensional random held. Simulated Annealing method is used to search for the minimal energy state from a reasonable large state space. Simulation and comparison results show that the proposed MRF model-based edge-directed interpolation method produces edges with strong geometric regularity.

Mathematical equivalence of zero-padding interpolation and circular sampling theorem interpolation with implications for direct Fourier image reconstruction

Abstract: The speed and accuracy of Direct Fourier image reconstruction methods have long been hampered by the need to interpolate between the polar grid of Fourier data that is obtained from the measured projection data and the Cartesian grid of Fourier data that is needed to recover an image using the 2D FFT. Fast but crude interpolation schemes such as bilinear interpolation often lead to unacceptable image artifacts, while more sophisticated but computationally intense techniques such as circular sampling theorem (CST) interpolation negate the speed advantages afforded by the use of the 2D FFT. One technique that has been found to yield high-quality images without much computational penalty is a hybrid one in which zero-padding interpolation is first used to increase the density of samples on the polar grid after which bilinear interpolation onto the Cartesian grid is performed. In this work, we attempt to account for the success of this approach relative to the CST approach in three ways. First and more importantly, we establish that zero-padding interpolation of periodic functions that are sampled in accordance with the Nyquist criterion--precisely the sort of function encountered in the angular dimension of the polar grid--is exact and equivalent to circular sampling theorem interpolation. Second, we point out that both approaches make comparable approximations in interpolating in the radial direction. Finally, we indicate that the error introduced by the bilinear interpolation step in the zero- padding approach can be minimized by choosing sufficiently large zero-padding factors.

A priori convergence of the Generalized Empirical Interpolation Method

Abstract: In an effort to extend the classical lagrangian interpolation tools, new interpolating methods that use general interpolating functions are explored. The Generalized Empirical Interpolation Method (GEIM) belongs to this class of new techniques. It generalizes the plain Empirical Interpolation Method by replacing the evaluation at interpolating points by application of a class of interpolating linear functions. Since its efficiency depends critically on the choice of the interpolating functions (that are chosen by a Greedy selection procedure), the purpose of this paper is therefore to provide a priori convergence rates for the Greedy algorithm that is used to build the GEIM interpolating spaces.

Asymmetric Lens Design Using Bicubic Splines: Application to the Color TV Lighthouse

Abstract: Any two-dimensional interpolation scheme which has continuous derivatives may be used to represent an optical surface for ray-tracing purposes. We present bicubic splines in their application to the design of asymmetric surfaces. An as example of a problem requiring an asymmetric system, we analyze the design problems of a color TV lighthouse lens.