Bicubic interpolation

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

Analysis and Synthesis of Tones by Spectral Interpolation

Abstract: A technique is presented for the analysis and digital resynthesis of instrumental sounds. The technique is based on a model that uses interpolation of amplitude spectra to reproduce short-time spectral variations. The main focus of this work is the analysis algorithm. Starting from a digital recording the authors were able to compute automatically the parameters of this model. Two analysis/synthesis methods are studied based on spectral interpolation. The first uses only spectral interpolation. The second method is a hybrid in which a sampled attack is spliced onto a sustain synthesized via spectral interpolation

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.

Classification -based method in optimal image interpolation

Abstract: Atkins, C. Brian. Ph.D., Purdue University, December 1998. Classification-Based Methods in Optimal Image Interpolation. Major Professors: Charles A. Bouman and Jan P. Allebach. In this thesis, we introduce two new approaches to optimal image interpolation which are based on the idea that image data falls into different categories or classes, such as edges of different orientation and smoother gradients. Both these methods work by first classifying the image data in a window around the pixel being interpolated, and then using an interpolation filter designed for the selected class. The first method, which we call Resolution Synthesis (RS), performs the classification by computing probabilities of class membership in a Gaussian mixture model. The second method, which we call Tree-based Resolution Synthesis (TRS), uses a regression tree. Both of these methods are based on stochastic models for image data whose parameters must have been estimated beforehand, by training on sample images. We demonstrate that under some assumptions, both of these methods are actually optimal in the sense that they yield minimum mean-squared error (MMSE) estimates of the target-resolution image, given the source image. We also introduce Enhanced Tree-based RS, which consists of TRS interpolation followed by an enhancement stage. During the enhancement stage, we recursively add adjustments to the pixels in the interpolated image. This has the dual effect of reducing interpolation artifacts while imparting additional sharpening. We present results of the above methods for interpolating images which are free of artifacts. In addition, we present results which demonstrate that RS can be trained for high-quality interpolation of images which

A new approach for data partitioning through high dimensional model representation

Abstract: A multivariate function f(x1,..., xN) can be evaluated via interpolation if its values are given at a finite number nodes of a hyperprismatic grid in the space of independent variables x1, x2,..., xN. Interpolation is a way to characterize an infinite data structure (function) by a finite number of data approximately. Hence it leaves an infinite arbitrariness unless a mathematical structure with finite number of flexibilities is imposed for the unknown function. Imposed structure has finite dimensionality. When the dimensionality increases unboundedly, the complexities grow rapidly in the standard methods. The main purpose here is to partition the given multivariate data into a set of low-variate data by using high dimensional model representation (HDMR) and then, to interpolate each individual data in the set via Lagrange interpolation formula. As a result, computational complexity of the given problem and needed CPU time to obtain the results through a series of programs in computers decrease.

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.