A well-known approach to image interpolation is cubic convolution, in which the ideal sinc function is modelled by a finite extent kernel, which consists of piecewise third order polynomials. In this paper we show that the concept of cubic convolution can be generalized. We derive kernels of up to ninth order and compare them both mutually and to cardinal splines of corresponding orders. From s...

Numerical solutions of one-dimensional heat and advection-diffusion equations are obtained by collocation method based on cubic B-spline. Usual finite difference scheme is used for time and space integrations. Cubic B-spline is applied as interpolation function. The stability analysis of the scheme is examined by the Von Neumann approach. The efficiency of the method is illustrated by some test...

Nearest-neighbor, linear, and various cubic interpolation functions are frequently used in image resampling. Quadratic functions have been disregarded largely because they have been thought to introduce phase distortions. This is shown not to be the case, and a family of quadratic functions is derived. The interpolating member of this family has visual quality close to that of the Catmull-Rom c...

It is shown that cubic spline interpolation with the not-a-knot side condition converges to any C-interpoland without any mesh-ratio restriction as the mesh size goes to zero. AMS (MOS) Subject Classifications: 41A15, 41A05

The waveform interpolation (WI) speech coding presents a good performance at low bit rate. However, the algorithm has a very high complexity in computation. In this paper, a low-complexity improved waveform interpolation speech coder at 2kbps is proposed. The improved coding scheme has greatly reduced the computational complexity and improved the reconstructed speech quality by using various te...

The interpolation of oneand two-dimensional images is considered. The usual linear or cubic spline interpolations try to connect given data points. On the other hand, image data give area integrals of the radiation intensity (i.e., photon counts) over pixels. Based on variational principles, we have developed schemes of quadratic and fourth-order polynomial interpolation which reproduce the giv...

We introduce a new structured kernel interpolation (SKI) framework, which generalises and unifies inducing point methods for scalable Gaussian processes (GPs). SKI methods produce kernel approximations for fast computations through kernel interpolation. The SKI framework clarifies how the quality of an inducing point approach depends on the number of inducing (aka interpolation) points, interpo...

The research status of industrial robot trajectory planning is discussed in detail, and the applicable occasions cubic polynomial interpolation, quintic B-spline curve, mixed interpolation other methods commonly used basic are comprehensively analyzed. At same time, various optimal for robots reviewed. advantages disadvantages compared important direction prospected.