Macro-elements of arbitrary smoothness are constructed on Powell-Sabin triangle splits. These elements are useful for solving boundaryvalue problems and for interpolation of Hermite data. It is shown that they are optimal with respect to spline degree, and we believe they are also optimal with respect to the number of degrees of freedom. The construction provides local bases for certain supersp...

Use of mathematical interpolation in Digital Signal Processing applications often seems to be a remarkable solution when applied for noise reduction. In the last two decades advancement in the Elasticity imaging of tissue is worth mentioning. Two dimensional spline technique for generating Elastograms is fairly a new approach for generating ultrasonic Elastograms. In the way of analyzing imagin...

In this paper, we investigate the problem of designing compact support interpolation kernels for a given class of signals. By using calculus of variations, we simplify the optimization problem from an infinite nonlinear problem to a finite dimensional linear case, and then find the optimum compact support function that best approximates a given filter in the least square sense (l2 norm). The be...

This paper describes the interpolation of head related transfer functions (HRTFs) for all directions. The interpolation of HRTFs enables us to reduce the number of measurements for new user’s HRTFs, and also reduce the data of HRTFs in auditory virtual systems. A linear interpolation and the spline interpolation are evaluated and the advantages of both methods are clarified. The interpolation m...

In this paper, we present a novel and robust spline interpolation algorithm given a noisy symmetric positive definite (SPD) tensor field. We construct a B-spline surface using the Riemannian metric of the manifold of SPD tensors. Each point of this surface corresponds to a diffusion tensor. We develop an algorithm for fitting such a Tensor Spline to a given tensor field and also an algorithm fo...

Interpolation of a sequence of points by spline curves generally requires the solution of a large system of equations. In this paper we provide a method which requires only local computation instead of a global system of equations and works for a large class of curves. This is a generalization of a method which previously developed for Bspline, NURBS and trigonometric CB-spline curves. Moreover...

Alexa’s method for linearly interpolating matrices is well-suited for application to camera matrices. This paper discusses implementation issues that arise when applying this method to camera interpolation. We show how to include the perspective matrix, even though Alexa’s operators cannot be applied directly to it. We discuss cases where Alexa’s operators fail to converge and show how to work ...