Gaussian derivatives are often used as differential operators to analyze the structure in images. In this paper, we will analyze the accuracy and computational cost of the most common implementations for differentiation and interpolation of Gaussian-blurred multi-dimensional data. We show that – for the computation of multiple Gaussian derivatives – the method based on B-splines obtains a highe...

A class of C rational cubic/linear trigonometric interpolation spline with two local parameters is proposed. Simple sufficient conditions for constructing positivity-preserving interpolation curves are developed. By using the boolean sum of quadratic trigonometric interpolating operators to blend together the proposed rational cubic/linear trigonometric interpolation splines as four boundary fu...

We interpret a type of fuzzy controller as an inter polator of B spline hypersurfaces B spline basis func tions of di erent orders are regarded as a class of mem bership functions MFs with some special properties These properties lead to several interesting conclusions about fuzzy controllers if such membership functions are employed to specify the linguistic terms of the input variables We sho...

We consider two-stage scattered data fitting with truncated hierarchical B-splines (THB-splines) for the adaptive reconstruction of industrial models. The first stage scheme is devoted to computation local least squares variational spline approximations, exploiting a simple fairness functional handle distributions locally varying density points. Hierarchical quasi-interpolation based on THB-spl...

The aim of this paper is to test different types of spatial interpolation for the materialpoint method. The interpolations include quadratic elements and cubic splines. A brief introduction to the material-point method is given. Simple liner-elastic problems are tested, including the classical cantilevered beam problem. As shown in the paper, the use of negative shape functions is not consisten...

Given a set of scattered data, we usually use a minimal energy method to find Lagrange interpolation based on bivariate spline spaces over a triangulation of the scattered data locations. It is known that the approximation order of the minimal energy spline interpolation is only 2 in terms of the size of triangulation. To improve this order of approximation, we propose several new schemes in th...

W e describe the use of splines for solv-i n g n o n l i n e a r model estimation problems, in which nonlinear functions with unknown shapes and values are involved, by converting the nonlinear estimation problems into linear ones at a higher-dimensional space. This contrasts with the typical use of the splines [1]–[3] for function interpolation where the functional values at some input points ...

B-splines provide an accurate and efficient method for interpolating regularly spaced data. In this paper, I study the applicability of B-spline interpolation in the context of the inverse interpolation method for regularizing irregular data. Numerical tests show that, in comparison with lower-order linear interpolation, B-splines lead to a faster iterative conversion in under-determined proble...

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