We analyze an alternative to classical Zernike fitting based on the cubic B-spline model, and compare the strengths and weaknesses of each representation over a set of different wavefronts that cover a wide range of shape complexity. The results obtained show that a Zernike low-degree polynomial expansion or a cubic B-spline with a low number of breakpoints are the best choices for fitting simp...

Colonic polyps are growths on the inner wall of the colon. They appear like elliptical protrusions which can be detected by curvature-derived shape discriminators. For reasons of computation efficiency, much of the past work in computeraided diagnostic CT colonography adopted kernel-based convolution methods in curvature estimation. However, kernel methods can yield erroneous results at thin st...

The collocation method based on cubic B-spline, is developed to approximate the solution of second kind nonlinear Fredholm integral equations. First of all, we collocate the solution by B-spline collocation method then the Newton-Cotes formula use to approximate the integrand. Convergence analysis has been investigated and proved that the quadrature rule is third order convergent. The presented...

There are thousands of articles published on variants of splines, including least squares cubic splines. One of the first least squares articles was de Boor and Rice [1], and a comprehensive explanatory textbook is Dierckx [2]. Unfortunately, every example in the literature and on the web of a least squares cubic spline makes use of B-splines. While B-splines have a certain elegance, they are s...

In this article a numerical technique is presented for the solution of Fokker-–Planck equation. This method uses the cubic B-spline scaling functions. The method consists of expanding the required approximate solution as the elements of cubic B-spline scaling function. Using the operational matrix of derivative, the problem will be reduced to a set of algebraic equations. Some numerical example...

Based on analysis of basic cubic spline interpolation, the clamped cubic spline interpolation is generalized in this paper. The methods are presented on the condition that the first derivative and second derivative of arbitrary node are given. The Clamped spline and Curvature-adjusted cubic spline are also generalized. The methods are presented on the condition that the first derivatives of arb...

Based on analysis of basic cubic spline interpolation, the clamped cubic spline interpolation is generalized in this paper. The methods are presented on the condition that the first derivative and second derivative of arbitrary node are given. The Clamped spline and Curvature-adjusted cubic spline are also generalized. The methods are presented on the condition that the first derivatives of arb...

Wave equation is one of the second order linear hyperbolic equation. Telegraph as a special case wave has interesting point to investigate in numerical view. In this paper, we consider methods for dimensional telegraph by using cubic B-spline collocation method. Collocation method solve partial differential model problem. Cubic spline interpolation an third polynomial. This polynomial interpola...

Based on the matrix perturbation technique. a fast-fitting algorithm using uniform cubic B-spline curves is presented. Our algorithm entails much less floating-point operations when compared with Gaussian elimination method. In addition, our result can be applied to solve the closed cubic B-spline curve-fitting problem. Experimental results are included for a practical version. These experiment...

introduction relative dose computation is a necessary step in radiation treatment planning. therefore, finding an approach that is both fast and accurate seems to be necessary. the purpose of this work was to investigate the feasibility of natural cubic spline to reconstruct dose maps for linear accelerator radiation treatment fields in comparison with those of the simulation. materials and met...