We introduce a view–point invariant representation of moving object trajectories that can be used in video database applications. It is assumed that trajectories lie on a surface that can be locally approximated with a plane. Raw trajectory data is first locally–approximated with a cubic spline via least squares fitting. For each sampled point of the obtained curve, a projective invariant featu...

This paper develops a new family of convexity-preserving splines of order n, hereby entitled the CPn-spline, that preserves convexity when derivatives at the data points satisfy some reasonable conditions. The spline comprises four components: a constant term, a first order term, and two nth order binomials. A slope-averaging-method is proposed for the general implementation of the new spline. ...

We propose a parametric tensioned version of the FVS macro-element to control the shape of the composite surface and remove artificial oscillations, bumps and other undesired behaviour. In particular, this approach is applied to C1 cubic spline surfaces over a four-directional mesh produced by two-stage scattered data fitting methods.

A Recursive form cubic B-spline basis function is used as basis in B-spline collocation method to solve second linear singularly perturbed two point boundary value problem. The performance of the method is tested by considering the numerical examples with different boundary conditions. Results of numerical examples show the robustness of the method when compared with the analytical solution.

In this paper, G continuous cubic spline interpolation of data points in R, based on a discrete approximation of the strain energy, is studied. Simple geometric conditions on data are presented that guarantee the existence of the interpolant. The interpolating spline is regular, loop-, cuspand fold-free.

In this paper, the geometric interpolation of planar data points and boundary tangent directions by a cubic G2 Pythagorean-hodograph (PH) spline curve is studied. It is shown that such an interpolant exists under some natural assumptions on the data. The construction of the spline is based upon the solution of a tridiagonal system of nonlinear equations. The asymptotic approximation order 4 is ...

Cubic splines are commonly used in numerical analysis. It has also become popular in the analysis of computer experiments, thanks to its adoption by the software JMP 8.0.2 2010. In this paper a Bayesian version of the cubic spline method is proposed, in which the random function that represents prior uncertainty about y is taken to be a specific stationary Gaussian process and y is the output o...

Abstract Bézier splines are widely available in various systems with the curves and surface designs. In general, the Bézier spline can be specified with the Bézier curve segments and a Bézier curve segment can be fitted to any number of control points. The number of control points determines the degree of the Bézier polynomial. This paper presents a method which determines control points for Bé...

This paper is an overview of three spline approaches of degree one, two and three. It represents the review and comparative study of Linear, conic and cubic splines for the vectorization of outlines of the planar images. It has various phases including extracting outlines of images, detecting corner points from the detected outlines, and curve fitting. The idea of simulated annealing has been i...

This Paper proposed the characterization of atherosclerosis lesions in vivo using Magnetic Resonance Imaging (MRI). For this, it uses an energy minimization approach to equalize the contrast of MR image. To enable the use of voxel gray values for interpretation of disease, we created a new method, energy minimization with a spline model, to correct the severe (80%) intensity in homogeneity that...