In this paper we show that the best constrained degree reduction of a given Bézier curve f of degree from n to m with C α−1-continuity at the boundary in L 2-norm is equivalent to the best weighted Euclidean approximation of the vector of Bernstein–Bézier (BB) coefficients of f from the vector of degree raised BB coefficients of polynomials of degree m with… (More)
In the implementation of subdivision scheme, three of the most important issues are smoothness, size of support, and approximation order. Our objective is to introduce an improved ternary 4-point approximating subdivision scheme derived from cubic polynomial interpolation, which has smaller support and higher smoothness, comparing to binary 4-point and… (More)
A new class of subdivision schemes is presented. Each scheme in this class is a quasi-interpolatory scheme with a tension parameter , which reproduces polynomials up to a certain degree. We find that these schemes extend and unify not only the well-known Deslauriers–Dubuc interpolatory schemes but the quadratic and cubic B-spline schemes. This paper… (More)
In this paper, we propose a level set based energy functional , the minimization of which results in simultaneous background modeling, foreground segmentation, and contour smoothing. The simultaneous dealing of background modeling and foreground segmentation has the effect that the two processes constrain each other positively, such that a good estimate of… (More)
In recent years high quality interaction devices have become very popular in our environment. The industries are also currently undergoing rapid change and various technologies have been explored to enable these capabilities. Projection systems using beam projectors and laser pointer became the ubiquitous infrastructure for command technology. Group… (More)
In the work, we rebuild the masks of well-known interpolatory symmetric subdivision schemes-binary 2n-point inter-polatory schemes, the ternary 4-point interpolatory scheme using only the symmetry and the necessary condition for smoothness and the butterfly scheme, and the modified butterfly scheme using the factorization property.
We use the matrices of transformations between Chebyshev and Bernstein basis and the matrices of degree elevation and reduction of Chebyshev polynomials to present a simple and efficient method for r times degree elevation and optimal r times degree reduction of Bézier curves with respect to the weighted L 2-norm for the interval [0, 1], using the weight… (More)
In this paper, we propose an efficient approximation algorithm using multilevel B-splines based on quasi-interpolants. Multilevel technique uses a coarse to fine hierarchy to generate a sequence of bicubic B-spline functions whose sum approaches the desired interpolation function. To compute a set of control points, quasi-interpolants gives a procedure for… (More)