It is shown that there is an optimal finite linear combination of B-splines, denominated modified B-splines, such that a pertinent low frequency condition called M−flatness is satisfied. A profound relationship of the modified B-splines with the Beta distribution implies an asymptotic sampling theorem with exact reconstruction requiring only small oversampling.

This paper presents a new kind of uniform splines, called hyperbolic polynomial B-splines, generated over the space Ω = span{sinh t, cosh t, tk−3, tk−4, . . . , t,1} in which k is an arbitrary integer larger than or equal to 3. Hyperbolic polynomial B-splines share most of the properties as those of the B-splines in the polynomial space. We give the subdivision formulae for this new kind of cur...

Easy to construct and optimally convergent generalisations of B-splines unstructured meshes are essential for the application isogeometric analysis domains with non-trivial topologies. Nonetheless, especially hexahedral meshes, construction smooth basis functions is still an open question. We introduce a simple partition unity that yields blended B-splines, referred as SB-splines, on semi-struc...

We present an approach for modeling and filtering digitally scanned images. The digital contour of an image is segmented to identify the linear segments, the nonlinear segments and critical corners. The nonlinear segments are modeled by B-splines. To remove the contour noise, we propose a weighted least q m s model to account for both the fitness of the splines as well as their approximate cur...

In this paper we consider discrete splines S(j), j ∈ Z, with equidistant nodes which may grow as O(|j|s) as |j| → ∞. Such splines are relevant for the purposes of digital signal processing. We give the definition of discrete B-splines and describe their properties. Discrete splines are defined as linear combinations of shifts of the B-splines. We present a solution to the problem of discrete sp...

In this work we consider the problem of recovering non-uniform splines from their projection onto spaces of algebraic polynomials. We show that under a certain Chebyshev-type separation condition on its knots, a spline whose inner-products with a polynomial basis and boundary conditions are known, can be recovered using Total Variation norm minimization. The proof of the uniqueness of the solut...