We provide an overview of spline and wavelet techniques with an emphasis on applications in pattern recognition. The presentation is divided in three parts. In the first one, we argue that the spline representation is ideally suited for all processing tasks that require a continuous model of the underlying signals or images. We show that most forms of spline fitting (interpolation, least-square...

i=0 Pn n=0 bijB m i (u)B n j (v) of bi-degree (m;n) has total degree m + n, however, the class of Gmn(u; v) is a subset of polynomials of total degree m + n. G (resp G) continuity implies curve segments share the same tangent(curvature) at join points(knots). In each of the G and G constructions, we develop a spline curve family whose member satis es given interpolation conditions. Each family ...

We construct a suitable B-spline representation for a family of bivariate spline functions with smoothness r ≥ 1 and polynomial degree 3r − 1. They are defined on a triangulation with PowellSabin refinement. The basis functions have a local support, they are nonnegative and they form a partition of unity. The construction involves the determination of triangles that must contain a specific set ...

We use a combination of both symbolic and numerical techniques to construct several degree bounded G0 and G1 continuous, piecewise spline approximations of real implicit algebraic surfaces for both computer graphics and geometric modeling. These approximations are based upon an adaptive triangulation (a G0 planar approximation) of the real components of the algebraic surface, and include both s...

The concept of symmetric recursive algorithm leads to new, sdimensional spline spaces. We present a general scheme for constructing a collection of multivariate S-splines with k-l continuous derivatives whose linear span contains all polynomials of degree at most k . This scheme is different from the one developed earlier by Dahmen and Micchelli and, independently, by Höllig, which was based on...