Many data mining tasks can be reformulated as optimization problems, in the solution of which approximation by surfaces plays a key role. The paper proposes a new efficient computational algorithm for spline surfaces over uniform grids. The algorithm is based on a recent result on approximation of a biquartic polynomial by bicubic ones, that ensures C2 continuity of the corresponding four bicub...

We present an iterative multiresolution algorithm for the translational and rotational alignment of digital images. An image is represented by an interpolating spline. Coarser versions of this continuous image model are obtained by using spline approximations at various scales (polynomial spline pyramid). We use a coarse-to-fine updating strategy to compute the alignment parameters iteratively,...

A family of fourth and second-order accurate numerical schemes is presented for the solution of nonlinear fourth-order boundary-value problems (BVPs) with two-point boundary conditions. Non-polynomial quintic spline functions are applied to construct the numerical algorithms. This approach generalizes nonpolynomial spline algorithms and provides a solution at every point of the range of integra...

A-splines are implicit real algebraic curves in Bernstein-B ezier (BB) form that are smooth. We use these in an algorithm for active contouring of images. One advantage of A-splines is that any change to the controlling weights only a ects the curve locally, which results in fast convergence. Our active A-splines are also level sets of a time-dependent function with the added exibility of a dyn...

A quadratic non-polynomial spline functions based method is developed to find approximations solution to a system of second-order boundary-value problems associated with obstacle, unilateral, and contact problems. The present approach has less computational cost and gives better approximations than those produced by other collocation, finite-difference and spline methods. Convergence analysis o...

Interrogative visualization refers to the process of interactive computer graphics display and accurate quantitative querying of physical data. Quantitative querying includes search for metric, combinato-rial and topological information. To support this paradigm, we build uniform, compact, co-registered representations (spline models) of multiple physical data elds over the same domain. Dense, ...

The evaluation of points and the computations of in¯ection points or cusps on a curve are often necessary in CAGD applications. When a curve is represented in a B-spline form, such computations can be made easier once it is transformed into a set of piecewise polynomial curves in power form. The usual practice of the transformation of a B-spline curve into a set of piecewise polynomial curves i...