The problem of interpolation of discrete set of data on the interval [a, b] representing the function f is investigated. A family of C splines with one free generating function is introduced in order to solve this problem. Cubic C splines belong to this family. The required conditions which must satisfy the generating function in order to obtain explicit interpolants are presented and examples ...

Image registration is inherently ill-posed, and lacks a unique solution. In the context of medical applications, it is desirable to avoid solutions that describe physically unsound deformations within the patient anatomy. Among the accepted methods of regularizing non-rigid image registration to provide solutions applicable to medical practice is the penalty of thin-plate bending energy. In thi...

1 Summary The extraction of roof edges requires the reconstruction of the original signal from a lattice of sampled values of grey level (i.e. the sampled image). This is an ill-posed task and therefore, adequate constraints of regularization have to be incorporated. A scheme employing one-dimensional Regularized Cubic B-Spline (RCBS) tting has been used successfully on the task of step edge de...

Edge detection attempts to reconstruct 3-D physical edges from a 2-D image. It is therefore an ill-posed problem, and a regularization procedure is required to convert it into a well-posed problem. This procedure introduces a regularization parameter for adjusting the extent of the regularization eeect: the larger the value of is, the stronger the regularization eeect. Therefore, could be inter...

Achieving accurate interpolation is an important requirement for many signal-processing applications. While nearest-neighbor and linear interpolation methods are popular due to their native GPU support, they unfortunately result in severe undesirable artifacts. Better interpolation methods are known but lack a native GPU support. Yet, a particularly attractive one is prefiltered cubicspline int...

In the present paper, the existence and uniqueness of deficient discrete cubic spline interpolant by matching the given function and first order difference at the intermediate points between successive mesh points for a uniform mesh has been discussed and also a error estimate concerning this deficient discrete cubic spline interpolant is obtained