A personal account of the author's encounters with multivariate splines during their early history. 1 Tensor product spline interpolation My first contact with multivariate splines occurred in August 1960. In my first year at the Harvard Graduate School, working as an RA for Garrett Birkhoff, I had not done too well but, nevertheless, had gotten married and so needed a better income than the RA...

This paper deals with fast image and video segmentation using active contours. Region based active contours using level-sets are powerful techniques for video segmentation but they suffer from large computational cost. A parametric active contour method based on B-Spline interpolation has been proposed in [1] to highly reduce the computational cost but this method is sensitive to noise. Here, w...

In this paper, we present an ef®cient sub-optimal algorithm for ®tting smooth planar parametric curves by G 1 arc splines. To ®t a parametric curve by an arc spline within a prescribed tolerance, we ®rst sample a set of points and tangents on the curve adaptively as well as with enough density, so that an interpolation biarc spline curve can be with any desired high accuracy. Then, we construct...

We consider using spline interpolation to improve the standard filtered back-projection (FBP) tomographic reconstruction algorithm. In particular, we propose to link the design of the filtering operator with the interpolation model that is applied to the sinogram. The key idea is to combine the ramp filtering and the spline fitting process into a single filtering operation. We consider three di...

A method for generating an interpolation closed G arc spline on a given closed point set is presented. For the odd case, i.e. when the number of the given points is odd, this paper disproves the traditional opinion that there is only one closed G arc spline interpolating the given points. In fact, the number of the resultant closed G arc splines fulfilling the interpolation condition for the od...