This chapter reviews the extensive and comprehensive literature on B-Splines. In the forthcoming text emphasis is given to hierarchy and formal definition of polynomial interpolation with specific focus to the subclass of functions that are called B-Splines. Also, the literature is reviewed with emphasis on methodologies and applications of B-Splines within a wide array of scientific disciplines. The review is conducted with the intent to inform the reader and also to acknowledge the merit of the scientific community for the great effort devoted to B-Splines. The chapter concludes emphasizing on the proposition that the unifying theory presented throughout this book has for what concerns two specific cases of B-Spline functions: univariate quadratic and cubic models.
Literature: Methodologies And Applications
Bio-signals and diagnostic images are collected routinely in time series. Within this context, the development of innovative approaches for signal interpolation assumes relevance and usefulness for the research community. Novel interpolation approaches are thus important in order to analyzing reliably the time series. Also, many image processing analysis tools make use of interpolation functions. B-Splines were demonstrated to be excellent interpolators (De Boor, 1978; Unser et al., 1993a, 1993b) and they improve significantly the interpolation error with respect to linear paradigms which are computationally less demanding. Quadratic and cubic B-Splines offer considerable approximation improvement over the linear paradigm, producing a 33.9% gain, while quintic and septic B-Splines do improve approximation over the cubic functions only slightly (3-8%) when compared to their computational demand (Mijering et al., 1999).