A Generalization of 2-Periodic Trigonometric Interpolation

It is well-known that the interpolation theory plays an important role in many fields of computer vision, especially in surface reconstruction and Image processing. In this paper, we introduce a new kind of 2-period interpolation of functions with period 2ß at the nodes x k = x k;n = kß=n; (k = 0; 1; \Delta \Delta \Delta ; 2n \Gamma 1). We find out the necessary and sufficient conditions for regularity of this new interpolation problem. Moreover, a closed form expression for the interpolation polynomial is given. Our interpolation is of more practical significance. Our results provide the theoretical basis for using our interpolation in practical problems. Key Words: Interpolation, Trigonometric polynomial, Regularity, Computer vision. 1 Introduction It is well-known that the interpolation theory plays an important role in many fields of computer vision, especially in surface reconstruction and Image processing. In many practical This work was partially supported by the Chinese N..