Image enlargement using symmetric B-spline basis on closed periodic zone

Abstract

Aiming at the weakness of ignoring symmetry property and using complicated iterative algorithms to solve for interpolation coefficients in the existing time domain B-spline interpolation methods, this paper presents a novel B-spline interpolation method using symmetric B-spline basis on closed periodic zone where interpolation coefficients can be fast computed by parallel algorithms. First we shift naïve B-spline basis to establish symmetric B-spline basis, next we use orthogonality properties of complex exponentials to establish orthogonal B-spline basis on closed periodic zone and derive parallel computing formula for coefficients of orthogonal Bspline basis; we further use relation between coefficients of orthogonal B-spline basis and coefficients of symmetric B-spline basis to achieve parallel computing formulas for interpolation coefficients of symmetric B-spline basis. At last, we extend the method to image enlargement. Experiment results show that, the new theory established in this paper can be used to explain result of B-spline interpolation from standpoint of signal processing. The method presented in this paper can easily carry out parallel computation for interpolation coefficients of symmetric B-spline basis and brings no phase deviation to enlarged image. Compared with neighborhood-based bilinear and bicubic interpolation methods, the new method produces enlargement with higher Peak Signal to Noise Ratio (PSNR) and sharper visual quality.