Mathematical analysis for CSI scheme with the interpolation kernel size increased

• Published in: IET image processing 2017-08, Vol.11 (8), p.595-604
• Main Authors: Hong, Shao-Hua, Wang, Lin, Lin, Tsung-Ching, Truong, Trieu-Kien
• Format: Article
• Language: English
• Subjects: arithmetic operation; computational complexity; CSI scheme; cubic convolution interpolation function; cubic‐spline interpolation scheme; discrete image data resampling; image sampling; interpolation; interpolation kernel size selection; least squares approximations; least‐square method; mathematical analysis; Research Article; splines (mathematics)
• ISSN: 1751-9659; 1751-9667; 1751-9667
• DOI: 10.1049/iet-ipr.2016.0512

The cubic-spline interpolation (CSI) scheme is known to be designed to resample the discrete image data based on the least-square method in conjunction with the cubic convolution interpolation (CCI) function. In this CSI scheme, the improved quality of resampling can be achieved as the interpolation kernel size increases. However, the improvement of the performance gets less and less. This means that the performance of the CSI scheme has not been significantly improved and converges toward a constant value when the interpolation kernel size exceeds a certain value. A proof of this result is given in this study and has never been seen in the literature to the authors' knowledge. Moreover, this study analyses the relationship between the performance and computational complexity of the CSI schemes with different interpolation kernel sizes and compares them from a structural point of view. Simulation results indicate that it is in agreement with the theoretic derivations. Since the arithmetic operations required are increasing linearly with the increment of the interpolation kernel size, selecting an interpolation kernel size gives the best trade-off between the performance and computational complexity in practical applications. However, the optimum choice of the interpolation kernel size depends crucially on effective demand.