Open AccessMathematical analysis for CSI scheme with the interpolation kernel size increased
Author(s) -
Hong ShaoHua,
Wang Lin,
Lin TsungChing,
Truong TrieuKien
Publication year - 2017
Publication title -
iet image processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.401
H-Index - 45
eISSN - 1751-9667
pISSN - 1751-9659
DOI - 10.1049/iet-ipr.2016.0512
Subject(s) - kernel (algebra) , stairstep interpolation , mathematics , interpolation (computer graphics) , spline interpolation , nearest neighbor interpolation , image scaling , algorithm , multivariate interpolation , bicubic interpolation , trilinear interpolation , bilinear interpolation , computer science , artificial intelligence , statistics , discrete mathematics , image processing , image (mathematics)
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.