Simplified 2-D Cubic Spline Interpolation Scheme Using Direct Computation Algorithm
It has been shown that the 2-D cubic spline interpolation (CSI) proposed by Truong et al. is one of the best algorithms for image resampling or compression. Such a CSI algorithm together with the image coding standard, e.g., JPEG, can be used to obtain a modified image codec while still maintaining a good quality of the reconstructed image for higher compression ratios. In this paper, a fast direct computation algorithm is developed to improve the computational efficiency of the original FFT-based 2-D CSI methods. In fact, this algorithm computes the 2-D CSI directly without explicitly calculating the complex division usually needed in the FFT or Winograd discrete Fourier transform (WDFT) algorithm. In addition, this paper describes a novel way to derivate the 2-D CSI from the 1-D CSI by using the row-column method. This new fast 2-D CSI provides a regular and simple structure based upon linear correlations. Therefore, it can be implemented by the use of a modification of Kung's pipeline structure and is naturally suitable for VLSI implementations. Experimental results show that the proposed new fast 2-D CSI algorithm can achieve almost the same CSI performance with much fewer arithmetic operations in comparison with existing efficient algorithms.
interpolation cubic spline interpolation (csi) image coding winograd discrete fourier transform (wdft) fast fourier transform (fft)