Simplified 2-D Cubic Spline Interpolation Scheme Using Direct Computation Algorithm

doi:10.1109/TIP.2010.2050723

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Simplified 2-D Cubic Spline Interpolation Scheme Using Direct Computation Algorithm

2010-11-01

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DOI：10.1109/TIP.2010.2050723

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Abstract

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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.

Keywords:

Cubic spline interpolation (CSI)

fast Fourier transform (FFT)

image coding

interpolation

Winograd discrete Fourier transform (WDFT)

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