Image interpolation by two-dimensional parametric cubic convolution

Jiazheng Shi, Stephen E Reichenbach

Research output: Contribution to journalArticle

62 Citations (Scopus)

Abstract

Cubic convolution is a popular method for image interpolation. Traditionally, the piecewise-cubic kernel has been derived in one dimension with one parameter and applied to two-dimensional (2-D) images in a separable fashion. However, images typically are statistically nonseparable, which motivates this investigation of nonseparable cubic convolution. This paper derives two new nonseparable, 2-D cubic-convolution kernels. The first kernel, with three parameters (designated 2D-3PCC), is the most general 2-D, piecewise-cubic interpolator defined on [-2, 2] × [-2, 2] with constraints for biaxial symmetry, diagonal (or 90° rotational) symmetry, continuity, and smoothness. The second kernel, with five parameters (designated 2D-5PCC), relaxes the constraint of diagonal symmetry, based on the observation that many images have rotationally asymmetric statistical properties. This paper also develops a closed-form solution for determining the optimal parameter values for parametric cubic-convolution kernels with respect to ensembles of scenes characterized by autocorrelation (or power spectrum). This solution establishes a practical foundation for adaptive interpolation based on local autocorrelation estimates. Quantitative fidelity analyses and visual experiments indicate that these new methods can outperform several popular interpolation methods. An analysis of the error budgets for reconstruction error associated with blurring and aliasing illustrates that the methods improve interpolation fidelity for images with aliased components. For images with little or no aliasing, the methods yield results similar to other popular methods. Both 2D-3PCC and 2D-5PCC are low-order polynomials with small spatial support and so are easy to implement and efficient to apply.

Original languageEnglish (US)
Pages (from-to)1857-1870
Number of pages14
JournalIEEE Transactions on Image Processing
Volume15
Issue number7
DOIs
StatePublished - Jul 1 2006

Fingerprint

Image Interpolation
Convolution
Interpolation
kernel
Nonseparable
Autocorrelation
Aliasing
Interpolation Method
Fidelity
Power spectrum
Symmetry
Rotational symmetry
Biaxial
Polynomials
Optimal Parameter
Closed-form Solution
Power Spectrum
Statistical property
One Dimension
Smoothness

Keywords

  • Cubic convolution
  • Image processing
  • Interpolation
  • Reconstruction
  • Resampling

ASJC Scopus subject areas

  • Software
  • Medicine(all)
  • Computer Graphics and Computer-Aided Design

Cite this

Image interpolation by two-dimensional parametric cubic convolution. / Shi, Jiazheng; Reichenbach, Stephen E.

In: IEEE Transactions on Image Processing, Vol. 15, No. 7, 01.07.2006, p. 1857-1870.

Research output: Contribution to journalArticle

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