Two-Dimensional Cubic Convolution

Stephen E. Reichenbach, Frank Geng

Research output: Contribution to journalArticlepeer-review

83 Scopus citations


This paper develops two-dimensional (2-D), nonseparable, piecewise cubic convolution (PCC) for image interpolation. Traditionally, PCC has been implemented based on a one-dimensional (1-D) derivation with a separable generalization to two dimensions. However, typical scenes and imaging systems are not separable, so the traditional approach is suboptimal. We develop a closed-form derivation for a two-parameter, 2-D PCC kernel with support [-2, 2] × [-2, 2] that is constrained for continuity, smoothness, symmetry, and flat-field response. Our analyses using several image models, including Markov random fields, demonstrate that the 2-D PCC yields small improvements in interpolation fidelity over the traditional, separable approach. The constraints on the derivation can be relaxed to provide greater flexibility and performance.

Original languageEnglish (US)
Pages (from-to)857-865
Number of pages9
JournalIEEE Transactions on Image Processing
Issue number8
StatePublished - Aug 2003


  • Cubic convolution
  • Image reconstruction
  • Image/video processing
  • Interpolation and spatial transformations

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design


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