Two-Dimensional Cubic Convolution

Research output: Contribution to journalArticle

63 Citations (Scopus)

Abstract

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
Volume12
Issue number8
DOIs
StatePublished - Aug 1 2003

Fingerprint

Convolution
Interpolation
Image Interpolation
Image Model
Nonseparable
Imaging System
Imaging systems
Fidelity
Random Field
Two Parameters
Smoothness
Two Dimensions
Closed-form
Interpolate
Flexibility
kernel
Symmetry
Demonstrate

Keywords

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

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design

Cite this

Two-Dimensional Cubic Convolution. / Reichenbach, Stephen E.; Geng, Frank.

In: IEEE Transactions on Image Processing, Vol. 12, No. 8, 01.08.2003, p. 857-865.

Research output: Contribution to journalArticle

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