Interpolation by Two-Dimensional Cubic Convolution

Jiazheng Shi, Stephen E Reichenbach

Research output: Contribution to journalConference article

Abstract

This paper presents results of image interpolation with an improved method for two-dimensional cubic convolution. Convolution with a piecewise cubic is one of the most popular methods for image reconstruction, but the traditional approach uses a separable two-dimensional convolution kernel that is based on a one-dimensional derivation. The traditional, separable method is sub-optimal for the usual case of non-separable images. The improved method in this paper implements the most general non-separable, two-dimensional, piecewise-cubic interpolator with constraints for symmetry, continuity, and smoothness. The improved method of two-dimensional cubic convolution has three parameters that can be tuned to yield maximal fidelity for specific scene ensembles characterized by autocorrelation or power-spectrum. This paper illustrates examples for several scene models (a circular disk of parametric size, a square pulse with parametric rotation, and a Markov random field with parametric spatial detail) and actual images -presenting the optimal parameters and the resulting fidelity for each model. In these examples, improved two-dimensional cubic convolution is superior to several other popular small-kernel interpolation methods.

Original languageEnglish (US)
Pages (from-to)135-146
Number of pages12
JournalProceedings of SPIE - The International Society for Optical Engineering
Volume5108
DOIs
StatePublished - Dec 1 2003
EventPROCEEDINGS OF SPIE SPIE - The International Society for Optical Engineering: Visual Information Processing XII - Orlando, FL, United States
Duration: Apr 21 2003Apr 21 2003

Fingerprint

Convolution
convolution integrals
interpolation
Interpolation
Interpolate
Nonseparable
Fidelity
Image Interpolation
repeaters
Kernel Methods
Interpolation Method
Optimal Parameter
Image Reconstruction
image reconstruction
Power spectrum
Image reconstruction
Power Spectrum
Autocorrelation
continuity
Random Field

Keywords

  • Cubic convolution
  • Digital image processing
  • Image reconstruction
  • Interpolation
  • Resampling

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

Cite this

Interpolation by Two-Dimensional Cubic Convolution. / Shi, Jiazheng; Reichenbach, Stephen E.

In: Proceedings of SPIE - The International Society for Optical Engineering, Vol. 5108, 01.12.2003, p. 135-146.

Research output: Contribution to journalConference article

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