Interpolation by Two-Dimensional Cubic Convolution

Jiazheng Shi, Stephen E. Reichenbach

Research output: Contribution to journalConference articlepeer-review

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 - 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

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

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