Interpolation by two-dimensional cubic convolution

Jiazheng Shi; Stephen E. Reichenbach

doi:10.1117/12.497405

8 August 2003 Interpolation by two-dimensional cubic convolution

Jiazheng Shi, Stephen E. Reichenbach

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Proceedings Volume 5108, Visual Information Processing XII; (2003) https://doi.org/10.1117/12.497405
Event: AeroSense 2003, 2003, Orlando, Florida, United States

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.

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Jiazheng Shi and Stephen E. Reichenbach "Interpolation by two-dimensional cubic convolution", Proc. SPIE 5108, Visual Information Processing XII, (8 August 2003); https://doi.org/10.1117/12.497405

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KEYWORDS

Convolution

Filtering (signal processing)

Image restoration

Image processing

Performance modeling

Digital image processing

Infrared imaging

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