Image reconstruction by convolution with symmetrical piecewise nth-order polynomial kernels

The reconstruction of images is an important operation in many applications. From sampling theory, it is well known that the sine-function is the ideal interpolation kernel which, however, cannot be used in practice. In order to be able to obtain an acceptable reconstruction, both in terms of comput...

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Bibliographic Details
Published inIEEE transactions on image processing Vol. 8; no. 2; pp. 192 - 201
Main Authors Meijering, E.H.W., Zuiderveld, K.J., Viergever, M.A.
Format Journal Article
LanguageEnglish
Published New York, NY IEEE 01.02.1999
Institute of Electrical and Electronics Engineers
Subjects
Applied sciences
Convolution
Exact sciences and technology
Hardware
Image analysis
Image processing
Image reconstruction
Image sampling
Information, signal and communications theory
Interpolation
Kernel
Kernels
Mathematical analysis
Mathematical models
Polynomials
Reconstruction
Signal processing
Spectra
Telecommunications and information theory
Testing
Interpolation
Convolution
Image processing
Sampling
Image reconstruction
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Summary:The reconstruction of images is an important operation in many applications. From sampling theory, it is well known that the sine-function is the ideal interpolation kernel which, however, cannot be used in practice. In order to be able to obtain an acceptable reconstruction, both in terms of computational speed and mathematical precision, it is required to design a kernel that is of finite extent and resembles the sinc-function as much as possible. In this paper, the applicability of the sine-approximating symmetrical piecewise nth-order polynomial kernels is investigated in satisfying these requirements. After the presentation of the general concept, kernels of first, third, fifth and seventh order are derived. An objective, quantitative evaluation of the reconstruction capabilities of these kernels is obtained by analyzing the spatial and spectral behavior using different measures, and by using them to translate, rotate, and magnify a number of real-life test images. From the experiments, it is concluded that while the improvement of cubic convolution over linear interpolation is significant, the use of higher order polynomials only yields marginal improvement.
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ISSN:1057-7149
1941-0042
DOI:10.1109/83.743854