DocumentCode :
1469299
Title :
Image reconstruction by convolution with symmetrical piecewise nth-order polynomial kernels
Author :
Meijering, Erik H W ; Zuiderveld, Karel J. ; Viergever, Max A.
Author_Institution :
Image Sci. Inst., Utrecht Univ., Netherlands
Volume :
8
Issue :
2
fYear :
1999
fDate :
2/1/1999 12:00:00 AM
Firstpage :
192
Lastpage :
201
Abstract :
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
Keywords :
convolution; image reconstruction; image sampling; interpolation; piecewise polynomial techniques; computational speed; cubic convolution; higher order polynomials; image reconstruction; image resampling; interpolation kernel; linear interpolation; mathematical precision; quantitative evaluation; quintic convolution; real-life test images; sampling theory; septic convolution; sine-function; spatial behavior; spectral behavior; symmetrical piecewise nth-order polynomial kernels; Convolution; Hardware; Helium; Image analysis; Image reconstruction; Image sampling; Interpolation; Kernel; Polynomials; Testing;
fLanguage :
English
Journal_Title :
Image Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1057-7149
Type :
jour
DOI :
10.1109/83.743854
Filename :
743854
Link To Document :
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