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 idea l interpolation kernel which, however, cannot be used in practice, In order to be able to obtain an acceptable reconstruction, both in terms of comput ational speed and mathematical precision, it is required to design a kernel that is of finite extent and resembles the sinc-function as much as possib le. In this paper, the applicability of the sine-approximating symmetrical piecewise,,th-order polynomial kernels is investigated in satisfying these requirements, After the presentation of the general concept, kernels of fir st, 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, an d by using them to translate, rotate, and magnify a number of real-life tes t images, From the experiments, it is concluded that while the improvement of cubic convolution over linear interpolation is significant, the use of h igher order polynomials only yields marginal improvement.