Optimal generating kernels for image pyramids by piecewise fitting

A novel class of generating kernels for image pyramids is introduced. When these kernels are convolved with intensity functions of images, continuous piecewise surfaces composed of polynomial tensor products are fitted to the intensity functions. The fittings are optimal in the sense that the mean square error between them and the original intensity functions is minimized. Two members of the class are introduced, and symmetry, normalization, unimodality, and equal contribution properties are proved. These kernels possess attractive properties such as small window size, fast inverse transformation, and minimum error. Experiments show that they compare favorably with existing ones in terms of mean square error