DIGITAL-FILTERS ASSOCIATED WITH BIVARIATE BOX SPLINE-WAVELETS

Battle-Lemarie's wavelet has a nice generalization in a bivariate sett ing. This generalization is called bivariate box spline wavelets. The magnitude of the filters associated with the bivariate box spline wave lets is shown to converge to an ideal high-pass filter when the degree of the bivariate box spline functions increases to co. The passing an d stopping bands of the ideal filter are dependent on the structure of the box spline function. Several possible idea! filters are shown. Wh ile these filters work for rectangularly sampled images, hexagonal box spline wavelets and filters are constructed to process hexagonally sa mpled images. The magnitude of the hexagonal filters converges to an i deal filter. Both convergences are shown to be exponentially fast. Fin ally, the computation and approximation of these filters are discussed . (C) 1997 SPIE and IS&T.