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.