  We demonstrate that it is possible to filter an image with an elliptic window
of varying size, elongation and orientation with a fixed computational cost per
pixel. Our method involves the application of a suitable global pre-integrator
followed by a pointwise-adaptive localization mesh. We present the basic theory
for the 1D case using a B-spline formalism and then appropriately extend it to
2D using radially-uniform box splines. The size and ellipticity of these
radially-uniform box splines is adaptively controlled. Moreover, they converge
to Gaussians as the order increases. Finally, we present a fast and practical
directional filtering algorithm that has the capability of adapting to the
local image features.
