Recursive anisotropic 2-D Gaussian filtering based on a triple-axis decomposition

We describe a recursive algorithm for anisotropic 2-D Gaussian filtering, based on separating the filter into the cascade of three, rather two, 1-D filters. The filters operate along axes obtained by integer horizontal and/or vertical pixel shifts. This eliminates interpolation, which removes spatial inhomogeneity in the filter, and produces more elliptically shaped kernels. It also results in a more regular filter structure, which facilitates implementation in DSP chips. Finally, it improves matching between filters with the same eccentricity and width, but different orientations. Our analysis and experiments indicate that the computational complexity is similar to an algorithm that operates along two axes (<11 ms for a 512 x 512 image using a 3.2-GHz Pentium 4 PC). On the other hand, given a limited set of basis filter axes, there is an orientation dependent lower bound on the achievable aspect ratios.