Equiripple two-dimensional interpolation filters

Operations such as geometric image correction, feature matching, and coordinate system transformations require the resampling of two-dimensional data arrays to interpolate between the known regularly-spaced signal samples. A conventional approach is to apply consecutive 1- dimensional interpolating filters first across the array and then in the orthogonal direction to obtain the desired (d
x
, d
y
) shift. This approach is equivalent to employing a separable 2-dimensional filter with impulse response
h(m,n) = h_{1}(m) \cdot h_{2}(n)
. In the method presented here, the coefficients
{h(m,n)}
are generated simultaneously so that the resulting transfer function best matches the desired response in the sense of minimizing the peak amplitude and phase errors over a designated portion of the frequency plane. It will be demonstrated that these interpolation filters, which are not necessarily separable, may be made substantially smaller than the separable design for the same error performance. They require fewer multiplications in the signal processing operations than the separable 2 filters, and in some cases fewer than the cascaded application of two 1D filters.