Fast Anisotropic Gauss Filtering

We derive the decomposition of the anisotropic Gaussian in a one dimensional Gauss filter in the x-direction followed by a one dimensional filter in a non-orthogonal direction phi. So also the anisotropic Gaussian can be decomposed by dimension. This appears to be extremely efficient from a computing perspective. An implementation scheme for normal convolution and for recursive filtering is proposed. Also directed derivative filters are demonstrated.

For the recursive implementation, filtering an 512x512 image is performed within 65 msec, independent fo the standard deviations and orientation of the filter. Accuracy of the filters is still reasonable when compared to truncation error or recrusive approximation error.

The anisotropic Gaussian filtering method allows fast calculation of edge and ridge maps, with high spatial and angular accuracy. For tracking applications, the normal anisotropic convolution scheme is more advantageous, with applications in the detection of dashed lines in engineering drawings. The recursive implementation is more atrracttive in feature detecton applications, for instance in affine invariant edge and ridge detection in computer vision.