Fast Anisotropic Gauss Filters

We derive the decomposition of the anisotropic Gaussian in a one dimensional Gauss filter in the x-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 covolution and for recursive filtering is proposed. Also directed derivative filters are demonstrated. For the recursive implementation, filtering an 512x512 image is performed within 40 msec on a current state of the art PC, gaining over 3 times in performance for a typical filter, independent of the standard deviation and orientation of the filter. Accuracy of the filters is still reasonable when compared to truncation error or recursive approximation error. The anisotropic Gaussian filtering method allows fast calculation of edge applications, the normal anisotropic convolution scheme is more advantageous with application in the detection of dashed lines in engineering drawing. The recursive implementation is more atrractive in feature detection application, for instance in affine invariant edge and ridge detection in computer vision. The proposed computational filtering method enables the practical applicability of orietation scale space analysis