Abstract

We derive the decomposition of the anisotropic Gaussian in a one dimensional Gauss filter in the x-direction followed by a one di- mensional filter in a non-orthogonal direction . 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 512 × 512 image is per- formed within 65 msec, independent of the standard deviations and ori- entation 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 and ridge maps, with high spatial and angular accuracy. For tracking applications, the normal anisotropic convolution scheme is more advan- tageous, with applications in the detection of dashed lines in engineering drawings. The recursive implementation is more attractive in feature detection applications, for instance in afine invariant edge and ridge de- tection in computer vision. The proposed computational filtering method enables the practical applicability of orientation scale-space analysis.