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Steerable Edge Detector
The steerable detectors are based on gaussian derivates. The complexity of the filters depends on the highest order derivate used, whcih for the edge detectors are the 5th order derivates of the gaussian. For 5th order steerable edge detectors rotations are computed using 12 pre-calculated base templates. The base templates are convolutions of the original image with 1st, 3rd, and 5th derivates of the gaussian. The animation shows the impulse response of a 5th order detector.
1st, 3rd, and 5th order edge detectors. Higher order detectors result in fewer false detections as well as more precise detection of the feature. This is due to the higher signal-to-noise ratio and orientation selectivity of the higher order detectors. The images below show typical templates for the different orders.

1st order

3rd order

5th order
The following images show the results of filtering a noisy test image with different orders of steerable edge detectors. The higher the order the detector is, the better the result.
Original image
1st order
3rd order
5th order