The steerable detectors are based on gaussian derivates. The complexity of the filters depends on the highest order derivate used, whcih for the ridge detectors are the 4th order derivates of the gaussian. For 4th order steerable ridge detectors rotations are computed using 8 pre-calculated base templates. The base templates are convolutions of the original image with 2nd and 4th derivates of the gaussian. The animation shows the impulse response of a 4th order detector.
2nd and 4th order ridge 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 two images below show typical templates for the two orders.
The following images show the results of filtering a dna cryo electron micrograph with a conventional ridge detector as well as 2nd and 4th order steerable ridge detectors. The 4th order steerable detector yields the best result.