Finally, the SUSAN algorithm and the six other methods mentioned above were looked at with respect to their multi-scale properties. As a filter's main smoothing parameter is varied from no smoothing to a large amount of smoothing, the number of image features (e.g., edges) should gradually be reduced. Ideally, before a feature's disappearance, it should not shift its position at all. (See [75] for an excellent introduction to scale-space filtering.) However, scale-space analysis of most noise filters and feature detectors shows different feature positions at different scales.
To produce the results shown in Figure 43, the seven noise filters were run on a 1D test image taken from a single line of a real image. The filters were either run at a variety of scales, or iterated, to give increased smoothing of the original image; each horizontal line in each final image represents a filter's output at a particular scale/iteration number, with least filtering at the bottom of each image. To give added clarity to the results an edge finder (the SUSAN edge finder, running with a 3 by 3 mask, with brightness threshold set to 5) is run on each output image, showing how image features evolve over different scales.
Figure 43: Scale-space analysis of five noise filters and the Canny edge
detector on an image formed from a single line of a real test
image. The bottom of each image corresponds to the smallest smoothing
scale.
The median and KNN filters quickly converged so that they were not
suitable for scale-space analysis. The other five filters' outputs are
shown. For Gaussian filtering, the scale of the smoothing was varied
to achieve different scales. In the other four cases iteration was
used. The SMCM filter had k=20 and SUSAN had t=20 and
. Also, the complete Canny edge detector [9]
was applied at different smoothing scales.
The results show that Canny (which includes Gaussian filtering), Gaussian filtering and midrange filtering have noticeable scale-space feature drift and that GIW, SMCM and SUSAN filtering have very little scale-space feature drift. Close inspection reveals the least drift with the SUSAN filter.