In this section the desired qualities of feature detectors are explained. The criteria eventually given have a slightly different emphasis from those previously used.
In [9] three criteria for edge detection are given. These have been used in similar form in a good deal of vision research. They are:
These criteria are equally appropriate for two dimensional feature detection, except for the complication that arises from using the term ``correct position'' in Criterion 2. There are many mathematical descriptions of the two dimensional image structure which define a ``corner'' or more general feature, leading to a lack of one agreed definition of the exact location of a feature. Thus in the case of two dimensional features, measuring fine localization error is not appropriate. However, it will be seen later that the error in localizing two dimensional features is often several pixels with some existing algorithms, greater even than the expected variation in positions determined by hand.
The purpose of developing new feature detectors was that they should be appropriate to being used as part of a real time system using real image sequences. Therefore it has become apparent that for the purpose of this work, one final criterion is important;
Obviously this criterion must not be allowed to dominate the development of a feature detector to an extent that the quality of the results is adversely affected. However a fast algorithm performing well in the other criteria is more desirable than a slow one.
Canny has formulated his criteria mathematically (in [8] and [9]). He uses the criteria functionals to derive ``optimized'' edge filters for each image type. Criteria 1 and 2 are clearly the most important ones in terms of ``optimizing'' the filter. Later analysis shows how the SUSAN brightness comparison function has been optimized to give the lowest number of false negatives and false positives. In the case of localization, the spatial domain part of the SUSAN detectors does not introduce any new concepts, and, following Canny and others, either a Gaussian or square distribution may be used (see later). Criterion 3 has not been of relevance in this work, as multiple responses have not been a problem at all. Finally, as will be seen, the SUSAN feature detectors are extremely computationally efficient.
In [71] a similar set of criteria are defined, not for optimizing filters, but for comparing the outputs of different edge detectors. There has been very little work on the area of objective quantitative tests for feature detectors. In [71] four quantitative criteria are defined, those being proportional to the number of false negatives, the number of false positives, the number of multiple detections and the number of incorrectly localized pixels. A linear combination of these measures is then used to obtain one quantity, the ``failure measure'' or ``FM''. The weights used to create this weighted sum are found according to a synthesis of some simple minimization rules with the constraint that the resulting edges found using this sum correspond to the best edges judged by eye. The weights will also depend on the proposed use of the reported edges.
The authors are of the opinion that this method of calculating the quality of an edge filter is not very meaningful, as the measures defined in [71] are found before post-processing takes place. Non-maximum suppression (a common enough operation) will normally eliminate multiple detections of a single edge completely. Binary thinning (particularly when continuously taking the initial response into account, as described in [63]) will greatly reduce the number of false negatives and false positives. All that remains is the localization error. Unfortunately, in the scheme described, the importance given to this error is between three and ten times less than that given to the number of false negatives or false positives.
However, in the absence of a better comparative method in the
literature, quantitative tests have been carried out using the FM
scheme, comparing the output from the first stage of the SUSAN edge
detector with the four filters tried in [71], namely,
Sobel, Prewitt, Roberts and the ``three-point energy
model'' (see [67], [50],
[51] and [72]). A test image identical to
the image described was created (i.e. a vertical step edge with added
Gaussian noise) giving a signal to noise ratio of 14.79. The
performance of the initial stage of the SUSAN detector was evaluated
for the four criteria defined; the result was that the SUSAN edge
detector gave FMs which were better than those obtained with the other
four detectors, independent of the set of weights used. Note that the
algorithms compared here with the first stage of SUSAN represent the
first (or enhancement) stage of edge detection, rather than complete
edge detectors, as this is appropriate to the comparative method
developed in [71].
It is worth noting here that in the absence of multiple features the SUSAN principle bypasses the ``uncertainty principle'' which applies to most feature detectors (and most obviously the Gaussian based ones) with respect to Canny's first and second criteria. This well understood problem means that the better the detection quality (including noise suppression) then the worse the localization of the detected feature. In the case of the SUSAN feature detectors, however, it is clear that the localization of the features is independent of the mask size, as long as no other features are found within the mask's region. Thus there is no conflict here between the two most ``important'' criteria.