The two extremes of such a measure should correspond to the worst and the best or ideal classifier. The worst classifier, on one hand, may be defined as that which has no discrimination between positives and negatives. A positive will have equal chance of being interpreted as a positive or a negative , and vice-versa. Figure 4 illustrates examples of ROC curves for an ideal, good, poor and worst classifier. The worst classier has no discriminating ability between a flaw and noise.
Any input has equal probability of being called a flaw or noise.
This is the area of the entire graph that lies beneath the curve, and is designated . The advantage of is that it is objective, that is, it does not depend on the relative importance attached to POD and POFA values. One disadvantage of is that it underestimates the area beneath a complete ROC, especially when the points are not well spread across the ROC space. Further more, it depends a lot on the uninteresting part of the ROC curve, that is, where both POD and POFA tend to 1.0. This is illustrated in Figure 5.