Previously, in the Understanding detection with cascade classifiers section in Chapter 4, Detecting and Merging Faces of Mammals, we considered the problem of searching for a set of high-contrast features at various positions and various levels of magnification or scale. As we saw, Haar and LBP cascade classifiers solve this problem. Thus, we may say they are scale-invariant (robust to changes in scale). However, we also noted that these solutions are not rotation-invariant (robust to changes in rotation). Why? Consider the individual features. Haar-like features include edges, lines, and dots, which are all symmetric. LBP features are gradients, which may be symmetric, too. A symmetric feature cannot give us a clear indication of the object's rotation.

Now, let's consider solutions that are both scale-invariant and rotation-invariant. They must use asymmetric features called corners. A corner has brighter neighbors across one range of directions and darker...