The Cascade of Classifiers

The performance of a single classifier is not suitable for object classification, since it produces a high hit rate, e.g., 0.999, but also a high error rate, e.g., 0.5. Nevertheless, the hit rate is significantly higher than the error rate. To construct an overall good classifier, several classifiers are arranged in a cascade, i.e., a degenerated decision tree. In every stage of the cascade, a decision is made whether the image contains the object or not. This computation reduces both rates. Since the hit rate is close to one, their multiplication results also in a value close to one, while the multiplication of the smaller error rates approaches zero. Furthermore, this speeds up the whole classification process, since large parts of the image do not contain relevant data. These areas can be discarded quickly in the first stages.

Figure: The first three stages of a cascade of classifiers to detect the object volksbot. Every stage contains several simple classifier trees that use Haar-like features with a threshold thr. and return values of $\sum{h(x)}$. $h(x)$ is determined by the path through the trees.

An overall effective cascade is learned by a simple iterative method. For every stage, the classification function $h(x)$ is learned until the required hit rate is reached. The process continues with the next stage using the correctly classified positive and the currently misclassified negative examples. These negative examples are random image parts generated from the given negative examples that pass the previous stages and thus are misclassified. This bootstrapping process is the most time consuming of the training phase. The number of CARTs used in each classifier may increase with additional stages. Fig. shows an example cascade of classifiers for detecting a volksbot in 2D depth images, whose results are given in Table .