  The design of complexity-aware cascaded detectors, combining features of very
different complexities, is considered. A new cascade design procedure is
introduced, by formulating cascade learning as the Lagrangian optimization of a
risk that accounts for both accuracy and complexity. A boosting algorithm,
denoted as complexity aware cascade training (CompACT), is then derived to
solve this optimization. CompACT cascades are shown to seek an optimal
trade-off between accuracy and complexity by pushing features of higher
complexity to the later cascade stages, where only a few difficult candidate
patches remain to be classified. This enables the use of features of vastly
different complexities in a single detector. In result, the feature pool can be
expanded to features previously impractical for cascade design, such as the
responses of a deep convolutional neural network (CNN). This is demonstrated
through the design of a pedestrian detector with a pool of features whose
complexities span orders of magnitude. The resulting cascade generalizes the
combination of a CNN with an object proposal mechanism: rather than a
pre-processing stage, CompACT cascades seamlessly integrate CNNs in their
stages. This enables state of the art performance on the Caltech and KITTI
datasets, at fairly fast speeds.
