  Statistical features, such as histogram, Bag-of-Words (BoW) and Fisher
Vector, were commonly used with hand-crafted features in conventional
classification methods, but attract less attention since the popularity of deep
learning methods. In this paper, we propose a learnable histogram layer, which
learns histogram features within deep neural networks in end-to-end training.
Such a layer is able to back-propagate (BP) errors, learn optimal bin centers
and bin widths, and be jointly optimized with other layers in deep networks
during training. Two vision problems, semantic segmentation and object
detection, are explored by integrating the learnable histogram layer into deep
networks, which show that the proposed layer could be well generalized to
different applications. In-depth investigations are conducted to provide
insights on the newly introduced layer.
