  We propose a new Arithmetic Distribution Neural Network (ADNN) for learning
the distributions of temporal pixels during background subtraction. In our
ADNN, the arithmetic distribution operations are utilized to propose the
arithmetic distribution layers, including the product distribution layer and
the sum distribution layer. Furthermore, in order to improve the accuracy of
the proposed approach, an improved Bayesian refinement model based on
neighboring information, with a GPU implementation, is introduced. In the
forward pass and backpropagation of the proposed arithmetic distribution
layers, histograms are considered as probability density functions rather than
matrices. Thus, the proposed approach is able to utilize the probability
information of the histogram and achieve promising results with a very simple
architecture compared to traditional convolutional neural networks. Evaluations
using standard benchmarks demonstrate the superiority of the proposed approach
compared to state-of-the-art traditional and deep learning methods. To the best
of our knowledge, this is the first method to propose network layers based on
arithmetic distribution operations for learning distributions during background
subtraction.
