The single-feature-based background model often fails in complex scenes, since a pixel is better described by several features, which highlight different characteristics of it. Therefore, the multi-feature-based background model has drawn much attention recently. In this paper, we propose a novel multi-feature-based background model, named stability of adaptive feature (SoAF) model, which utilizes the stabilities of different features in a pixel to adaptively weigh the contributions of these features for foreground detection. We do this mainly due to the fact that the features of pixels in the background are often more stable. In SoAF, a pixel is described by several features and each of these features is depicted by a unimodal model that offers an initial label of the target pixel. Then, we measure the stability of each feature by its histogram statistics over a time sequence and use them as weights to assemble the aforementioned unimodal models to yield the final label. The experiments on some standard benchmarks, which contain the complex scenes, demonstrate that the proposed approach achieves promising performance in comparison with some state-of-the-art approaches.

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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.