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The reconfiguration problem is considered a key challenge in distributed systems, especially in dynamic asynchronous message-passing systems. To keep the data reliability and availability in long-lived systems, any protocols should support reconfigurations, to dynamically add resources, or remove old and slow machines with newer faster ones. Previous results in reconfigurations either rely on consensus, or study the problem restricted to crash failures only. However, it is difficult to argue that real-world systems experience crash failures only. In this paper, we study the dynamic reconfiguration problem in fully asynchronous message-passing systems with Byzantine faults. We first specify dynamic Byzantine broadcast, and then specify a clean and explicit liveness condition. We show that dynamic Byzantine broadcast is solvable by presenting a dynamic Byzantine consistent broadcast algorithm and a dynamic Byzantine reliable broadcast algorithm.

Background subtraction has been widely used in the detection of a moving object from a still scene. Due to the uncertainty in the classification of the pixels in the foreground and background, we propose a novel fuzzy approach for background subtraction using fuzzy histograms based on fuzzy c-means clustering and the fuzzy nearness degree, called FCFN. In this method, the temporal characteristics of the pixels are described by a fuzzy histogram using the fuzzy c-means algorithm. The segmentation threshold is adaptively calculated according to the distribution of the fuzzy nearness degree of the individual pixel. Fuzzy adaptive background maintenance is adopted in the background update framework. The performance of the FCFN is evaluated against several state-of-the-art methods in the complex dynamic scenes. The experimental results demonstrate that the proposed method doubles the improvements in performance than the classic fuzzy background modeling methods and outperforms most state-of-the-art methods.