高斯混合模型為一普遍的前背景脫離技術，其即時性的模型更新方式可有效地解決動態背景問題。然而建立在即時更新上的背景模型會因長時間的像素變化，使得該模型因錯誤資訊不斷累積而造成前景判別的錯誤，產生了諸如前景消失等現象。即時性的更新方式強調了目前資訊的重要性，但卻忽略了過去時間所累積的資訊，使得前景偵測系統會隨著時間的增加而逐漸降低其辨識能力。故本論文考量不同長度時間下像素出現頻率的累積資訊，長時間像素出現頻率累積所產生的背景模型因為考量了過去時間的資訊，使其較僅以目前資訊進行更新的模型更具穩定性；而短時間的頻率所累積資訊可針對不規律雜訊及停留殘影等短暫時間內造成的問題進行背景模型修整。透過不同長度時間的模型建立方式不僅可將過去累積的資訊進行有效地利用更提高了背景模型在長時間下的穩定性。

Cumulants in time intervals with different durations are proposed for modeling dynamic backgrounds. Different from most background models using inter-frame updates to capture the time-dependent variation of a pixel, this work extracts the variation across a certain time interval, and compares the variation patterns revealed from the intervals of different durations. The advantages of the proposed method include the following: (1) interval-based features are more robust to background noises than single pixel-based features, (2) pattern variations across intervals of different duration can distinguish moving foregrounds from wavering backgrounds in a more reliable way than inter-frame pixel-based approaches. In addition to the proposed method, this thesis also proposes a solution to the false foregrounds often seen in inter-frame pixel-based background models. The proposed background model and solution are validated by experiments with videos of different scenes and scenarios.

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