觀測值為相依(dependent) 的分散式偵測直到現在仍然是一個困難且複雜的問題, 文獻 [16] 考
慮的是一種具有兩個感測器的串聯網路, 感測器1與感測器2之間具有共同的觀測值X2以及相對應之
條件獨立(conditionally independent) 的觀測值X1、X3, 而此種串聯網路系統的決策機制是: 感測
器1會先做出1個bit 的決策, 然後再把這個決策傳送給感測器2 , 而感測器2會利用這個決策的資訊
以及自身的觀測值來做出系統整體的最後決策。對於這種具有兩個感測器的串連偵測網路, 文獻 [16]
的作者推導出對於所有感測器來說的最佳化決策法則的必要條件。
現今對於保全的影像監控系統通常都是作為事件發生後的證據來源, 這樣的影像監控系統在事件
發生時並無法自動地提供即時的警報, 藉由文獻 [16] 之理論結果的啟發, 在相同的系統模型下我們推
導出不同期望值及不同變異數之高斯分佈下的相對最佳化決策法則, 並將此最佳化決策法則使用在有
重疊影像區域之分散式事件偵測的應用上, 如此一來本文的研究便能使影像監控系統可以自動地提供
即時的警報, 最後我們將此最佳化決策法則與另外兩個次佳方案的決策法則在此應用下比較其效能,
而實作的結果也確實驗證了最佳化決策法則的最佳性。

Distributed detection with dependent observations is still a difficult and complicated prob-
lem now. The work in [16] considers a tandem network with two sensors. Sensor 1 and sensor
2 have their common observation X2 and conditionally independent observations X1 and X3,
respectively. The mechanism for the decision of such tandem network is that sensor 1 makes
one-bit decision first and then sends its decision to sensor 2, after which sensor 2 makes the
final decision based on the sensor 1’s decision and its own observation. The authors in [16]
derived the necessary conditions for the optimal sensor decision rules for both sensors in this
two-sensor tandem detection network.
The video surveillance systems are usually a source of evidence nowadays after the occur-
rence of events. However, such video surveillance systems are unable to provide real time alerts
automatically when event occurs. Inspired by the theoretical results given in [16], we derived
the corresponding optimal decision rules for the case in which the Gaussian distributions under
two hypotheses are with different means and different variances. We then applied the optimal
decision rules to the distributed event detection system with an overlapping image region. As
a result, our study enables the system to provide real time alerts automatically. This thesis
also compares the performance of optimal decision rule with the performance of another two
suboptimal decision rules, and the experiment results show that the optimal decision strategy
outperforms the other two suboptimal strategies.

摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
圖目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
表目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
1 序論1
1.1 文獻回顧. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 本論文之貢獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 有重疊訊息之分散式偵測5
2.1 最佳決策法則. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 不同期望值及不同變異數之高斯分佈下的最佳決策法則. . . . . . . . . . . . . . . . 8
2.3 次佳決策法則. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3 有重疊訊息的分散式偵測於影像監控之應用19
3.1 實作之方法與平台架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 實作結果. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4 結論 28
參考文獻 29

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