一張影像的邊緣可以提供給其他較複雜的程序，像是物體識別，相當重要的資訊，所以，影像邊緣偵測是影像處理中基本且重要的技術。有很多傳統的方法是用影像與遮罩做旋積，可以算出影像中每個像素的梯度值，再根據梯度值來找出該影像的邊緣。傳統的邊緣偵測方法很容易受到雜訊的干擾，因此這篇論文主要探討利用數學結構法來偵測一張受雜訊干擾影像的邊緣。數學結構法提供了抗雜訊的邊緣偵測法，近年來也有越來越多基於數學結構法的邊緣偵測法被提出。
我們分析在數學結構法中用兩種不同結構元素輸出的影像優缺點，將這兩張影像加起來得到一張灰階圖，再根據不同的門檻值將灰階圖轉成二值圖。然後，我們提出一個合作賽局理論架構來適當地選出兩張二值圖。最後，我們用提出的方法將這兩張影像結合出一張影像，在結合的過程中，我們偵測出比傳統方法更為完整的邊緣，還把影像中孤立的邊緣點去除，來減少錯誤的資訊。

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