論文針對影像間的誤差做了研究，進而找出影像間的轉換關係，在這裡的轉換關係為旋轉、平移和旋轉與縮放。探討的內容是如何從已知的兩張影像，經過程式計算求出兩張影像間的誤差或轉換關係，使用的數學模型為最小二乘法與梯度下降法。在第三章中，先設定一張標準影像和一張要比對的影像，求出影像間的轉換關係，此時影像間的轉換關係是已知的，再將兩張影像根據計算的結果進行轉換，進而做比對。比對的方法是取這兩張影像的每個像素點的 RGB 值，將這些 RGB 值處理成陣列形式，再來把兩張影像的值依序分別相減，若是比對完的結果大致上都為黑色，代表兩張影像相似且該轉換關係正確，再來，將影像間的轉換關係放大，變成大角度旋轉、大角度旋轉與大縮放，確認是否依舊能求出影像間的轉換關係。在第四章中，則針對兩張未知轉換關係的影像進行實際比對，證實是否真的能求出之間的轉換關係。最後，針對幾個應用進行討論。

This paper will discuss how to obtain the transformation relationship from two similar images. In this paper, The transformation relationship is rotation, translation, rotation and scaling. One image is subtracted from another image by subtracting the RGB value of each pixel of the image from the first point to the last point of the image subtract sequentially. If the result of the comparison is generally black, it means that the two images are similar and the transformation relationship is correct. In the second chapter, it will introduce some mathematical model, including the least square method and gradient descent. In the third chapter, the transformation is set to be discussed in case of rotation, translation, rotation and scaling, that is, in the known transformation relationship. Then, we want to discuss if the rotation angle and scaling become larger, the result is still correct. In the forth chapter, two images are actually taken, so the transformation relationship is unknown. We want to check the result is correct. In the fifth chapter, there are some applications and conclusions.

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