工業上常常都會需要檢測產品是否符合標準，像是產品的標誌等等，而檢測前都是以工業用相機拍攝，再去比較符合之標誌照片與不符合之標誌照片間的差異有多少。
在論文裡，以二次矩來做研究，在二次矩的應用上， I_x+I_y 是一個不變量，不會因為旋轉而有所改變，因此可以利用縮放前的 I_x+I_y 與縮放後的I_x'+I_y' 去做比較，會發現 (I_x'+I_y')/(I_x+I_y ) 等於縮放倍率的四次方，所以可以利用二次矩來找出圖片縮放了多少。
而 I_xy 與 I_x'y' 之關係則是相減可以找出兩張圖旋轉角度為多少，因為每張圖都有特定的二次矩，而都會有一條軸使得 I_xy=0 及 I_x'y'=0，因此相減可以找出其旋轉角度。
將此應用在照片比對上，能快速的找到縮放倍率及旋轉角度，對工業檢測上能有很大的幫助，也能快速找到相似圖片間的差異。
在此論文的最後又將二次矩應用在影像辨識上，從圖片中各別抓取數字，並求其二次矩，用二次矩去辨識該數字為何，在現實生活中可以應用在停車場辨識車牌號碼等，利用各個數字間的二次矩去辨認該數字是多少，以此來辨識每台車的車牌號。

In the past, matching errors may occur to the simplest template matching due to changes in the picture. Additionally, it is time consuming. Therefore, we apply second moment to carry out image matching, which not only considerably reduces the calculation but also is noticeably faster than before.
First, I_x , I_y and I_xy are calculated with the application of second moment. Then, these three values are used to find the zoom ratio and rotation angle of the two photos to be compared. Next, zoom and rotate one of the photos, calculate the center of gravity of the two photos, translate and overlap the center of gravity, and then directly subtract the photos to distinguish the similarities between the two photos. Experimental results can accurately calculate the difference angle and zoom ratio, so that the comparisons will be more precise.

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