Hotelling Transform

The Hotelling Transform is a conventional image processing transformation. The equation is as follows.Suppose the points pis are the feature points that we found from SMSB. The covariance matrix is calculated by the mathematical relations. In this part, the eigen values and vectors are obtained. As the eigen values and vectors found, the geometric attack can be detected by some mathematical ralations.

Fig.3  Hotelling Transform 

Fig.4  eigen analysis

 Fig.3 shows equations of Hotelling Transforfm. Pi is extracted from the SMSB and Co is the covariance matrix calculated from the mean vector and summation from every feature points. After getting the covariance vectors, the eigen analysis can be used to find out the eigen vectors and values. Thus, the eigen vectors and values represent the characteristic of one image. Fig. 4 shows a concept of eigen analysis. The eigen sets of original image and attacked ones can be used to determine what kind of geometric attack is.