Page 101 - Algorithm Collections for Digital Signal Processing Applications using MATLAB

3. Numerical Linear Algebra 89

Figure 3-1. Hotelling transformation for binary image rotation

the Binary image created with ‘0’ (i.e.) Black. The image obtained is called
Transformed binary image using Hotelling transformation. Realize that the
Xposition and Yposition of Black pixels in the Transformed binary image
are independent to each other.
Note in the original Binary image, the Xpositions and Ypositions are
dependent to each other and hence the co-variance matrix is not the diagonal
matrix as mentioned below

CM=

102.2500 -80.9500
-80.9500 102.2500

But in the transformed Binary image, Xpositions and Ypositions are
independent to each other and hence the covariance matrix computed is the
diagonal matrix as given below

CT =

21.3000 0.0000
0.0000 183.2000

Note that the Diagonal values are Eigen values of the covariance
matrix C.