How to use "Hotelling Transform equation" to have new 3D image representation ??!

Hey everybody, Hope you all are doing well

I am trying to get new 3D representation of the color RGB image pixels be obtained from the Hotelling Transform equation, applying principle component analysis to finally have 3 principle component analysis.

Can any one help me through that,i don't know how to implement like such program....

Thank you

Answer 1

[Youssef Khmou]

hi Mariam,

This question should be treated by Image processing specialist, however there a link that provides some information related to that transformation ::

http://vaplab.ee.ncu.edu.tw/~swsun/pages/VQ_final/vq_hot.htm

There is also a partially available e-Book in Google Books that analyses the transformation :

http://books.google.co.ma/books?id=wM8QRLJXJFwC&pg=PT88&lpg=PT88&dq=hotelling+transform+equation&source=bl&ots=CMvZYO-aiH&sig=0hAi8z_DmSDEZKp2vhzDZUhKIbM&hl=en&sa=X&ei=0ZDDUeeHDMWXhQf41YGwAw&redir_esc=y

Therefore, from these two resources it is clear that you need to use the eigenvalue decomposition, with values sorted in decreasing order,

 [A,B]=eig(X); % where X is the image : TO BE VERFIED
 Eigen=sort(diag(B),'descend');

Use the Hotteling transformation : y=A(x-E[x]) such mean E[y]=0 .

Solve for A, and compute the covariance matrix of the vector y .

These steps are clearly stated in the second link ( Books google) .

I hope this helps as a first answer .