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

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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

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