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I am trying to enhance the contrast in the images I get after scanning a surface using Thermography (Principal Component Thermography ~Rajic, which is basically an application of Principal Component Analysis) to see the defects clearly.

But my question here is to understand the difference between empirical orthogonal functions and Principal Components as shown below: figure SVD is used to decompose matrix A into U, R, and V.

In my case, I have 20 images. And after doing a raster like operation to unroll an image in a column, I get my matrix A which has 20 columns and each of them represents one image.

Any intuitive explanation will be really appreciated.

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marked as duplicate by kjetil b halvorsen, gung Dec 1 '17 at 12:42

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  • $\begingroup$ Does this help? stats.stackexchange.com/questions/88118 $\endgroup$ – amoeba Jul 5 '17 at 13:21
  • $\begingroup$ Also, you have 20 images, but what is the dimensionality of each image? Do you center rows or columns before doing SVD? $\endgroup$ – amoeba Jul 5 '17 at 13:23
  • $\begingroup$ Each image is 180*180. I put each image in column, so my matrix A comes out to be 32400*20 and then I center rows before doing SVD. Am I right? $\endgroup$ – Rumi-Thermo Jul 6 '17 at 4:40
  • $\begingroup$ Yes. So "EOFs" are of length 32400, meaning these are PCA eigenvectors aka "principal directions" aka "principal axes" aka (in image processing) "eigenfaces". What is called "PCs" on this figure are PC scores (normalized to unit length). See the thread linked above. Does it make it clear? $\endgroup$ – amoeba Jul 6 '17 at 7:19
  • $\begingroup$ @amoeba. I got a bit confused here. After going through your explanation on this link [link] stats.stackexchange.com/questions/134282/…) I got that "V" here are "principal axes/directions" and XV=US are the Principal components ("scores"). But now here you are saying U to be "principal directions/principal axes". $\endgroup$ – Rumi-Thermo Jul 6 '17 at 8:19

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