face analysis
The following form of the SVD
A = ∑ si ui vi'
aids in data compression. Look at the pictures of me below.

We see that the full picture has approximately
125*100=12,500
data points, since the picture is approximately 125x100 pixels. However, the rank 20 compressed representation has approximately
20*(125+100+1)=4,520
data points of storage, which is approximately a third of the storage and almost as good a resolution as the original picture!

Faces are inherently reflectively symmetric across the midline of the face. Therefore, if we found a Symmetry Preserving SVD (SPSVD) of a face, then not only would we have a reduction of storage from the low rank approximation, but the symmetry constraint would further the compression of the data by a half. Below you will find a series of symmetric approximation to the original (first frame) face. The last frame is the best approximation to the original face that preserves symmetry calculated by SPSVD. For more information, click SPSVD on Faces.

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