How does Matlab calculate the eccentricity of a region

In matlab, there is a built-in function to calculate properties of a region.
http://www.mathworks.com/help/images/ref/regionprops.html#bqkf8jf

And as said in help message:
'Eccentricity' — Scalar that specifies the eccentricity of the ellipse that has the same second-moments as the region. The eccentricity is the ratio of the distance between the foci of the ellipse and its major axis length. The value is between 0 and 1. (0 and 1 are degenerate cases; an ellipse whose eccentricity is 0 is actually a circle, while an ellipse whose eccentricity is 1 is a line segment.) This property is supported only for 2-D input label matrices.

So, the idea is to fit using a ellipse with same second-moments as the region.
What does it mean?
The answer is in this thread:
http://stackoverflow.com/questions/1532168/what-are-the-second-moments-of-a-region

To simplify, the idea is to calculate the co-variance matrix, then do eign-value decomposition. Eigen-values are those axis length, minor and major one. While eigen-vectors are the directions of minor/major axis.

length of major axis = 2a, minor axis = 2b, then the foci = c, then:
eccentricity E = c/a = sqrt(1-(b/a)^2)
a^2-b^2 = c^2.

Face recognition again

These days, some interesting news in face recognition field are re-posted widely on social network.

DeepFace: Closing the Gap to Human-Level Performance in Face Verification (Facebook AI lab)
It is said the performance is close to human being.

Then, more incredible, someone claimed their algorithm outperforms humankind.
http://www.zhizhihu.com/html/y2014/4520.html
https://medium.com/the-physics-arxiv-blog/2c567adbf7fc
http://www.52ml.net/14704.html

face++
http://www.faceplusplus.com/uc/app/home?app_id=14807

Most of the result is achieved on LFW (labeled face in the wild)
http://vis-www.cs.umass.edu/lfw/index.html

My adviser want me to do some face recognition stuff.