Help about "shadow" and "octant centroid" features in an image!

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Hi I've read this article but I can't understand the 2.1 and 2.2 parts about shadow features and octant centroid features. Could anyone help me please? I want to implement this article but I'm confused about this 2 parts!

Thanks a lot in advance!

http://arxiv.org/pdf/1003.1894.pdf[^]