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I guess this tutorial will help with a high-level description of the algorithm: http://docs.opencv.org/3.0.0/da/df5/tutorial_py_sift_intro.html#gsc.tab=0. Also mentioned there the original paper: David G. Lowe. 2004. Distinctive Image Features from Scale-Invariant Keypoints. Int. J. Comput. Vision 60, 2 (November 2004), 91-110.
