how to normalize SIFT features according to dominant local orientations

Hi

I am implementing a method for object recognition based on an article which says that: "To ensure that the descriptors are invariant to rotations, SIFT vectors are normalized with respect to the dominant local orientations which is estimated using the second moment matrix (or scatter matrix) around each feature point." I had SIFT vectors and orientation at each point, but I couldnt realize the second part for using scatter matrix or second moment matrix for normalizing the vector. anybody has any idea? Thanks in advance.