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You probably want
Mat H2 = S * H1 * inv(S);
Where S is
Mat S = Mat::eye(3,3,CV_63F);
S.at<double>(0,0) = scale_x;
S.at<double>(1,1) = scale_y;
You probably want
Mat H2 = S * H1 * inv(S);
Where S is
Mat S = Mat::eye(3,3,CV_63F);
Mat::eye(3,3,CV_64F);
S.at<double>(0,0) = scale_x;
S.at<double>(1,1) = scale_y;