main.cpp

#include <opencv2/core.hpp>
#include <opencv2/imgcodecs.hpp>
#include <opencv2/highgui.hpp>
#include <opencv2/xfeatures2d/nonfree.hpp>
#include <iostream>
#include "GaussianBlur_modified.hpp"
#include "substraction_kernel.hpp"
#include "helper.hpp"
using namespace cv;
using namespace std;

#include "precomp.hpp"
#include <stdarg.h>
#include <opencv2/core/hal/hal.hpp>

// define global variables
int timer_helper_subpixel = 10;
uint64_t cycles_subpixel = 0;
int timer_helper_harris = 10;
uint64_t cycles_harris = 0;
long long Extrema_Localization_count = 0;
long long Adjusting_keypoint_locations_count = 0;
long long Eliminating_Edge_Responses_count = 0;
uint64_t cycles_conv = 0;
uint64_t cycles_mem = 0;
uint64_t buildGaussianPyramidCycles = 0;
uint64_t buildDoGCycles = 0;


// source code of SIFT from opencv
namespace cv
{
    namespace xfeatures2d
    {
        
        /*!
         SIFT implementation.
         
         The class implements SIFT algorithm by D. Lowe.
         */
        class SIFT_Impl : public SIFT
        {
        public:
            explicit SIFT_Impl( int nfeatures = 0, int nOctaveLayers = 3,
                               double contrastThreshold = 0.04, double edgeThreshold = 10,
                               double sigma = 1.6);
            
            //! returns the descriptor size in floats (128)
            int descriptorSize() const CV_OVERRIDE;
            
            //! returns the descriptor type
            int descriptorType() const CV_OVERRIDE;
            
            //! returns the default norm type
            int defaultNorm() const CV_OVERRIDE;
            
            //! finds the keypoints and computes descriptors for them using SIFT algorithm.
            //! Optionally it can compute descriptors for the user-provided keypoints
            void detectAndCompute(InputArray img, InputArray mask,
                                  std::vector<KeyPoint>& keypoints,
                                  OutputArray descriptors,
                                  bool useProvidedKeypoints = false) CV_OVERRIDE;
            
            void buildGaussianPyramid( const Mat& base, std::vector<Mat>& pyr, int nOctaves ) const;
            void buildDoGPyramid( const std::vector<Mat>& pyr, std::vector<Mat>& dogpyr ) const;
            void findScaleSpaceExtrema( const std::vector<Mat>& gauss_pyr, const std::vector<Mat>& dog_pyr,
                                       std::vector<KeyPoint>& keypoints ) const;
            
        protected:
            CV_PROP_RW int nfeatures;
            CV_PROP_RW int nOctaveLayers;
            CV_PROP_RW double contrastThreshold;
            CV_PROP_RW double edgeThreshold;
            CV_PROP_RW double sigma;
        };
        
        Ptr<SIFT> SIFT::create( int _nfeatures, int _nOctaveLayers,
                               double _contrastThreshold, double _edgeThreshold, double _sigma )
        {
            return makePtr<SIFT_Impl>(_nfeatures, _nOctaveLayers, _contrastThreshold, _edgeThreshold, _sigma);
        }
        
        /******************************* Defs and macros *****************************/
        
        // default width of descriptor histogram array
        static const int SIFT_DESCR_WIDTH = 4;
        
        // default number of bins per histogram in descriptor array
        static const int SIFT_DESCR_HIST_BINS = 8;
        
        // assumed gaussian blur for input image
        static const float SIFT_INIT_SIGMA = 0.5f;
        
        // width of border in which to ignore keypoints
        static const int SIFT_IMG_BORDER = 5;
        
        // maximum steps of keypoint interpolation before failure
        static const int SIFT_MAX_INTERP_STEPS = 5;
        
        // default number of bins in histogram for orientation assignment
        static const int SIFT_ORI_HIST_BINS = 36;
        
        // determines gaussian sigma for orientation assignment
        static const float SIFT_ORI_SIG_FCTR = 1.5f;
        
        // determines the radius of the region used in orientation assignment
        static const float SIFT_ORI_RADIUS = 3 * SIFT_ORI_SIG_FCTR;
        
        // orientation magnitude relative to max that results in new feature
        static const float SIFT_ORI_PEAK_RATIO = 0.8f;
        
        // determines the size of a single descriptor orientation histogram
        static const float SIFT_DESCR_SCL_FCTR = 3.f;
        
        // threshold on magnitude of elements of descriptor vector
        static const float SIFT_DESCR_MAG_THR = 0.2f;
        
        // factor used to convert floating-point descriptor to unsigned char
        static const float SIFT_INT_DESCR_FCTR = 512.f;
        
#define DoG_TYPE_SHORT 0
#if DoG_TYPE_SHORT
        // intermediate type used for DoG pyramids
        typedef short sift_wt;
        static const int SIFT_FIXPT_SCALE = 48;
#else
        // intermediate type used for DoG pyramids
        typedef float sift_wt;
        static const int SIFT_FIXPT_SCALE = 1;
#endif
        
        static inline void
        unpackOctave(const KeyPoint& kpt, int& octave, int& layer, float& scale)
        {
            octave = kpt.octave & 255;
            layer = (kpt.octave >> 8) & 255;
            octave = octave < 128 ? octave : (-128 | octave);
            scale = octave >= 0 ? 1.f/(1 << octave) : (float)(1 << -octave);
        }
        
        static Mat createInitialImage( const Mat& img, bool doubleImageSize, float sigma )
        {
            Mat gray, gray_fpt;
            if( img.channels() == 3 || img.channels() == 4 )
            {
                cvtColor(img, gray, COLOR_BGR2GRAY);
                gray.convertTo(gray_fpt, DataType<sift_wt>::type, SIFT_FIXPT_SCALE, 0);
            }
            else
                img.convertTo(gray_fpt, DataType<sift_wt>::type, SIFT_FIXPT_SCALE, 0);
            
            float sig_diff;
            
            if( doubleImageSize )
            {
                sig_diff = sqrtf( std::max(sigma * sigma - SIFT_INIT_SIGMA * SIFT_INIT_SIGMA * 4, 0.01f) );
                Mat dbl;
#if DoG_TYPE_SHORT
                resize(gray_fpt, dbl, Size(gray_fpt.cols*2, gray_fpt.rows*2), 0, 0, INTER_LINEAR_EXACT);
#else
                resize(gray_fpt, dbl, Size(gray_fpt.cols*2, gray_fpt.rows*2), 0, 0, INTER_LINEAR);
#endif
                GaussianBlur(dbl, dbl, Size(), sig_diff, sig_diff);
                return dbl;
            }
            else
            {
                sig_diff = sqrtf( std::max(sigma * sigma - SIFT_INIT_SIGMA * SIFT_INIT_SIGMA, 0.01f) );
                GaussianBlur(gray_fpt, gray_fpt, Size(), sig_diff, sig_diff);
                return gray_fpt;
            }
        }
        
        
        void SIFT_Impl::buildGaussianPyramid( const Mat& base, std::vector<Mat>& pyr, int nOctaves ) const
        {
            std::vector<double> sig(nOctaveLayers + 3);
            pyr.resize(nOctaves*(nOctaveLayers + 3));
            
            // precompute Gaussian sigmas using the following formula:
            //  \sigma_{total}^2 = \sigma_{i}^2 + \sigma_{i-1}^2
            sig[0] = sigma;
            double k = std::pow( 2., 1. / nOctaveLayers );
            for( int i = 1; i < nOctaveLayers + 3; i++ )
            {
                double sig_prev = std::pow(k, (double)(i-1))*sigma;
                double sig_total = sig_prev*k;
                sig[i] = std::sqrt(sig_total*sig_total - sig_prev*sig_prev);
                
            }
            
            for( int o = 0; o < nOctaves; o++ )
            {
                for( int i = 0; i < nOctaveLayers + 3; i++ )
                {
                    Mat& dst = pyr[o*(nOctaveLayers + 3) + i];
                    if( o == 0  &&  i == 0 ) {
                        dst = base;
                    }
                    // base of new octave is halved image from end of previous octave
                    else if( i == 0 )
                    {
                        const Mat& src = pyr[(o-1)*(nOctaveLayers + 3) + nOctaveLayers];
                        resize(src, dst, Size(src.cols/2, src.rows/2),
                               0, 0, INTER_NEAREST); // resize image when changing to another octave
                    }
                    else
                    {
                        const Mat& src = pyr[o*(nOctaveLayers + 3) + i-1];
//                        GaussianBlur(src, dst, Size(), sig[i], sig[i]);
                        GaussianBlur_modified(src, dst, Size(), sig[i], sig[i]);
                    }
                }
            }
        }
        
        
        class buildDoGPyramidComputer : public ParallelLoopBody
        {
        public:
            buildDoGPyramidComputer(
                                    int _nOctaveLayers,
                                    const std::vector<Mat>& _gpyr,
                                    std::vector<Mat>& _dogpyr)
            : nOctaveLayers(_nOctaveLayers),
            gpyr(_gpyr),
            dogpyr(_dogpyr) { }
            
            void operator()( const cv::Range& range ) const CV_OVERRIDE
            {
                const int begin = range.start;
                const int end = range.end;
                
                for( int a = begin; a < end; a++ )
                {
                    const int o = a / (nOctaveLayers + 2); // o-th octave
                    const int i = a % (nOctaveLayers + 2); // i-th layer
                    
                    const Mat& src1 = gpyr[o*(nOctaveLayers + 3) + i];
                    const Mat& src2 = gpyr[o*(nOctaveLayers + 3) + i + 1];
                    Mat& dst = dogpyr[o*(nOctaveLayers + 2) + i];
//                    subtract(src2, src1, dst, noArray(), DataType<sift_wt>::type);
                    substraction_kernel(src1, src2, dst);
                }
            }
            
        private:
            int nOctaveLayers;
            const std::vector<Mat>& gpyr;
            std::vector<Mat>& dogpyr;
        };
        
        void SIFT_Impl::buildDoGPyramid( const std::vector<Mat>& gpyr, std::vector<Mat>& dogpyr ) const
        {
            int nOctaves = (int)gpyr.size()/(nOctaveLayers + 3);
            dogpyr.resize( nOctaves*(nOctaveLayers + 2) );
            
            parallel_for_(Range(0, nOctaves * (nOctaveLayers + 2)), buildDoGPyramidComputer(nOctaveLayers, gpyr, dogpyr));
            // range is DOG pyramid size
        }
        
        // Computes a gradient orientation histogram at a specified pixel
        static float calcOrientationHist( const Mat& img, Point pt, int radius,
                                         float sigma, float* hist, int n )
        {
            int i, j, k, len = (radius*2+1)*(radius*2+1);
            
            float expf_scale = -1.f/(2.f * sigma * sigma);
            AutoBuffer<float> buf(len*4 + n+4);
            float *X = buf.data(), *Y = X + len, *Mag = X, *Ori = Y + len, *W = Ori + len;
            float* temphist = W + len + 2;
            
            for( i = 0; i < n; i++ )
                temphist[i] = 0.f;
            
            for( i = -radius, k = 0; i <= radius; i++ )
            {
                int y = pt.y + i;
                if( y <= 0 || y >= img.rows - 1 )
                    continue;
                for( j = -radius; j <= radius; j++ )
                {
                    int x = pt.x + j;
                    if( x <= 0 || x >= img.cols - 1 )
                        continue;
                    
                    float dx = (float)(img.at<sift_wt>(y, x+1) - img.at<sift_wt>(y, x-1));
                    float dy = (float)(img.at<sift_wt>(y-1, x) - img.at<sift_wt>(y+1, x));
                    
                    X[k] = dx; Y[k] = dy; W[k] = (i*i + j*j)*expf_scale;
                    k++;
                }
            }
            
            len = k;
            
            // compute gradient values, orientations and the weights over the pixel neighborhood
            cv::hal::exp32f(W, W, len);
            cv::hal::fastAtan2(Y, X, Ori, len, true);
            cv::hal::magnitude32f(X, Y, Mag, len);
            
            k = 0;
#if CV_AVX2
            if( USE_AVX2 )
            {
                __m256 __nd360 = _mm256_set1_ps(n/360.f);
                __m256i __n = _mm256_set1_epi32(n);
                int CV_DECL_ALIGNED(32) bin_buf[8];
                float CV_DECL_ALIGNED(32) w_mul_mag_buf[8];
                for ( ; k <= len - 8; k+=8 )
                {
                    __m256i __bin = _mm256_cvtps_epi32(_mm256_mul_ps(__nd360, _mm256_loadu_ps(&Ori[k])));
                    
                    __bin = _mm256_sub_epi32(__bin, _mm256_andnot_si256(_mm256_cmpgt_epi32(__n, __bin), __n));
                    __bin = _mm256_add_epi32(__bin, _mm256_and_si256(__n, _mm256_cmpgt_epi32(_mm256_setzero_si256(), __bin)));
                    
                    __m256 __w_mul_mag = _mm256_mul_ps(_mm256_loadu_ps(&W[k]), _mm256_loadu_ps(&Mag[k]));
                    
                    _mm256_store_si256((__m256i *) bin_buf, __bin);
                    _mm256_store_ps(w_mul_mag_buf, __w_mul_mag);
                    
                    temphist[bin_buf[0]] += w_mul_mag_buf[0];
                    temphist[bin_buf[1]] += w_mul_mag_buf[1];
                    temphist[bin_buf[2]] += w_mul_mag_buf[2];
                    temphist[bin_buf[3]] += w_mul_mag_buf[3];
                    temphist[bin_buf[4]] += w_mul_mag_buf[4];
                    temphist[bin_buf[5]] += w_mul_mag_buf[5];
                    temphist[bin_buf[6]] += w_mul_mag_buf[6];
                    temphist[bin_buf[7]] += w_mul_mag_buf[7];
                }
            }
#endif
            for( ; k < len; k++ )
            {
                int bin = cvRound((n/360.f)*Ori[k]);
                if( bin >= n )
                    bin -= n;
                if( bin < 0 )
                    bin += n;
                temphist[bin] += W[k]*Mag[k];
            }
            
            // smooth the histogram
            temphist[-1] = temphist[n-1];
            temphist[-2] = temphist[n-2];
            temphist[n] = temphist[0];
            temphist[n+1] = temphist[1];
            
            i = 0;
#if CV_AVX2
            if( USE_AVX2 )
            {
                __m256 __d_1_16 = _mm256_set1_ps(1.f/16.f);
                __m256 __d_4_16 = _mm256_set1_ps(4.f/16.f);
                __m256 __d_6_16 = _mm256_set1_ps(6.f/16.f);
                for( ; i <= n - 8; i+=8 )
                {
#if CV_FMA3
                    __m256 __hist = _mm256_fmadd_ps(
                                                    _mm256_add_ps(_mm256_loadu_ps(&temphist[i-2]), _mm256_loadu_ps(&temphist[i+2])),
                                                    __d_1_16,
                                                    _mm256_fmadd_ps(
                                                                    _mm256_add_ps(_mm256_loadu_ps(&temphist[i-1]), _mm256_loadu_ps(&temphist[i+1])),
                                                                    __d_4_16,
                                                                    _mm256_mul_ps(_mm256_loadu_ps(&temphist[i]), __d_6_16)));
#else
                    __m256 __hist = _mm256_add_ps(
                                                  _mm256_mul_ps(
                                                                _mm256_add_ps(_mm256_loadu_ps(&temphist[i-2]), _mm256_loadu_ps(&temphist[i+2])),
                                                                __d_1_16),
                                                  _mm256_add_ps(
                                                                _mm256_mul_ps(
                                                                              _mm256_add_ps(_mm256_loadu_ps(&temphist[i-1]), _mm256_loadu_ps(&temphist[i+1])),
                                                                              __d_4_16),
                                                                _mm256_mul_ps(_mm256_loadu_ps(&temphist[i]), __d_6_16)));
#endif
                    _mm256_storeu_ps(&hist[i], __hist);
                }
            }
#endif
            for( ; i < n; i++ )
            {
                hist[i] = (temphist[i-2] + temphist[i+2])*(1.f/16.f) +
                (temphist[i-1] + temphist[i+1])*(4.f/16.f) +
                temphist[i]*(6.f/16.f);
            }
            
            float maxval = hist[0];
            for( i = 1; i < n; i++ )
                maxval = std::max(maxval, hist[i]);
            
            return maxval;
        }
        
        
        //
        // Interpolates a scale-space extremum's location and scale to subpixel
        // accuracy to form an image feature. Rejects features with low contrast.
        // Based on Section 4 of Lowe's paper.
        static bool adjustLocalExtrema( const std::vector<Mat>& dog_pyr, KeyPoint& kpt, int octv,
                                       int& layer, int& r, int& c, int nOctaveLayers,
                                       float contrastThreshold, float edgeThreshold, float sigma )
        {
            const float img_scale = 1.f/(255*SIFT_FIXPT_SCALE);
            const float deriv_scale = img_scale*0.5f;
            const float second_deriv_scale = img_scale;
            const float cross_deriv_scale = img_scale*0.25f;
            
            float xi=0, xr=0, xc=0, contr=0;
            int i = 0;
            
            uint64_t start, end;
            
            for( ; i < SIFT_MAX_INTERP_STEPS; i++ )
            {
                Adjusting_keypoint_locations_count ++;
                start = rdtsc();
                int idx = octv*(nOctaveLayers+2) + layer;
                const Mat& img = dog_pyr[idx];
                const Mat& prev = dog_pyr[idx-1];
                const Mat& next = dog_pyr[idx+1];
                
                Vec3f dD((img.at<sift_wt>(r, c+1) - img.at<sift_wt>(r, c-1))*deriv_scale,
                         (img.at<sift_wt>(r+1, c) - img.at<sift_wt>(r-1, c))*deriv_scale,
                         (next.at<sift_wt>(r, c) - prev.at<sift_wt>(r, c))*deriv_scale);
                // first order derivative
                
                float v2 = (float)img.at<sift_wt>(r, c)*2;
                float dxx = (img.at<sift_wt>(r, c+1) + img.at<sift_wt>(r, c-1) - v2)*second_deriv_scale;
                float dyy = (img.at<sift_wt>(r+1, c) + img.at<sift_wt>(r-1, c) - v2)*second_deriv_scale;
                float dss = (next.at<sift_wt>(r, c) + prev.at<sift_wt>(r, c) - v2)*second_deriv_scale;
                float dxy = (img.at<sift_wt>(r+1, c+1) - img.at<sift_wt>(r+1, c-1) -
                             img.at<sift_wt>(r-1, c+1) + img.at<sift_wt>(r-1, c-1))*cross_deriv_scale;
                float dxs = (next.at<sift_wt>(r, c+1) - next.at<sift_wt>(r, c-1) -
                             prev.at<sift_wt>(r, c+1) + prev.at<sift_wt>(r, c-1))*cross_deriv_scale;
                float dys = (next.at<sift_wt>(r+1, c) - next.at<sift_wt>(r-1, c) -
                             prev.at<sift_wt>(r+1, c) + prev.at<sift_wt>(r-1, c))*cross_deriv_scale;
                
                Matx33f H(dxx, dxy, dxs,
                          dxy, dyy, dys,
                          dxs, dys, dss);
            
                Vec3f X = H.solve(dD, DECOMP_LU);
                
                xi = -X[2];
                xr = -X[1];
                xc = -X[0];
                
                end = rdtsc();
                if (timer_helper_subpixel-- > 0) {
                    cycles_subpixel += (end-start);
                    if(timer_helper_subpixel == 0){
                    }
                }
                
                if( std::abs(xi) < 0.5f && std::abs(xr) < 0.5f && std::abs(xc) < 0.5f )
                    break;
                
                if( std::abs(xi) > (float)(INT_MAX/3) ||
                   std::abs(xr) > (float)(INT_MAX/3) ||
                   std::abs(xc) > (float)(INT_MAX/3) )
                    return false;
                
                c += cvRound(xc);
                r += cvRound(xr);
                layer += cvRound(xi);
                
                if( layer < 1 || layer > nOctaveLayers ||
                   c < SIFT_IMG_BORDER || c >= img.cols - SIFT_IMG_BORDER  ||
                   r < SIFT_IMG_BORDER || r >= img.rows - SIFT_IMG_BORDER )
                    return false;
            }
            
            // ensure convergence of interpolation
            if( i >= SIFT_MAX_INTERP_STEPS )
                return false;
            
            {
                Eliminating_Edge_Responses_count ++;
                start = rdtsc();
                int idx = octv*(nOctaveLayers+2) + layer; //2 add 1mul
                const Mat& img = dog_pyr[idx];
                const Mat& prev = dog_pyr[idx-1]; // 1add
                const Mat& next = dog_pyr[idx+1]; // 1add
                Matx31f dD((img.at<sift_wt>(r, c+1) - img.at<sift_wt>(r, c-1))*deriv_scale,
                           (img.at<sift_wt>(r+1, c) - img.at<sift_wt>(r-1, c))*deriv_scale,
                           (next.at<sift_wt>(r, c) - prev.at<sift_wt>(r, c))*deriv_scale);
                float t = dD.dot(Matx31f(xc, xr, xi));
                
                contr = img.at<sift_wt>(r, c)*img_scale + t * 0.5f; //1add 2mul
                if( std::abs( contr ) * nOctaveLayers < contrastThreshold ) //1add 1mul
                    return false;
                
                // principal curvatures are computed using the trace and det of Hessian
                float v2 = img.at<sift_wt>(r, c)*2.f;
                float dxx = (img.at<sift_wt>(r, c+1) + img.at<sift_wt>(r, c-1) - v2)*second_deriv_scale;
                float dyy = (img.at<sift_wt>(r+1, c) + img.at<sift_wt>(r-1, c) - v2)*second_deriv_scale;
                float dxy = (img.at<sift_wt>(r+1, c+1) - img.at<sift_wt>(r+1, c-1) -
                             img.at<sift_wt>(r-1, c+1) + img.at<sift_wt>(r-1, c-1)) * cross_deriv_scale;
                float tr = dxx + dyy;
                float det = dxx * dyy - dxy * dxy;
                end = rdtsc();
                if (timer_helper_harris-- > 0) {
                    cycles_harris += (end-start);
                    if(timer_helper_harris == 0){
                    }
                }
                if( det <= 0 || tr*tr*edgeThreshold >= (edgeThreshold + 1)*(edgeThreshold + 1)*det )
                    return false;
            }
            
            kpt.pt.x = (c + xc) * (1 << octv);
            kpt.pt.y = (r + xr) * (1 << octv);
            kpt.octave = octv + (layer << 8) + (cvRound((xi + 0.5)*255) << 16);
            kpt.size = sigma*powf(2.f, (layer + xi) / nOctaveLayers)*(1 << octv)*2;
            kpt.response = std::abs(contr);
            
            return true;
        }
        
        
        class findScaleSpaceExtremaComputer : public ParallelLoopBody
        {
        public:
            findScaleSpaceExtremaComputer(
                                          int _o,
                                          int _i,
                                          int _threshold,
                                          int _idx,
                                          int _step,
                                          int _cols,
                                          int _nOctaveLayers,
                                          double _contrastThreshold,
                                          double _edgeThreshold,
                                          double _sigma,
                                          const std::vector<Mat>& _gauss_pyr,
                                          const std::vector<Mat>& _dog_pyr,
                                          TLSData<std::vector<KeyPoint> > &_tls_kpts_struct)
            
            : o(_o),
            i(_i),
            threshold(_threshold),
            idx(_idx),
            step(_step),
            cols(_cols),
            nOctaveLayers(_nOctaveLayers),
            contrastThreshold(_contrastThreshold),
            edgeThreshold(_edgeThreshold),
            sigma(_sigma),
            gauss_pyr(_gauss_pyr),
            dog_pyr(_dog_pyr),
            tls_kpts_struct(_tls_kpts_struct) { }
            void operator()( const cv::Range& range ) const CV_OVERRIDE
            {
                const int begin = range.start;
                const int end = range.end;
                
                static const int n = SIFT_ORI_HIST_BINS;
                float hist[n];
                
                const Mat& img = dog_pyr[idx];
                const Mat& prev = dog_pyr[idx-1];
                const Mat& next = dog_pyr[idx+1];
                
                std::vector<KeyPoint> *tls_kpts = tls_kpts_struct.get();
                
                KeyPoint kpt;
                for( int r = begin; r < end; r++)
                {
                    const sift_wt* currptr = img.ptr<sift_wt>(r);
                    const sift_wt* prevptr = prev.ptr<sift_wt>(r);
                    const sift_wt* nextptr = next.ptr<sift_wt>(r);
                    
                    for( int c = SIFT_IMG_BORDER; c < cols-SIFT_IMG_BORDER; c++)
                    {
                        sift_wt val = currptr[c];
                        Extrema_Localization_count ++;
                        // find local extrema with pixel accuracy
                        if( std::abs(val) > threshold &&
                           ((val > 0 && val >= currptr[c-1] && val >= currptr[c+1] &&
                             val >= currptr[c-step-1] && val >= currptr[c-step] && val >= currptr[c-step+1] &&
                             val >= currptr[c+step-1] && val >= currptr[c+step] && val >= currptr[c+step+1] &&
                             val >= nextptr[c] && val >= nextptr[c-1] && val >= nextptr[c+1] &&
                             val >= nextptr[c-step-1] && val >= nextptr[c-step] && val >= nextptr[c-step+1] &&
                             val >= nextptr[c+step-1] && val >= nextptr[c+step] && val >= nextptr[c+step+1] &&
                             val >= prevptr[c] && val >= prevptr[c-1] && val >= prevptr[c+1] &&
                             val >= prevptr[c-step-1] && val >= prevptr[c-step] && val >= prevptr[c-step+1] &&
                             val >= prevptr[c+step-1] && val >= prevptr[c+step] && val >= prevptr[c+step+1]) ||
                            (val < 0 && val <= currptr[c-1] && val <= currptr[c+1] &&
                             val <= currptr[c-step-1] && val <= currptr[c-step] && val <= currptr[c-step+1] &&
                             val <= currptr[c+step-1] && val <= currptr[c+step] && val <= currptr[c+step+1] &&
                             val <= nextptr[c] && val <= nextptr[c-1] && val <= nextptr[c+1] &&
                             val <= nextptr[c-step-1] && val <= nextptr[c-step] && val <= nextptr[c-step+1] &&
                             val <= nextptr[c+step-1] && val <= nextptr[c+step] && val <= nextptr[c+step+1] &&
                             val <= prevptr[c] && val <= prevptr[c-1] && val <= prevptr[c+1] &&
                             val <= prevptr[c-step-1] && val <= prevptr[c-step] && val <= prevptr[c-step+1] &&
                             val <= prevptr[c+step-1] && val <= prevptr[c+step] && val <= prevptr[c+step+1])))
                        {
                            int r1 = r, c1 = c, layer = i;
                            //TODO: ask TA about how to optimize/benchmarking it?
                            if( !adjustLocalExtrema(dog_pyr, kpt, o, layer, r1, c1,
                                                    nOctaveLayers, (float)contrastThreshold,
                                                    (float)edgeThreshold, (float)sigma) )
                                continue;
                            float scl_octv = kpt.size*0.5f/(1 << o);
                            float omax = calcOrientationHist(gauss_pyr[o*(nOctaveLayers+3) + layer],
                                                             Point(c1, r1),
                                                             cvRound(SIFT_ORI_RADIUS * scl_octv),
                                                             SIFT_ORI_SIG_FCTR * scl_octv,
                                                             hist, n);
                            float mag_thr = (float)(omax * SIFT_ORI_PEAK_RATIO);
                            for( int j = 0; j < n; j++ )
                            {
                                int l = j > 0 ? j - 1 : n - 1;
                                int r2 = j < n-1 ? j + 1 : 0;
                                
                                if( hist[j] > hist[l]  &&  hist[j] > hist[r2]  &&  hist[j] >= mag_thr )
                                {
                                    float bin = j + 0.5f * (hist[l]-hist[r2]) / (hist[l] - 2*hist[j] + hist[r2]);
                                    bin = bin < 0 ? n + bin : bin >= n ? bin - n : bin;
                                    kpt.angle = 360.f - (float)((360.f/n) * bin);
                                    if(std::abs(kpt.angle - 360.f) < FLT_EPSILON)
                                        kpt.angle = 0.f;
                                    {
                                        tls_kpts->push_back(kpt);
                                    }
                                }
                            }
                        }
                    }
                }
            }
        private:
            int o, i;
            int threshold;
            int idx, step, cols;
            int nOctaveLayers;
            double contrastThreshold;
            double edgeThreshold;
            double sigma;
            const std::vector<Mat>& gauss_pyr;
            const std::vector<Mat>& dog_pyr;
            TLSData<std::vector<KeyPoint> > &tls_kpts_struct;
        };
        
        //
        // Detects features at extrema in DoG scale space.  Bad features are discarded
        // based on contrast and ratio of principal curvatures.
        void SIFT_Impl::findScaleSpaceExtrema( const std::vector<Mat>& gauss_pyr, const std::vector<Mat>& dog_pyr,
                                              std::vector<KeyPoint>& keypoints ) const
        {
            const int nOctaves = (int)gauss_pyr.size()/(nOctaveLayers + 3);
            const int threshold = cvFloor(0.5 * contrastThreshold / nOctaveLayers * 255 * SIFT_FIXPT_SCALE);
            
            keypoints.clear(); // empty keypoints
            TLSData<std::vector<KeyPoint> > tls_kpts_struct; // multi-threads
            
            for( int o = 0; o < nOctaves; o++ )
                for( int i = 1; i <= nOctaveLayers; i++ )
                {
                    const int idx = o*(nOctaveLayers+2)+i;
                    const Mat& img = dog_pyr[idx];
                    const int step = (int)img.step1();
                    const int rows = img.rows, cols = img.cols;
                    
                    parallel_for_(Range(SIFT_IMG_BORDER, rows-SIFT_IMG_BORDER),
                                  findScaleSpaceExtremaComputer(
                                                                o, i, threshold, idx, step, cols,
                                                                nOctaveLayers,
                                                                contrastThreshold,
                                                                edgeThreshold,
                                                                sigma,
                                                                gauss_pyr, dog_pyr, tls_kpts_struct));
                }
            
            std::vector<std::vector<KeyPoint>*> kpt_vecs;
            tls_kpts_struct.gather(kpt_vecs);
            for (size_t i = 0; i < kpt_vecs.size(); ++i) {
                keypoints.insert(keypoints.end(), kpt_vecs[i]->begin(), kpt_vecs[i]->end());
            }
        }
        
        
        static void calcSIFTDescriptor( const Mat& img, Point2f ptf, float ori, float scl,
                                       int d, int n, float* dst )
        {
            Point pt(cvRound(ptf.x), cvRound(ptf.y));
            float cos_t = cosf(ori*(float)(CV_PI/180));
            float sin_t = sinf(ori*(float)(CV_PI/180));
            float bins_per_rad = n / 360.f;
            float exp_scale = -1.f/(d * d * 0.5f);
            float hist_width = SIFT_DESCR_SCL_FCTR * scl;
            int radius = cvRound(hist_width * 1.4142135623730951f * (d + 1) * 0.5f);
            // Clip the radius to the diagonal of the image to avoid autobuffer too large exception
            radius = std::min(radius, (int) sqrt(((double) img.cols)*img.cols + ((double) img.rows)*img.rows));
            cos_t /= hist_width;
            sin_t /= hist_width;
            
            int i, j, k, len = (radius*2+1)*(radius*2+1), histlen = (d+2)*(d+2)*(n+2);
            int rows = img.rows, cols = img.cols;
            
            AutoBuffer<float> buf(len*6 + histlen);
            float *X = buf.data(), *Y = X + len, *Mag = Y, *Ori = Mag + len, *W = Ori + len;
            float *RBin = W + len, *CBin = RBin + len, *hist = CBin + len;
            
            for( i = 0; i < d+2; i++ )
            {
                for( j = 0; j < d+2; j++ )
                    for( k = 0; k < n+2; k++ )
                        hist[(i*(d+2) + j)*(n+2) + k] = 0.;
            }
            
            for( i = -radius, k = 0; i <= radius; i++ )
                for( j = -radius; j <= radius; j++ )
                {
                    // Calculate sample's histogram array coords rotated relative to ori.
                    // Subtract 0.5 so samples that fall e.g. in the center of row 1 (i.e.
                    // r_rot = 1.5) have full weight placed in row 1 after interpolation.
                    float c_rot = j * cos_t - i * sin_t;
                    float r_rot = j * sin_t + i * cos_t;
                    float rbin = r_rot + d/2 - 0.5f;
                    float cbin = c_rot + d/2 - 0.5f;
                    int r = pt.y + i, c = pt.x + j;
                    
                    if( rbin > -1 && rbin < d && cbin > -1 && cbin < d &&
                       r > 0 && r < rows - 1 && c > 0 && c < cols - 1 )
                    {
                        float dx = (float)(img.at<sift_wt>(r, c+1) - img.at<sift_wt>(r, c-1));
                        float dy = (float)(img.at<sift_wt>(r-1, c) - img.at<sift_wt>(r+1, c));
                        X[k] = dx; Y[k] = dy; RBin[k] = rbin; CBin[k] = cbin;
                        W[k] = (c_rot * c_rot + r_rot * r_rot)*exp_scale;
                        k++;
                    }
                }
            
            len = k;
            cv::hal::fastAtan2(Y, X, Ori, len, true);
            cv::hal::magnitude32f(X, Y, Mag, len);
            cv::hal::exp32f(W, W, len);
            
            k = 0;
#if CV_AVX2
            if( USE_AVX2 )
            {
                int CV_DECL_ALIGNED(32) idx_buf[8];
                float CV_DECL_ALIGNED(32) rco_buf[64];
                const __m256 __ori = _mm256_set1_ps(ori);
                const __m256 __bins_per_rad = _mm256_set1_ps(bins_per_rad);
                const __m256i __n = _mm256_set1_epi32(n);
                for( ; k <= len - 8; k+=8 )
                {
                    __m256 __rbin = _mm256_loadu_ps(&RBin[k]);
                    __m256 __cbin = _mm256_loadu_ps(&CBin[k]);
                    __m256 __obin = _mm256_mul_ps(_mm256_sub_ps(_mm256_loadu_ps(&Ori[k]), __ori), __bins_per_rad);
                    __m256 __mag = _mm256_mul_ps(_mm256_loadu_ps(&Mag[k]), _mm256_loadu_ps(&W[k]));
                    
                    __m256 __r0 = _mm256_floor_ps(__rbin);
                    __rbin = _mm256_sub_ps(__rbin, __r0);
                    __m256 __c0 = _mm256_floor_ps(__cbin);
                    __cbin = _mm256_sub_ps(__cbin, __c0);
                    __m256 __o0 = _mm256_floor_ps(__obin);
                    __obin = _mm256_sub_ps(__obin, __o0);
                    
                    __m256i __o0i = _mm256_cvtps_epi32(__o0);
                    __o0i = _mm256_add_epi32(__o0i, _mm256_and_si256(__n, _mm256_cmpgt_epi32(_mm256_setzero_si256(), __o0i)));
                    __o0i = _mm256_sub_epi32(__o0i, _mm256_andnot_si256(_mm256_cmpgt_epi32(__n, __o0i), __n));
                    
                    __m256 __v_r1 = _mm256_mul_ps(__mag, __rbin);
                    __m256 __v_r0 = _mm256_sub_ps(__mag, __v_r1);
                    
                    __m256 __v_rc11 = _mm256_mul_ps(__v_r1, __cbin);
                    __m256 __v_rc10 = _mm256_sub_ps(__v_r1, __v_rc11);
                    
                    __m256 __v_rc01 = _mm256_mul_ps(__v_r0, __cbin);
                    __m256 __v_rc00 = _mm256_sub_ps(__v_r0, __v_rc01);
                    
                    __m256 __v_rco111 = _mm256_mul_ps(__v_rc11, __obin);
                    __m256 __v_rco110 = _mm256_sub_ps(__v_rc11, __v_rco111);
                    
                    __m256 __v_rco101 = _mm256_mul_ps(__v_rc10, __obin);
                    __m256 __v_rco100 = _mm256_sub_ps(__v_rc10, __v_rco101);
                    
                    __m256 __v_rco011 = _mm256_mul_ps(__v_rc01, __obin);
                    __m256 __v_rco010 = _mm256_sub_ps(__v_rc01, __v_rco011);
                    
                    __m256 __v_rco001 = _mm256_mul_ps(__v_rc00, __obin);
                    __m256 __v_rco000 = _mm256_sub_ps(__v_rc00, __v_rco001);
                    
                    __m256i __one = _mm256_set1_epi32(1);
                    __m256i __idx = _mm256_add_epi32(
                                                     _mm256_mullo_epi32(
                                                                        _mm256_add_epi32(
                                                                                         _mm256_mullo_epi32(_mm256_add_epi32(_mm256_cvtps_epi32(__r0), __one), _mm256_set1_epi32(d + 2)),
                                                                                         _mm256_add_epi32(_mm256_cvtps_epi32(__c0), __one)),
                                                                        _mm256_set1_epi32(n + 2)),
                                                     __o0i);
                    
                    _mm256_store_si256((__m256i *)idx_buf, __idx);
                    
                    _mm256_store_ps(&(rco_buf[0]),  __v_rco000);
                    _mm256_store_ps(&(rco_buf[8]),  __v_rco001);
                    _mm256_store_ps(&(rco_buf[16]), __v_rco010);
                    _mm256_store_ps(&(rco_buf[24]), __v_rco011);
                    _mm256_store_ps(&(rco_buf[32]), __v_rco100);
                    _mm256_store_ps(&(rco_buf[40]), __v_rco101);
                    _mm256_store_ps(&(rco_buf[48]), __v_rco110);
                    _mm256_store_ps(&(rco_buf[56]), __v_rco111);
#define HIST_SUM_HELPER(id)                                  \
hist[idx_buf[(id)]] += rco_buf[(id)];                    \
hist[idx_buf[(id)]+1] += rco_buf[8 + (id)];              \
hist[idx_buf[(id)]+(n+2)] += rco_buf[16 + (id)];         \
hist[idx_buf[(id)]+(n+3)] += rco_buf[24 + (id)];         \
hist[idx_buf[(id)]+(d+2)*(n+2)] += rco_buf[32 + (id)];   \
hist[idx_buf[(id)]+(d+2)*(n+2)+1] += rco_buf[40 + (id)]; \
hist[idx_buf[(id)]+(d+3)*(n+2)] += rco_buf[48 + (id)];   \
hist[idx_buf[(id)]+(d+3)*(n+2)+1] += rco_buf[56 + (id)];
                    
                    HIST_SUM_HELPER(0);
                    HIST_SUM_HELPER(1);
                    HIST_SUM_HELPER(2);
                    HIST_SUM_HELPER(3);
                    HIST_SUM_HELPER(4);
                    HIST_SUM_HELPER(5);
                    HIST_SUM_HELPER(6);
                    HIST_SUM_HELPER(7);
                    
#undef HIST_SUM_HELPER
                }
            }
#endif
            for( ; k < len; k++ )
            {
                float rbin = RBin[k], cbin = CBin[k];
                float obin = (Ori[k] - ori)*bins_per_rad;
                float mag = Mag[k]*W[k];
                
                int r0 = cvFloor( rbin );
                int c0 = cvFloor( cbin );
                int o0 = cvFloor( obin );
                rbin -= r0;
                cbin -= c0;
                obin -= o0;
                
                if( o0 < 0 )
                    o0 += n;
                if( o0 >= n )
                    o0 -= n;
                
                // histogram update using tri-linear interpolation
                float v_r1 = mag*rbin, v_r0 = mag - v_r1;
                float v_rc11 = v_r1*cbin, v_rc10 = v_r1 - v_rc11;
                float v_rc01 = v_r0*cbin, v_rc00 = v_r0 - v_rc01;
                float v_rco111 = v_rc11*obin, v_rco110 = v_rc11 - v_rco111;
                float v_rco101 = v_rc10*obin, v_rco100 = v_rc10 - v_rco101;
                float v_rco011 = v_rc01*obin, v_rco010 = v_rc01 - v_rco011;
                float v_rco001 = v_rc00*obin, v_rco000 = v_rc00 - v_rco001;
                
                int idx = ((r0+1)*(d+2) + c0+1)*(n+2) + o0;
                hist[idx] += v_rco000;
                hist[idx+1] += v_rco001;
                hist[idx+(n+2)] += v_rco010;
                hist[idx+(n+3)] += v_rco011;
                hist[idx+(d+2)*(n+2)] += v_rco100;
                hist[idx+(d+2)*(n+2)+1] += v_rco101;
                hist[idx+(d+3)*(n+2)] += v_rco110;
                hist[idx+(d+3)*(n+2)+1] += v_rco111;
            }
            
            // finalize histogram, since the orientation histograms are circular
            for( i = 0; i < d; i++ )
                for( j = 0; j < d; j++ )
                {
                    int idx = ((i+1)*(d+2) + (j+1))*(n+2);
                    hist[idx] += hist[idx+n];
                    hist[idx+1] += hist[idx+n+1];
                    for( k = 0; k < n; k++ )
                        dst[(i*d + j)*n + k] = hist[idx+k];
                }
            // copy histogram to the descriptor,
            // apply hysteresis thresholding
            // and scale the result, so that it can be easily converted
            // to byte array
            float nrm2 = 0;
            len = d*d*n;
            k = 0;
#if CV_AVX2
            if( USE_AVX2 )
            {
                float CV_DECL_ALIGNED(32) nrm2_buf[8];
                __m256 __nrm2 = _mm256_setzero_ps();
                __m256 __dst;
                for( ; k <= len - 8; k += 8 )
                {
                    __dst = _mm256_loadu_ps(&dst[k]);
#if CV_FMA3
                    __nrm2 = _mm256_fmadd_ps(__dst, __dst, __nrm2);
#else
                    __nrm2 = _mm256_add_ps(__nrm2, _mm256_mul_ps(__dst, __dst));
#endif
                }
                _mm256_store_ps(nrm2_buf, __nrm2);
                nrm2 = nrm2_buf[0] + nrm2_buf[1] + nrm2_buf[2] + nrm2_buf[3] +
                nrm2_buf[4] + nrm2_buf[5] + nrm2_buf[6] + nrm2_buf[7];
            }
#endif
            for( ; k < len; k++ )
                nrm2 += dst[k]*dst[k];
            
            float thr = std::sqrt(nrm2)*SIFT_DESCR_MAG_THR;
            
            i = 0, nrm2 = 0;
#if 0 //CV_AVX2
            // This code cannot be enabled because it sums nrm2 in a different order,
            // thus producing slightly different results
            if( USE_AVX2 )
            {
                float CV_DECL_ALIGNED(32) nrm2_buf[8];
                __m256 __dst;
                __m256 __nrm2 = _mm256_setzero_ps();
                __m256 __thr = _mm256_set1_ps(thr);
                for( ; i <= len - 8; i += 8 )
                {
                    __dst = _mm256_loadu_ps(&dst[i]);
                    __dst = _mm256_min_ps(__dst, __thr);
                    _mm256_storeu_ps(&dst[i], __dst);
#if CV_FMA3
                    __nrm2 = _mm256_fmadd_ps(__dst, __dst, __nrm2);
#else
                    __nrm2 = _mm256_add_ps(__nrm2, _mm256_mul_ps(__dst, __dst));
#endif
                }
                _mm256_store_ps(nrm2_buf, __nrm2);
                nrm2 = nrm2_buf[0] + nrm2_buf[1] + nrm2_buf[2] + nrm2_buf[3] +
                nrm2_buf[4] + nrm2_buf[5] + nrm2_buf[6] + nrm2_buf[7];
            }
#endif
            for( ; i < len; i++ )
            {
                float val = std::min(dst[i], thr);
                dst[i] = val;
                nrm2 += val*val;
            }
            nrm2 = SIFT_INT_DESCR_FCTR/std::max(std::sqrt(nrm2), FLT_EPSILON);
            
#if 1
            k = 0;
#if CV_AVX2
            if( USE_AVX2 )
            {
                __m256 __dst;
                __m256 __min = _mm256_setzero_ps();
                __m256 __max = _mm256_set1_ps(255.0f); // max of uchar
                __m256 __nrm2 = _mm256_set1_ps(nrm2);
                for( k = 0; k <= len - 8; k+=8 )
                {
                    __dst = _mm256_loadu_ps(&dst[k]);
                    __dst = _mm256_min_ps(_mm256_max_ps(_mm256_round_ps(_mm256_mul_ps(__dst, __nrm2), _MM_FROUND_TO_NEAREST_INT |_MM_FROUND_NO_EXC), __min), __max);
                    _mm256_storeu_ps(&dst[k], __dst);
                }
            }
#endif
            for( ; k < len; k++ )
            {
                dst[k] = saturate_cast<uchar>(dst[k]*nrm2);
            }
#else
            float nrm1 = 0;
            for( k = 0; k < len; k++ )
            {
                dst[k] *= nrm2;
                nrm1 += dst[k];
            }
            nrm1 = 1.f/std::max(nrm1, FLT_EPSILON);
            for( k = 0; k < len; k++ )
            {
                dst[k] = std::sqrt(dst[k] * nrm1);//saturate_cast<uchar>(std::sqrt(dst[k] * nrm1)*SIFT_INT_DESCR_FCTR);
            }
#endif
        }
        
        class calcDescriptorsComputer : public ParallelLoopBody
        {
        public:
            calcDescriptorsComputer(const std::vector<Mat>& _gpyr,
                                    const std::vector<KeyPoint>& _keypoints,
                                    Mat& _descriptors,
                                    int _nOctaveLayers,
                                    int _firstOctave)
            : gpyr(_gpyr),
            keypoints(_keypoints),
            descriptors(_descriptors),
            nOctaveLayers(_nOctaveLayers),
            firstOctave(_firstOctave) { }
            
            void operator()( const cv::Range& range ) const CV_OVERRIDE
            {
                const int begin = range.start;
                const int end = range.end;
                
                static const int d = SIFT_DESCR_WIDTH, n = SIFT_DESCR_HIST_BINS;
                
                for ( int i = begin; i<end; i++ )
                {
                    KeyPoint kpt = keypoints[i];
                    int octave, layer;
                    float scale;
                    unpackOctave(kpt, octave, layer, scale);
                    CV_Assert(octave >= firstOctave && layer <= nOctaveLayers+2);
                    float size=kpt.size*scale;
                    Point2f ptf(kpt.pt.x*scale, kpt.pt.y*scale);
                    const Mat& img = gpyr[(octave - firstOctave)*(nOctaveLayers + 3) + layer];
                    
                    float angle = 360.f - kpt.angle;
                    if(std::abs(angle - 360.f) < FLT_EPSILON)
                        angle = 0.f;
                    calcSIFTDescriptor(img, ptf, angle, size*0.5f, d, n, descriptors.ptr<float>((int)i));
                }
            }
        private:
            const std::vector<Mat>& gpyr;
            const std::vector<KeyPoint>& keypoints;
            Mat& descriptors;
            int nOctaveLayers;
            int firstOctave;
        };
        
        static void calcDescriptors(const std::vector<Mat>& gpyr, const std::vector<KeyPoint>& keypoints,
                                    Mat& descriptors, int nOctaveLayers, int firstOctave )
        {
            parallel_for_(Range(0, static_cast<int>(keypoints.size())), calcDescriptorsComputer(gpyr, keypoints, descriptors, nOctaveLayers, firstOctave));
        }
        
        //////////////////////////////////////////////////////////////////////////////////////////
        
        SIFT_Impl::SIFT_Impl( int _nfeatures, int _nOctaveLayers,
                             double _contrastThreshold, double _edgeThreshold, double _sigma )
        : nfeatures(_nfeatures), nOctaveLayers(_nOctaveLayers),
        contrastThreshold(_contrastThreshold), edgeThreshold(_edgeThreshold), sigma(_sigma)
        {
        }
        
        int SIFT_Impl::descriptorSize() const
        {
            return SIFT_DESCR_WIDTH*SIFT_DESCR_WIDTH*SIFT_DESCR_HIST_BINS;
        }
        
        int SIFT_Impl::descriptorType() const
        {
            return CV_32F;
        }
        
        int SIFT_Impl::defaultNorm() const
        {
            return NORM_L2;
        }
        
        
        void SIFT_Impl::detectAndCompute(InputArray _image, InputArray _mask,
                                         std::vector<KeyPoint>& keypoints,
                                         OutputArray _descriptors,
                                         bool useProvidedKeypoints)
        {
            uint64_t start, end, tt;
            int firstOctave = -1, actualNOctaves = 0, actualNLayers = 0;
            Mat image = _image.getMat(), mask = _mask.getMat();
            
            if( image.empty() || image.depth() != CV_8U )
                CV_Error( Error::StsBadArg, "image is empty or has incorrect depth (!=CV_8U)" );
            
            if( !mask.empty() && mask.type() != CV_8UC1 )
                CV_Error( Error::StsBadArg, "mask has incorrect type (!=CV_8UC1)" );
            
            if( useProvidedKeypoints )
            {
                firstOctave = 0;
                int maxOctave = INT_MIN;
                for( size_t i = 0; i < keypoints.size(); i++ )
                {
                    int octave, layer;
                    float scale;
                    unpackOctave(keypoints[i], octave, layer, scale);
                    firstOctave = std::min(firstOctave, octave);
                    maxOctave = std::max(maxOctave, octave);
                    actualNLayers = std::max(actualNLayers, layer-2);
                }
                
                firstOctave = std::min(firstOctave, 0);
                CV_Assert( firstOctave >= -1 && actualNLayers <= nOctaveLayers );
                actualNOctaves = maxOctave - firstOctave + 1;
            }
            
            Mat base = createInitialImage(image, firstOctave < 0, (float)sigma); //will double
            std::vector<Mat> gpyr, dogpyr;
            int nOctaves = actualNOctaves > 0 ? actualNOctaves : cvRound(std::log( (double)std::min( base.cols, base.rows ) ) / std::log(2.) - 2) - firstOctave -2; //nOctaves
            
            start = rdtsc();
            buildGaussianPyramid(base, gpyr, nOctaves); // gaussian blur
            end = rdtsc();
            tt = end - start;
            buildGaussianPyramidCycles += tt;
            
            start = rdtsc();
            buildDoGPyramid(gpyr, dogpyr); //substract
            end = rdtsc();
            tt = end - start;
            buildDoGCycles += tt;
            
            if( !useProvidedKeypoints )
            {
                findScaleSpaceExtrema(gpyr, dogpyr, keypoints); //find local extrema
                
                KeyPointsFilter::removeDuplicatedSorted( keypoints ); //remove duplicated

                if( nfeatures > 0 )
                    KeyPointsFilter::retainBest(keypoints, nfeatures);
                
                if( firstOctave < 0 )
                    for( size_t i = 0; i < keypoints.size(); i++ )
                    {
                        KeyPoint& kpt = keypoints[i];
                        float scale = 1.f/(float)(1 << -firstOctave);
                        kpt.octave = (kpt.octave & ~255) | ((kpt.octave + firstOctave) & 255);
                        kpt.pt *= scale;
                        kpt.size *= scale;
                    }
                
                if( !mask.empty() )
                    KeyPointsFilter::runByPixelsMask( keypoints, mask );
            }
        }
        
        
    }
}





#define is_aligned(POINTER, BYTE_COUNT) \
(((uintptr_t)(const void *)(POINTER)) % (BYTE_COUNT) == 0)


int main( int argc, char** argv )
{
    printf("Start Running!\n");
    for (int iters = 0; iters < 128; iters++) {
       cv::Mat input = cv::imread("/Users/stevenliu/Downloads/demo1024.JPG", 0); //Load as grayscale
       resize(input, input, Size(1024, 1024));

       Mat output;
       Mat mask = Mat();

       cv::Ptr<Feature2D> f2d = xfeatures2d::SIFT::create();

       cv::xfeatures2d::SIFT_Impl sift_instance = cv::xfeatures2d::SIFT_Impl();

       std::vector<KeyPoint> keypoints_1;
       std::vector<KeyPoint> keypoints_2;

       sift_instance.detectAndCompute(input, mask, keypoints_2, output);
    }
    
    printf("Cycles spent on buildGaussianPyramid: %lld\nCycles spent on buildDoGPyramid: %lld\n", buildGaussianPyramidCycles >> 7, buildDoGCycles >> 7);
    
    return 0;
}