src/kcf.cpp

   1 #include "kcf.h"
   2 #include <numeric>
   3 #include <thread>
   4 #include <future>
   5 #include <algorithm>
   6
   7 #ifdef FFTW
   8   #include "fft_fftw.h"
   9   #define FFT Fftw
  10 #elif CUFFT
  11   #include "fft_cufft.h"
  12   #define FFT cuFFT
  13 #else
  14   #include "fft_opencv.h"
  15   #define FFT FftOpencv
  16 #endif
  17
  18 #ifdef OPENMP
  19 #include <omp.h>
  20 #endif //OPENMP
  21
  22 #define DEBUG_PRINT(obj) if (m_debug || m_visual_debug) {std::cout << #obj << " @" << __LINE__ << std::endl << (obj) << std::endl;}
  23 #define DEBUG_PRINTM(obj) if (m_debug) {std::cout << #obj << " @" << __LINE__ << " " << (obj).size() << " CH: " << (obj).channels() << std::endl << (obj) << std::endl;}
  24
  25 KCF_Tracker::KCF_Tracker(double padding, double kernel_sigma, double lambda, double interp_factor, double output_sigma_factor, int cell_size) :
  26     fft(*new FFT()),
  27     p_padding(padding), p_output_sigma_factor(output_sigma_factor), p_kernel_sigma(kernel_sigma),
  28     p_lambda(lambda), p_interp_factor(interp_factor), p_cell_size(cell_size) {}
  29
  30 KCF_Tracker::KCF_Tracker()
  31     : fft(*new FFT()) {}
  32
  33 KCF_Tracker::~KCF_Tracker()
  34 {
  35     delete &fft;
  36 #ifdef CUFFT
  37     CudaSafeCall(cudaFreeHost(xf_sqr_norm));
  38     CudaSafeCall(cudaFreeHost(yf_sqr_norm));
  39     CudaSafeCall(cudaFree(gauss_corr_res));
  40 #else
  41     free(xf_sqr_norm);
  42     free(yf_sqr_norm);
  43 #endif
  44 }
  45
  46 void KCF_Tracker::init(cv::Mat &img, const cv::Rect & bbox, int fit_size_x, int fit_size_y)
  47 {
  48     //check boundary, enforce min size
  49     double x1 = bbox.x, x2 = bbox.x + bbox.width, y1 = bbox.y, y2 = bbox.y + bbox.height;
  50     if (x1 < 0) x1 = 0.;
  51     if (x2 > img.cols-1) x2 = img.cols - 1;
  52     if (y1 < 0) y1 = 0;
  53     if (y2 > img.rows-1) y2 = img.rows - 1;
  54
  55     if (x2-x1 < 2*p_cell_size) {
  56         double diff = (2*p_cell_size -x2+x1)/2.;
  57         if (x1 - diff >= 0 && x2 + diff < img.cols){
  58             x1 -= diff;
  59             x2 += diff;
  60         } else if (x1 - 2*diff >= 0) {
  61             x1 -= 2*diff;
  62         } else {
  63             x2 += 2*diff;
  64         }
  65     }
  66     if (y2-y1 < 2*p_cell_size) {
  67         double diff = (2*p_cell_size -y2+y1)/2.;
  68         if (y1 - diff >= 0 && y2 + diff < img.rows){
  69             y1 -= diff;
  70             y2 += diff;
  71         } else if (y1 - 2*diff >= 0) {
  72             y1 -= 2*diff;
  73         } else {
  74             y2 += 2*diff;
  75         }
  76     }
  77
  78     p_pose.w = x2-x1;
  79     p_pose.h = y2-y1;
  80     p_pose.cx = x1 + p_pose.w/2.;
  81     p_pose.cy = y1 + p_pose.h /2.;
  82
  83
  84     cv::Mat input_gray, input_rgb = img.clone();
  85     if (img.channels() == 3){
  86         cv::cvtColor(img, input_gray, CV_BGR2GRAY);
  87         input_gray.convertTo(input_gray, CV_32FC1);
  88     }else
  89         img.convertTo(input_gray, CV_32FC1);
  90
  91     // don't need too large image
  92     if (p_pose.w * p_pose.h > 100.*100. && (fit_size_x == -1 || fit_size_y == -1)) {
  93         std::cout << "resizing image by factor of " << 1/p_downscale_factor << std::endl;
  94         p_resize_image = true;
  95         p_pose.scale(p_downscale_factor);
  96         cv::resize(input_gray, input_gray, cv::Size(0,0), p_downscale_factor, p_downscale_factor, cv::INTER_AREA);
  97         cv::resize(input_rgb, input_rgb, cv::Size(0,0), p_downscale_factor, p_downscale_factor, cv::INTER_AREA);
  98     } else if (!(fit_size_x == -1 && fit_size_y == -1)) {
  99         if (fit_size_x%p_cell_size != 0 || fit_size_y%p_cell_size != 0) {
 100             std::cerr << "Fit size does not fit to hog cell size. The dimensions have to be divisible by HOG cell size, which is: " << p_cell_size << std::endl;;
 101             std::exit(EXIT_FAILURE);
 102         }
 103         double tmp;
 104         if (( tmp = (p_pose.w * (1. + p_padding) / p_cell_size) * p_cell_size ) != fit_size_x)
 105             p_scale_factor_x = fit_size_x/tmp;
 106         if (( tmp = (p_pose.h * (1. + p_padding) / p_cell_size) * p_cell_size ) != fit_size_y)
 107             p_scale_factor_y = fit_size_y/tmp;
 108         std::cout << "resizing image horizontaly by factor of " << p_scale_factor_x
 109                   << " and verticaly by factor of " << p_scale_factor_y << std::endl;
 110         p_fit_to_pw2 = true;
 111         p_pose.scale_x(p_scale_factor_x);
 112         p_pose.scale_y(p_scale_factor_y);
 113         if (p_scale_factor_x != 1 && p_scale_factor_y != 1) {
 114             if (p_scale_factor_x < 1 && p_scale_factor_y < 1) {
 115                 cv::resize(input_gray, input_gray, cv::Size(0, 0), p_scale_factor_x, p_scale_factor_y, cv::INTER_AREA);
 116                 cv::resize(input_rgb, input_rgb, cv::Size(0, 0), p_scale_factor_x, p_scale_factor_y, cv::INTER_AREA);
 117             } else {
 118                 cv::resize(input_gray, input_gray, cv::Size(0, 0), p_scale_factor_x, p_scale_factor_y, cv::INTER_LINEAR);
 119                 cv::resize(input_rgb, input_rgb, cv::Size(0, 0), p_scale_factor_x, p_scale_factor_y, cv::INTER_LINEAR);
 120             }
 121         }
 122     }
 123
 124     //compute win size + fit to fhog cell size
 125     p_windows_size[0] = round(p_pose.w * (1. + p_padding) / p_cell_size) * p_cell_size;
 126     p_windows_size[1] = round(p_pose.h * (1. + p_padding) / p_cell_size) * p_cell_size;
 127
 128     p_scales.clear();
 129     if (m_use_scale)
 130         for (int i = -p_num_scales/2; i <= p_num_scales/2; ++i)
 131             p_scales.push_back(std::pow(p_scale_step, i));
 132     else
 133         p_scales.push_back(1.);
 134
 135      if (m_use_angle) {
 136         for (int i = p_angle_min; i <=p_angle_max ; i += p_angle_step)
 137             p_angles.push_back(i);
 138      } else {
 139         p_angles.push_back(0);
 140      }
 141
 142 #ifdef CUFFT
 143     if (p_windows_size[1]/p_cell_size*(p_windows_size[0]/p_cell_size/2+1) > 1024) {
 144         std::cerr << "Window after forward FFT is too big for CUDA kernels. Plese use -f to set "
 145         "the window dimensions so its size is less or equal to " << 1024*p_cell_size*p_cell_size*2+1 <<
 146         " pixels . Currently the size of the window is: " <<  p_windows_size[0] << "x" <<  p_windows_size[1] <<
 147         " which is  " <<  p_windows_size[0]*p_windows_size[1] << " pixels. " << std::endl;
 148         std::exit(EXIT_FAILURE);
 149     }
 150
 151     if (m_use_linearkernel){
 152         std::cerr << "cuFFT supports only Gaussian kernel." << std::endl;
 153         std::exit(EXIT_FAILURE);
 154     }
 155     cudaSetDeviceFlags(cudaDeviceMapHost);
 156     CudaSafeCall(cudaHostAlloc((void**)&xf_sqr_norm, p_num_scales*sizeof(float), cudaHostAllocMapped));
 157     CudaSafeCall(cudaHostGetDevicePointer((void**)&xf_sqr_norm_d, (void*)xf_sqr_norm, 0));
 158
 159     CudaSafeCall(cudaHostAlloc((void**)&yf_sqr_norm, sizeof(float), cudaHostAllocMapped));
 160     CudaSafeCall(cudaHostGetDevicePointer((void**)&yf_sqr_norm_d, (void*)yf_sqr_norm, 0));
 161 #else
 162     xf_sqr_norm = (float*) malloc(p_num_scales*sizeof(float));
 163     yf_sqr_norm = (float*) malloc(sizeof(float));
 164 #endif
 165
 166     p_current_scale = 1.;
 167
 168     double min_size_ratio = std::max(5.*p_cell_size/p_windows_size[0], 5.*p_cell_size/p_windows_size[1]);
 169     double max_size_ratio = std::min(floor((img.cols + p_windows_size[0]/3)/p_cell_size)*p_cell_size/p_windows_size[0], floor((img.rows + p_windows_size[1]/3)/p_cell_size)*p_cell_size/p_windows_size[1]);
 170     p_min_max_scale[0] = std::pow(p_scale_step, std::ceil(std::log(min_size_ratio) / log(p_scale_step)));
 171     p_min_max_scale[1] = std::pow(p_scale_step, std::floor(std::log(max_size_ratio) / log(p_scale_step)));
 172
 173     std::cout << "init: img size " << img.cols << " " << img.rows << std::endl;
 174     std::cout << "init: win size. " << p_windows_size[0] << " " << p_windows_size[1] << std::endl;
 175     std::cout << "init: min max scales factors: " << p_min_max_scale[0] << " " << p_min_max_scale[1] << std::endl;
 176
 177     p_output_sigma = std::sqrt(p_pose.w*p_pose.h) * p_output_sigma_factor / static_cast<double>(p_cell_size);
 178
 179     //window weights, i.e. labels
 180     p_num_of_feats = 31;
 181     if(m_use_color) p_num_of_feats += 3;
 182     if(m_use_cnfeat) p_num_of_feats += 10;
 183     p_roi_width = p_windows_size[0]/p_cell_size;
 184     p_roi_height = p_windows_size[1]/p_cell_size;
 185
 186     fft.init(p_windows_size[0]/p_cell_size, p_windows_size[1]/p_cell_size, p_num_of_feats, p_num_scales, m_use_big_batch);
 187     p_yf = fft.forward(gaussian_shaped_labels(p_output_sigma, p_windows_size[0]/p_cell_size, p_windows_size[1]/p_cell_size));
 188     fft.set_window(cosine_window_function(p_windows_size[0]/p_cell_size, p_windows_size[1]/p_cell_size));
 189
 190 #ifdef CUFFT
 191       CudaSafeCall(cudaMalloc((void**)&gauss_corr_res, (p_windows_size[0]/p_cell_size)*(p_windows_size[1]/p_cell_size)*p_num_scales*sizeof(float)));
 192 #endif
 193     //obtain a sub-window for training initial model
 194     int size_x_scaled = floor(p_windows_size[0]);
 195     int size_y_scaled = floor(p_windows_size[1]);
 196
 197     cv::Mat patch_gray = get_subwindow(input_gray, this->p_pose.cx, this->p_pose.cy, size_x_scaled, size_y_scaled);
 198     geometric_transformations(patch_gray, p_windows_size[0], p_windows_size[1], 1, 0, false);
 199
 200     cv::Mat patch_rgb = cv::Mat::zeros(size_y_scaled, size_x_scaled, CV_32F);
 201     if ((m_use_color || m_use_cnfeat) && input_rgb.channels() == 3) {
 202         patch_rgb = get_subwindow(input_rgb, this->p_pose.cx, this->p_pose.cy, size_x_scaled, size_y_scaled);
 203         geometric_transformations(patch_rgb,  p_windows_size[0], p_windows_size[1], 1, 0, false);
 204     }
 205     std::vector<cv::Mat> path_feat = get_features(patch_rgb, patch_gray);
 206     p_model_xf = fft.forward_window(path_feat);
 207     DEBUG_PRINTM(p_model_xf);
 208
 209     if (m_use_linearkernel) {
 210         ComplexMat xfconj = p_model_xf.conj();
 211         p_model_alphaf_num = xfconj.mul(p_yf);
 212         p_model_alphaf_den = (p_model_xf * xfconj);
 213     } else {
 214         //Kernel Ridge Regression, calculate alphas (in Fourier domain)
 215         ComplexMat kf = gaussian_correlation(p_model_xf, p_model_xf, p_kernel_sigma, true);
 216         DEBUG_PRINTM(kf);
 217         p_model_alphaf_num = p_yf * kf;
 218         DEBUG_PRINTM(p_model_alphaf_num);
 219         p_model_alphaf_den = kf * (kf + p_lambda);
 220         DEBUG_PRINTM(p_model_alphaf_den);
 221     }
 222     p_model_alphaf = p_model_alphaf_num / p_model_alphaf_den;
 223     DEBUG_PRINTM(p_model_alphaf);
 224 //        p_model_alphaf = p_yf / (kf + p_lambda);   //equation for fast training
 225 }
 226
 227 void KCF_Tracker::setTrackerPose(BBox_c &bbox, cv::Mat & img, int fit_size_x, int fit_size_y)
 228 {
 229     init(img, bbox.get_rect(), fit_size_x, fit_size_y);
 230 }
 231
 232 void KCF_Tracker::updateTrackerPosition(BBox_c &bbox)
 233 {
 234     if (p_resize_image) {
 235         BBox_c tmp = bbox;
 236         tmp.scale(p_downscale_factor);
 237         p_pose.cx = tmp.cx;
 238         p_pose.cy = tmp.cy;
 239     } else if (p_fit_to_pw2) {
 240         BBox_c tmp = bbox;
 241         tmp.scale_x(p_scale_factor_x);
 242         tmp.scale_y(p_scale_factor_y);
 243         p_pose.cx = tmp.cx;
 244         p_pose.cy = tmp.cy;
 245     } else {
 246         p_pose.cx = bbox.cx;
 247         p_pose.cy = bbox.cy;
 248     }
 249 }
 250
 251 BBox_c KCF_Tracker::getBBox()
 252 {
 253     BBox_c tmp = p_pose;
 254     tmp.w *= p_current_scale;
 255     tmp.h *= p_current_scale;
 256     tmp.a = p_current_angle;
 257
 258     if (p_resize_image)
 259         tmp.scale(1/p_downscale_factor);
 260     if (p_fit_to_pw2) {
 261         tmp.scale_x(1/p_scale_factor_x);
 262         tmp.scale_y(1/p_scale_factor_y);
 263     }
 264
 265     return tmp;
 266 }
 267
 268 void KCF_Tracker::track(cv::Mat &img)
 269 {
 270     if (m_debug || m_visual_debug)
 271         std::cout << "\nNEW FRAME" << std::endl;
 272     cv::Mat input_gray, input_rgb = img.clone();
 273     if (img.channels() == 3){
 274         cv::cvtColor(img, input_gray, CV_BGR2GRAY);
 275         input_gray.convertTo(input_gray, CV_32FC1);
 276     }else
 277         img.convertTo(input_gray, CV_32FC1);
 278
 279     // don't need too large image
 280     if (p_resize_image) {
 281         cv::resize(input_gray, input_gray, cv::Size(0, 0), p_downscale_factor, p_downscale_factor, cv::INTER_AREA);
 282         cv::resize(input_rgb, input_rgb, cv::Size(0, 0), p_downscale_factor, p_downscale_factor, cv::INTER_AREA);
 283     } else if (p_fit_to_pw2 && p_scale_factor_x != 1 && p_scale_factor_y != 1) {
 284         if (p_scale_factor_x < 1 && p_scale_factor_y < 1) {
 285             cv::resize(input_gray, input_gray, cv::Size(0, 0), p_scale_factor_x, p_scale_factor_y, cv::INTER_AREA);
 286             cv::resize(input_rgb, input_rgb, cv::Size(0, 0), p_scale_factor_x, p_scale_factor_y, cv::INTER_AREA);
 287         } else {
 288             cv::resize(input_gray, input_gray, cv::Size(0, 0), p_scale_factor_x, p_scale_factor_y, cv::INTER_LINEAR);
 289             cv::resize(input_rgb, input_rgb, cv::Size(0, 0), p_scale_factor_x, p_scale_factor_y, cv::INTER_LINEAR);
 290         }
 291     }
 292
 293
 294     std::vector<cv::Mat> patch_feat;
 295     double max_response = -1.;
 296     cv::Mat max_response_map;
 297     cv::Point2i max_response_pt;
 298     int scale_index = 0;
 299     int angle_index = 0;
 300     std::vector<double> scale_responses;
 301
 302     if (m_use_multithreading){
 303         std::vector<std::future<cv::Mat>> async_res(p_scales.size());
 304         for (size_t i = 0; i < p_scales.size(); ++i) {
 305             async_res[i] = std::async(std::launch::async,
 306                                       [this, &input_gray, &input_rgb, i]() -> cv::Mat
 307                                       {
 308                                           int size_x_scaled = floor(p_windows_size[0]*p_current_scale * this->p_scales[i]);
 309                                           int size_y_scaled = floor(p_windows_size[1]*p_current_scale * this->p_scales[i]);
 310
 311                                           cv::Mat patch_gray = get_subwindow(input_gray, this->p_pose.cx, this->p_pose.cy, size_x_scaled, size_y_scaled);
 312                                           geometric_transformations(patch_gray, p_windows_size[0], p_windows_size[1], p_current_scale * this->p_scales[i]);
 313
 314                                           cv::Mat patch_rgb = cv::Mat::zeros(size_y_scaled, size_x_scaled, CV_32F);
 315                                           if ((m_use_color || m_use_cnfeat) && input_rgb.channels() == 3) {
 316                                               patch_rgb = get_subwindow(input_rgb, this->p_pose.cx, this->p_pose.cy, size_x_scaled, size_y_scaled);
 317                                               geometric_transformations(patch_rgb, p_windows_size[0], p_windows_size[1], p_current_scale * this->p_scales[i]);
 318                                           }
 319
 320                                           std::vector<cv::Mat> patch_feat_async = get_features(patch_rgb, patch_gray);
 321                                           ComplexMat zf = fft.forward_window(patch_feat_async);
 322                                           if (m_use_linearkernel)
 323                                               return fft.inverse((p_model_alphaf * zf).sum_over_channels());
 324                                           else {
 325                                               ComplexMat kzf = gaussian_correlation(zf, this->p_model_xf, this->p_kernel_sigma);
 326                                               return fft.inverse(this->p_model_alphaf * kzf);
 327                                           }
 328                                       });
 329         }
 330
 331         for (size_t i = 0; i < p_scales.size(); ++i) {
 332             // wait for result
 333             async_res[i].wait();
 334             cv::Mat response = async_res[i].get();
 335
 336             double min_val, max_val;
 337             cv::Point2i min_loc, max_loc;
 338             cv::minMaxLoc(response, &min_val, &max_val, &min_loc, &max_loc);
 339
 340             double weight = p_scales[i] < 1. ? p_scales[i] : 1./p_scales[i];
 341             if (max_val*weight > max_response) {
 342                 max_response = max_val*weight;
 343                 max_response_map = response;
 344                 max_response_pt = max_loc;
 345                 scale_index = i;
 346             }
 347             scale_responses.push_back(max_val*weight);
 348         }
 349     } else if (m_use_big_batch){
 350 #pragma omp parallel for ordered
 351         for (size_t i = 0; i < p_scales.size(); ++i) {
 352             int size_x_scaled = floor(p_windows_size[0]*p_current_scale * this->p_scales[i]);
 353             int size_y_scaled = floor(p_windows_size[1]*p_current_scale * this->p_scales[i]);
 354
 355             cv::Mat patch_gray = get_subwindow(input_gray, this->p_pose.cx, this->p_pose.cy, size_x_scaled, size_y_scaled);
 356             geometric_transformations(patch_gray, p_windows_size[0], p_windows_size[1], p_current_scale * this->p_scales[i]);
 357
 358             cv::Mat patch_rgb = cv::Mat::zeros(size_y_scaled, size_x_scaled, CV_32F);
 359             if ((m_use_color || m_use_cnfeat) && input_rgb.channels() == 3) {
 360                 patch_rgb = get_subwindow(input_rgb, this->p_pose.cx, this->p_pose.cy, size_x_scaled, size_y_scaled);
 361                 geometric_transformations(patch_rgb, p_windows_size[0], p_windows_size[1],  p_current_scale * this->p_scales[i]);
 362             }
 363             std::vector<cv::Mat> tmp = get_features(input_rgb, input_gray);
 364 #pragma omp ordered
 365             patch_feat.insert(std::end(patch_feat), std::begin(tmp), std::end(tmp));
 366         }
 367         ComplexMat zf = fft.forward_window(patch_feat);
 368         DEBUG_PRINTM(zf);
 369         cv::Mat response;
 370
 371         if (m_use_linearkernel)
 372             response = fft.inverse((zf.mul2(p_model_alphaf)).sum_over_channels());
 373         else {
 374             ComplexMat kzf = gaussian_correlation(zf, p_model_xf, p_kernel_sigma);
 375             DEBUG_PRINTM(p_model_alphaf);
 376             DEBUG_PRINTM(kzf);
 377             response = fft.inverse(kzf.mul(p_model_alphaf));
 378         }
 379         DEBUG_PRINTM(response);
 380         std::vector<cv::Mat> scales;
 381         cv::split(response,scales);
 382
 383         /* target location is at the maximum response. we must take into
 384            account the fact that, if the target doesn't move, the peak
 385            will appear at the top-left corner, not at the center (this is
 386            discussed in the paper). the responses wrap around cyclically. */
 387         for (size_t i = 0; i < p_scales.size(); ++i) {
 388             double min_val, max_val;
 389             cv::Point2i min_loc, max_loc;
 390             cv::minMaxLoc(scales[i], &min_val, &max_val, &min_loc, &max_loc);
 391             DEBUG_PRINT(max_loc);
 392
 393             double weight = p_scales[i] < 1. ? p_scales[i] : 1./p_scales[i];
 394
 395             if (max_val*weight > max_response) {
 396                 max_response = max_val*weight;
 397                 max_response_map = scales[i];
 398                 max_response_pt = max_loc;
 399                 scale_index = i;
 400             }
 401             scale_responses.push_back(max_val*weight);
 402         }
 403     } else {
 404 #pragma omp parallel for ordered  private(patch_feat) schedule(dynamic)
 405         for (size_t i = 0; i < p_scales.size(); ++i) {
 406                 for (size_t j = 0; j < p_angles.size(); ++j) {
 407                     int size_x_scaled = floor(p_windows_size[0]*p_current_scale * p_scales[i]);
 408                     int size_y_scaled = floor(p_windows_size[1]*p_current_scale * p_scales[i]);
 409
 410                     cv::Mat patch_gray = get_subwindow(input_gray, p_pose.cx, p_pose.cy, size_x_scaled, size_y_scaled);
 411                     geometric_transformations(patch_gray, p_windows_size[0], p_windows_size[1], p_current_scale * p_scales[i], p_current_angle + p_angles[j]);
 412
 413                     cv::Mat patch_rgb = cv::Mat::zeros(size_y_scaled, size_x_scaled, CV_32F);
 414                     if ((m_use_color || m_use_cnfeat) && input_rgb.channels() == 3) {
 415                         patch_rgb = get_subwindow(input_rgb, p_pose.cx, p_pose.cy, size_x_scaled, size_y_scaled);
 416                         geometric_transformations(patch_rgb, p_windows_size[0], p_windows_size[1], p_current_scale * p_scales[i],  p_current_angle + p_angles[j]);
 417                     }
 418
 419                     patch_feat = get_features(patch_rgb, patch_gray);
 420                     ComplexMat zf = fft.forward_window(patch_feat);
 421                     DEBUG_PRINTM(zf);
 422                     cv::Mat response;
 423                     if (m_use_linearkernel)
 424                         response = fft.inverse((p_model_alphaf * zf).sum_over_channels());
 425                     else {
 426                         ComplexMat kzf = gaussian_correlation(zf, p_model_xf, p_kernel_sigma);
 427                         DEBUG_PRINTM(p_model_alphaf);
 428                         DEBUG_PRINTM(kzf);
 429                         DEBUG_PRINTM(p_model_alphaf * kzf);
 430                         response = fft.inverse(p_model_alphaf * kzf);
 431                     }
 432                     DEBUG_PRINTM(response);
 433
 434                     /* target location is at the maximum response. we must take into
 435                     account the fact that, if the target doesn't move, the peak
 436                     will appear at the top-left corner, not at the center (this is
 437                     discussed in the paper). the responses wrap around cyclically. */
 438                     double min_val, max_val;
 439                     cv::Point2i min_loc, max_loc;
 440                     cv::minMaxLoc(response, &min_val, &max_val, &min_loc, &max_loc);
 441                     DEBUG_PRINT(max_loc);
 442
 443                     double weight = p_scales[i] < 1. ? p_scales[i] : 1./p_scales[i];
 444                     if (m_visual_debug){
 445                         std::string scale = std::to_string(p_scales[i]);
 446                         scale.erase ( scale.find_last_not_of('0') + 1, std::string::npos );
 447                         scale.erase ( scale.find_last_not_of('.') + 1, std::string::npos );
 448
 449                         std::string angle = std::to_string(p_current_angle + p_angles[j]);
 450                         angle.erase ( angle.find_last_not_of('0') + 1, std::string::npos );
 451                         angle.erase ( angle.find_last_not_of('.') + 1, std::string::npos );
 452                         std::cout << "Max value for scale: " << scale << " and angle:" << angle <<  " is: " << std::to_string(max_val*weight) << std::endl;
 453                         cv::Mat copy_response = response.clone();
 454
 455                         // crop the spectrum, if it has an odd number of rows or columns
 456                         copy_response = copy_response(cv::Rect(0, 0, copy_response.cols & -2, copy_response.rows & -2));
 457
 458                         // rearrange the quadrants of Fourier image  so that the origin is at the image center
 459                         int cx = copy_response.cols/2;
 460                         int cy = copy_response.rows/2;
 461
 462                         cv::Mat q0(copy_response, cv::Rect(0, 0, cx, cy));   // Top-Left - Create a ROI per quadrant
 463                         cv::Mat q1(copy_response, cv::Rect(cx, 0, cx, cy));  // Top-Right
 464                         cv::Mat q2(copy_response, cv::Rect(0, cy, cx, cy));  // Bottom-Left
 465                         cv::Mat q3(copy_response, cv::Rect(cx, cy, cx, cy)); // Bottom-Right
 466
 467                         cv::Mat tmp;                           // swap quadrants (Top-Left with Bottom-Right)
 468                         q0.copyTo(tmp);
 469                         q3.copyTo(q0);
 470                         tmp.copyTo(q3);
 471
 472                         q1.copyTo(tmp);                    // swap quadrant (Top-Right with Bottom-Left)
 473                         q2.copyTo(q1);
 474                         tmp.copyTo(q2);
 475
 476                         cv::resize(copy_response, copy_response, cv::Size(p_debug_image_size, p_debug_image_size), 0., 0., cv::INTER_LINEAR);
 477                         cv::putText(copy_response, angle,  cv::Point(0, copy_response.rows-1), cv::FONT_HERSHEY_COMPLEX_SMALL, 0.5, cv::Scalar(255,255,255),1,cv::LINE_AA);
 478                         if ((p_count-1)%5 == 0)
 479                             cv::putText(copy_response, scale,  cv::Point(0, 10), cv::FONT_HERSHEY_COMPLEX_SMALL, 0.5, cv::Scalar(255,255,255),1,cv::LINE_AA);
 480
 481                         p_debug_scale_responses.push_back(copy_response);
 482                     }
 483 #pragma omp critical
 484                     {
 485                         if (max_val*weight > max_response) {
 486                             max_response = max_val*weight;
 487                             max_response_map = response;
 488                             max_response_pt = max_loc;
 489                             scale_index = i;
 490                             angle_index = j;
 491                         }
 492                     }
 493 #pragma omp ordered
 494                     scale_responses.push_back(max_val*weight);
 495             }
 496         }
 497         if (m_visual_debug){
 498             cv::Mat all_responses(cv::Size(p_angles.size()*p_debug_image_size, p_scales.size()*p_debug_image_size), p_debug_scale_responses[0].type(), cv::Scalar::all(0));
 499             cv::Mat all_subwindows(cv::Size(p_angles.size()*p_debug_image_size, p_scales.size()*p_debug_image_size), p_debug_subwindows[0].type(), cv::Scalar::all(0));
 500             for (size_t i = 0; i < p_scales.size(); ++i) {
 501                 for (size_t j = 0; j < p_angles.size(); ++j) {
 502                     cv::Mat in_roi(all_responses, cv::Rect(j*p_debug_image_size, i*p_debug_image_size, p_debug_image_size, p_debug_image_size));
 503                     p_debug_scale_responses[5*i+j].copyTo(in_roi);
 504                     in_roi = all_subwindows(cv::Rect(j*p_debug_image_size, i*p_debug_image_size, p_debug_image_size, p_debug_image_size));
 505                     p_debug_subwindows[5*i+j].copyTo(in_roi);
 506                 }
 507             }
 508             cv::namedWindow("All subwindows", CV_WINDOW_AUTOSIZE);
 509             cv::imshow("All subwindows", all_subwindows);
 510             cv::namedWindow("All responses", CV_WINDOW_AUTOSIZE);
 511             cv::imshow("All responses", all_responses);
 512             cv::waitKey();
 513             p_debug_scale_responses.clear();
 514             p_debug_subwindows.clear();
 515         }
 516     }
 517     DEBUG_PRINTM(max_response_map);
 518     DEBUG_PRINT(max_response_pt);
 519
 520     //sub pixel quadratic interpolation from neighbours
 521     if (max_response_pt.y > max_response_map.rows / 2) //wrap around to negative half-space of vertical axis
 522         max_response_pt.y = max_response_pt.y - max_response_map.rows;
 523     if (max_response_pt.x > max_response_map.cols / 2) //same for horizontal axis
 524         max_response_pt.x = max_response_pt.x - max_response_map.cols;
 525
 526     cv::Point2f new_location(max_response_pt.x, max_response_pt.y);
 527     DEBUG_PRINT(new_location);
 528
 529     if (m_use_subpixel_localization)
 530         new_location = sub_pixel_peak(max_response_pt, max_response_map);
 531     DEBUG_PRINT(new_location);
 532
 533     if (m_visual_debug)
 534         std::cout << "Old p_pose, cx: " << p_pose.cx << " cy: " << p_pose.cy << std::endl;
 535
 536     p_pose.cx += p_current_scale*p_cell_size*new_location.x;
 537     p_pose.cy += p_current_scale*p_cell_size*new_location.y;
 538
 539     if (m_visual_debug)
 540         std::cout << "New p_pose, cx: " << p_pose.cx << " cy: " << p_pose.cy << std::endl;
 541
 542     if (p_fit_to_pw2) {
 543         if (p_pose.cx < 0) p_pose.cx = 0;
 544         if (p_pose.cx > (img.cols*p_scale_factor_x)-1) p_pose.cx = (img.cols*p_scale_factor_x)-1;
 545         if (p_pose.cy < 0) p_pose.cy = 0;
 546         if (p_pose.cy > (img.rows*p_scale_factor_y)-1) p_pose.cy = (img.rows*p_scale_factor_y)-1;
 547     } else {
 548         if (p_pose.cx < 0) p_pose.cx = 0;
 549         if (p_pose.cx > img.cols-1) p_pose.cx = img.cols-1;
 550         if (p_pose.cy < 0) p_pose.cy = 0;
 551         if (p_pose.cy > img.rows-1) p_pose.cy = img.rows-1;
 552     }
 553
 554     //sub grid scale interpolation
 555     double new_scale = p_scales[scale_index];
 556     if (m_use_subgrid_scale)
 557         new_scale = sub_grid_scale(scale_responses, scale_index);
 558
 559     p_current_scale *= new_scale;
 560
 561     if (p_current_scale < p_min_max_scale[0])
 562         p_current_scale = p_min_max_scale[0];
 563     if (p_current_scale > p_min_max_scale[1])
 564         p_current_scale = p_min_max_scale[1];
 565
 566     int tmp_angle = p_current_angle + p_angles[angle_index];
 567     p_current_angle = tmp_angle < 0 ? -std::abs(tmp_angle)%360 : tmp_angle%360;
 568
 569     //obtain a subwindow for training at newly estimated target position
 570     int size_x_scaled = floor(p_windows_size[0]*p_current_scale);
 571     int size_y_scaled = floor(p_windows_size[1]*p_current_scale);
 572
 573     cv::Mat patch_gray = get_subwindow(input_gray, this->p_pose.cx, this->p_pose.cy, size_x_scaled, size_y_scaled);
 574     geometric_transformations(patch_gray, p_windows_size[0], p_windows_size[1],  p_current_scale, p_current_angle,  false);
 575
 576     cv::Mat patch_rgb = cv::Mat::zeros(size_y_scaled, size_x_scaled, CV_32F);
 577     if ((m_use_color || m_use_cnfeat) && input_rgb.channels() == 3) {
 578         patch_rgb = get_subwindow(input_rgb, this->p_pose.cx, this->p_pose.cy, size_x_scaled, size_y_scaled);
 579         geometric_transformations(patch_rgb, p_windows_size[0], p_windows_size[1],  p_current_scale, p_current_angle,  false);
 580     }
 581     patch_feat = get_features(patch_rgb, patch_gray);
 582     ComplexMat xf = fft.forward_window(patch_feat);
 583
 584     //subsequent frames, interpolate model
 585     p_model_xf = p_model_xf * (1. - p_interp_factor) + xf * p_interp_factor;
 586
 587     ComplexMat alphaf_num, alphaf_den;
 588
 589     if (m_use_linearkernel) {
 590         ComplexMat xfconj = xf.conj();
 591         alphaf_num = xfconj.mul(p_yf);
 592         alphaf_den = (xf * xfconj);
 593     } else {
 594         //Kernel Ridge Regression, calculate alphas (in Fourier domain)
 595         ComplexMat kf = gaussian_correlation(xf, xf, p_kernel_sigma, true);
 596 //        ComplexMat alphaf = p_yf / (kf + p_lambda); //equation for fast training
 597 //        p_model_alphaf = p_model_alphaf * (1. - p_interp_factor) + alphaf * p_interp_factor;
 598         alphaf_num = p_yf * kf;
 599         alphaf_den = kf * (kf + p_lambda);
 600     }
 601
 602     p_model_alphaf_num = p_model_alphaf_num * (1. - p_interp_factor) + alphaf_num * p_interp_factor;
 603     p_model_alphaf_den = p_model_alphaf_den * (1. - p_interp_factor) + alphaf_den * p_interp_factor;
 604     p_model_alphaf = p_model_alphaf_num / p_model_alphaf_den;
 605 }
 606
 607 // ****************************************************************************
 608
 609 std::vector<cv::Mat> KCF_Tracker::get_features(cv::Mat & patch_rgb, cv::Mat & patch_gray)
 610 {
 611
 612     // get hog(Histogram of Oriented Gradients) features
 613     std::vector<cv::Mat> hog_feat = FHoG::extract(patch_gray, 2, p_cell_size, 9);
 614
 615     //get color rgb features (simple r,g,b channels)
 616     std::vector<cv::Mat> color_feat;
 617
 618     if (m_use_color && patch_rgb.channels() == 3) {
 619         //use rgb color space
 620         cv::Mat patch_rgb_norm;
 621         patch_rgb.convertTo(patch_rgb_norm, CV_32F, 1. / 255., -0.5);
 622         cv::Mat ch1(patch_rgb_norm.size(), CV_32FC1);
 623         cv::Mat ch2(patch_rgb_norm.size(), CV_32FC1);
 624         cv::Mat ch3(patch_rgb_norm.size(), CV_32FC1);
 625         std::vector<cv::Mat> rgb = {ch1, ch2, ch3};
 626         cv::split(patch_rgb_norm, rgb);
 627         color_feat.insert(color_feat.end(), rgb.begin(), rgb.end());
 628     }
 629
 630     if (m_use_cnfeat && patch_rgb.channels() == 3) {
 631         std::vector<cv::Mat> cn_feat = CNFeat::extract(patch_rgb);
 632         color_feat.insert(color_feat.end(), cn_feat.begin(), cn_feat.end());
 633     }
 634
 635     hog_feat.insert(hog_feat.end(), color_feat.begin(), color_feat.end());
 636     return hog_feat;
 637 }
 638
 639 cv::Mat KCF_Tracker::gaussian_shaped_labels(double sigma, int dim1, int dim2)
 640 {
 641     cv::Mat labels(dim2, dim1, CV_32FC1);
 642     int range_y[2] = {-dim2 / 2, dim2 - dim2 / 2};
 643     int range_x[2] = {-dim1 / 2, dim1 - dim1 / 2};
 644
 645     double sigma_s = sigma*sigma;
 646
 647     for (int y = range_y[0], j = 0; y < range_y[1]; ++y, ++j){
 648         float * row_ptr = labels.ptr<float>(j);
 649         double y_s = y*y;
 650         for (int x = range_x[0], i = 0; x < range_x[1]; ++x, ++i){
 651             row_ptr[i] = std::exp(-0.5 * (y_s + x*x) / sigma_s);//-1/2*e^((y^2+x^2)/sigma^2)
 652         }
 653     }
 654
 655     //rotate so that 1 is at top-left corner (see KCF paper for explanation)
 656     cv::Mat rot_labels = circshift(labels, range_x[0], range_y[0]);
 657     //sanity check, 1 at top left corner
 658     assert(rot_labels.at<float>(0,0) >= 1.f - 1e-10f);
 659
 660     return rot_labels;
 661 }
 662
 663 cv::Mat KCF_Tracker::circshift(const cv::Mat &patch, int x_rot, int y_rot)
 664 {
 665     cv::Mat rot_patch(patch.size(), CV_32FC1);
 666     cv::Mat tmp_x_rot(patch.size(), CV_32FC1);
 667
 668     //circular rotate x-axis
 669     if (x_rot < 0) {
 670         //move part that does not rotate over the edge
 671         cv::Range orig_range(-x_rot, patch.cols);
 672         cv::Range rot_range(0, patch.cols - (-x_rot));
 673         patch(cv::Range::all(), orig_range).copyTo(tmp_x_rot(cv::Range::all(), rot_range));
 674
 675         //rotated part
 676         orig_range = cv::Range(0, -x_rot);
 677         rot_range = cv::Range(patch.cols - (-x_rot), patch.cols);
 678         patch(cv::Range::all(), orig_range).copyTo(tmp_x_rot(cv::Range::all(), rot_range));
 679     }else if (x_rot > 0){
 680         //move part that does not rotate over the edge
 681         cv::Range orig_range(0, patch.cols - x_rot);
 682         cv::Range rot_range(x_rot, patch.cols);
 683         patch(cv::Range::all(), orig_range).copyTo(tmp_x_rot(cv::Range::all(), rot_range));
 684
 685         //rotated part
 686         orig_range = cv::Range(patch.cols - x_rot, patch.cols);
 687         rot_range = cv::Range(0, x_rot);
 688         patch(cv::Range::all(), orig_range).copyTo(tmp_x_rot(cv::Range::all(), rot_range));
 689     }else {    //zero rotation
 690         //move part that does not rotate over the edge
 691         cv::Range orig_range(0, patch.cols);
 692         cv::Range rot_range(0, patch.cols);
 693         patch(cv::Range::all(), orig_range).copyTo(tmp_x_rot(cv::Range::all(), rot_range));
 694     }
 695
 696     //circular rotate y-axis
 697     if (y_rot < 0) {
 698         //move part that does not rotate over the edge
 699         cv::Range orig_range(-y_rot, patch.rows);
 700         cv::Range rot_range(0, patch.rows - (-y_rot));
 701         tmp_x_rot(orig_range, cv::Range::all()).copyTo(rot_patch(rot_range, cv::Range::all()));
 702
 703         //rotated part
 704         orig_range = cv::Range(0, -y_rot);
 705         rot_range = cv::Range(patch.rows - (-y_rot), patch.rows);
 706         tmp_x_rot(orig_range, cv::Range::all()).copyTo(rot_patch(rot_range, cv::Range::all()));
 707     }else if (y_rot > 0){
 708         //move part that does not rotate over the edge
 709         cv::Range orig_range(0, patch.rows - y_rot);
 710         cv::Range rot_range(y_rot, patch.rows);
 711         tmp_x_rot(orig_range, cv::Range::all()).copyTo(rot_patch(rot_range, cv::Range::all()));
 712
 713         //rotated part
 714         orig_range = cv::Range(patch.rows - y_rot, patch.rows);
 715         rot_range = cv::Range(0, y_rot);
 716         tmp_x_rot(orig_range, cv::Range::all()).copyTo(rot_patch(rot_range, cv::Range::all()));
 717     }else { //zero rotation
 718         //move part that does not rotate over the edge
 719         cv::Range orig_range(0, patch.rows);
 720         cv::Range rot_range(0, patch.rows);
 721         tmp_x_rot(orig_range, cv::Range::all()).copyTo(rot_patch(rot_range, cv::Range::all()));
 722     }
 723
 724     return rot_patch;
 725 }
 726
 727 //hann window actually (Power-of-cosine windows)
 728 cv::Mat KCF_Tracker::cosine_window_function(int dim1, int dim2)
 729 {
 730     cv::Mat m1(1, dim1, CV_32FC1), m2(dim2, 1, CV_32FC1);
 731     double N_inv = 1./(static_cast<double>(dim1)-1.);
 732     for (int i = 0; i < dim1; ++i)
 733         m1.at<float>(i) = 0.5*(1. - std::cos(2. * CV_PI * static_cast<double>(i) * N_inv));
 734     N_inv = 1./(static_cast<double>(dim2)-1.);
 735     for (int i = 0; i < dim2; ++i)
 736         m2.at<float>(i) = 0.5*(1. - std::cos(2. * CV_PI * static_cast<double>(i) * N_inv));
 737     cv::Mat ret = m2*m1;
 738     return ret;
 739 }
 740
 741 // Returns sub-window of image input centered at [cx, cy] coordinates),
 742 // with size [width, height]. If any pixels are outside of the image,
 743 // they will replicate the values at the borders.
 744 cv::Mat KCF_Tracker::get_subwindow(const cv::Mat &input, int cx, int cy, int width, int height)
 745 {
 746     cv::Mat patch;
 747
 748     int x1 = cx - width/2;
 749     int y1 = cy - height/2;
 750     int x2 = cx + width/2;
 751     int y2 = cy + height/2;
 752
 753     //out of image
 754     if (x1 >= input.cols || y1 >= input.rows || x2 < 0 || y2 < 0) {
 755         patch.create(height, width, input.type());
 756         patch.setTo(0.f);
 757         return patch;
 758     }
 759
 760     int top = 0, bottom = 0, left = 0, right = 0;
 761
 762     //fit to image coordinates, set border extensions;
 763     if (x1 < 0) {
 764         left = -x1;
 765         x1 = 0;
 766     }
 767     if (y1 < 0) {
 768         top = -y1;
 769         y1 = 0;
 770     }
 771     if (x2 >= input.cols) {
 772         right = x2 - input.cols + width % 2;
 773         x2 = input.cols;
 774     } else
 775         x2 += width % 2;
 776
 777     if (y2 >= input.rows) {
 778         bottom = y2 - input.rows + height % 2;
 779         y2 = input.rows;
 780     } else
 781         y2 += height % 2;
 782
 783     if (x2 - x1 == 0 || y2 - y1 == 0)
 784         patch = cv::Mat::zeros(height, width, CV_32FC1);
 785     else
 786         cv::copyMakeBorder(input(cv::Range(y1, y2), cv::Range(x1, x2)), patch, top, bottom, left, right, cv::BORDER_REPLICATE);
 787
 788     //sanity check
 789     assert(patch.cols == width && patch.rows == height);
 790
 791     return patch;
 792 }
 793
 794 void KCF_Tracker::geometric_transformations(cv::Mat& patch, int size_x, int size_y, double scale,int angle, bool allow_debug)
 795 {
 796      if (m_use_angle) {
 797          cv::Point2f center((patch.cols-1)/2., (patch.rows-1)/2.);
 798          cv::Mat r = cv::getRotationMatrix2D(center, angle, 1.0);
 799
 800          cv::warpAffine(patch, patch, r, cv::Size(patch.cols, patch.rows), cv::INTER_LINEAR, cv::BORDER_REPLICATE);
 801      }
 802
 803      //resize to default size
 804      if (patch.channels() != 3){
 805         if (scale > 1.){
 806             //if we downsample use  INTER_AREA interpolation
 807             cv::resize(patch, patch, cv::Size(size_x, size_y), 0., 0., cv::INTER_AREA);
 808         }else {
 809             cv::resize(patch, patch, cv::Size(size_x, size_y), 0., 0., cv::INTER_LINEAR);
 810         }
 811      } else {
 812          if (scale > 1.){
 813              //if we downsample use  INTER_AREA interpolation
 814              cv::resize(patch, patch, cv::Size(size_x/p_cell_size, size_y/p_cell_size), 0., 0., cv::INTER_AREA);
 815          }else {
 816              cv::resize(patch, patch, cv::Size(size_x/p_cell_size, size_y/p_cell_size), 0., 0., cv::INTER_LINEAR);
 817          }
 818          if (m_visual_debug && allow_debug) {
 819              cv::Mat input_clone = patch.clone();
 820              cv::resize(input_clone, input_clone, cv::Size(p_debug_image_size, p_debug_image_size), 0., 0., cv::INTER_LINEAR);
 821
 822              std::string angle_string = std::to_string(p_current_angle + angle);
 823              if (p_count%5 == 0) {
 824                  std::string scale_string = std::to_string(scale);
 825                  scale_string.erase ( scale_string.find_last_not_of('0') + 1, std::string::npos );
 826                  scale_string.erase ( scale_string.find_last_not_of('.') + 1, std::string::npos );
 827                  cv::putText(input_clone, scale_string,  cv::Point(0, 10), cv::FONT_HERSHEY_COMPLEX_SMALL, 0.5, cv::Scalar(0,255,0),1,cv::LINE_AA);
 828              }
 829
 830              cv::putText(input_clone, angle_string,  cv::Point(1, input_clone.rows-5), cv::FONT_HERSHEY_COMPLEX_SMALL, 0.5, cv::Scalar(0,255,0),1,cv::LINE_AA);
 831
 832              p_debug_subwindows.push_back(input_clone);
 833              p_count += 1;
 834          }
 835      }
 836  }
 837
 838 ComplexMat KCF_Tracker::gaussian_correlation(const ComplexMat &xf, const ComplexMat &yf, double sigma, bool auto_correlation)
 839 {
 840 #ifdef CUFFT
 841     xf.sqr_norm(xf_sqr_norm_d);
 842     if (!auto_correlation)
 843         yf.sqr_norm(yf_sqr_norm_d);
 844 #else
 845     xf.sqr_norm(xf_sqr_norm);
 846     if (auto_correlation){
 847       yf_sqr_norm[0] = xf_sqr_norm[0];
 848     } else {
 849        yf.sqr_norm(yf_sqr_norm);
 850     }
 851 #endif
 852     ComplexMat xyf;
 853     xyf = auto_correlation ? xf.sqr_mag() : xf.mul2(yf.conj());
 854     DEBUG_PRINTM(xyf);
 855 #ifdef CUFFT
 856     if(auto_correlation)
 857         cuda_gaussian_correlation(fft.inverse_raw(xyf), gauss_corr_res, xf_sqr_norm_d, xf_sqr_norm_d, sigma, xf.n_channels, xf.n_scales, p_roi_height, p_roi_width);
 858     else
 859         cuda_gaussian_correlation(fft.inverse_raw(xyf), gauss_corr_res, xf_sqr_norm_d, yf_sqr_norm_d, sigma, xf.n_channels, xf.n_scales, p_roi_height, p_roi_width);
 860
 861     return fft.forward_raw(gauss_corr_res, xf.n_scales==p_num_scales);
 862 #else
 863     //ifft2 and sum over 3rd dimension, we dont care about individual channels
 864     cv::Mat ifft2_res = fft.inverse(xyf);
 865     DEBUG_PRINTM(ifft2_res);
 866     cv::Mat xy_sum;
 867     if (xf.channels() != p_num_scales*p_num_of_feats)
 868         xy_sum.create(ifft2_res.size(), CV_32FC1);
 869     else
 870         xy_sum.create(ifft2_res.size(), CV_32FC(p_scales.size()));
 871     xy_sum.setTo(0);
 872     for (int y = 0; y < ifft2_res.rows; ++y) {
 873         float * row_ptr = ifft2_res.ptr<float>(y);
 874         float * row_ptr_sum = xy_sum.ptr<float>(y);
 875         for (int x = 0; x < ifft2_res.cols; ++x) {
 876             for (int sum_ch = 0; sum_ch < xy_sum.channels(); ++sum_ch) {
 877                 row_ptr_sum[(x*xy_sum.channels())+sum_ch] += std::accumulate(row_ptr + x*ifft2_res.channels() + sum_ch*(ifft2_res.channels()/xy_sum.channels()), (row_ptr + x*ifft2_res.channels() + (sum_ch+1)*(ifft2_res.channels()/xy_sum.channels())), 0.f);
 878             }
 879         }
 880     }
 881     DEBUG_PRINTM(xy_sum);
 882
 883     std::vector<cv::Mat> scales;
 884     cv::split(xy_sum,scales);
 885     cv::Mat in_all(scales[0].rows * xf.n_scales, scales[0].cols, CV_32F);
 886
 887     float numel_xf_inv = 1.f/(xf.cols * xf.rows * (xf.channels()/xf.n_scales));
 888     for (int i = 0; i < xf.n_scales; ++i){
 889         cv::Mat in_roi(in_all, cv::Rect(0, i*scales[0].rows, scales[0].cols, scales[0].rows));
 890         cv::exp(- 1.f / (sigma * sigma) * cv::max((xf_sqr_norm[i] + yf_sqr_norm[0] - 2 * scales[i]) * numel_xf_inv, 0), in_roi);
 891         DEBUG_PRINTM(in_roi);
 892     }
 893
 894     DEBUG_PRINTM(in_all);
 895     return fft.forward(in_all);
 896 #endif
 897 }
 898
 899 float get_response_circular(cv::Point2i & pt, cv::Mat & response)
 900 {
 901     int x = pt.x;
 902     int y = pt.y;
 903     if (x < 0)
 904         x = response.cols + x;
 905     if (y < 0)
 906         y = response.rows + y;
 907     if (x >= response.cols)
 908         x = x - response.cols;
 909     if (y >= response.rows)
 910         y = y - response.rows;
 911
 912     return response.at<float>(y,x);
 913 }
 914
 915 cv::Point2f KCF_Tracker::sub_pixel_peak(cv::Point & max_loc, cv::Mat & response)
 916 {
 917     //find neighbourhood of max_loc (response is circular)
 918     // 1 2 3
 919     // 4   5
 920     // 6 7 8
 921     cv::Point2i p1(max_loc.x-1, max_loc.y-1), p2(max_loc.x, max_loc.y-1), p3(max_loc.x+1, max_loc.y-1);
 922     cv::Point2i p4(max_loc.x-1, max_loc.y), p5(max_loc.x+1, max_loc.y);
 923     cv::Point2i p6(max_loc.x-1, max_loc.y+1), p7(max_loc.x, max_loc.y+1), p8(max_loc.x+1, max_loc.y+1);
 924
 925     // clang-format off
 926     // fit 2d quadratic function f(x, y) = a*x^2 + b*x*y + c*y^2 + d*x + e*y + f
 927     cv::Mat A = (cv::Mat_<float>(9, 6) <<
 928                  p1.x*p1.x, p1.x*p1.y, p1.y*p1.y, p1.x, p1.y, 1.f,
 929                  p2.x*p2.x, p2.x*p2.y, p2.y*p2.y, p2.x, p2.y, 1.f,
 930                  p3.x*p3.x, p3.x*p3.y, p3.y*p3.y, p3.x, p3.y, 1.f,
 931                  p4.x*p4.x, p4.x*p4.y, p4.y*p4.y, p4.x, p4.y, 1.f,
 932                  p5.x*p5.x, p5.x*p5.y, p5.y*p5.y, p5.x, p5.y, 1.f,
 933                  p6.x*p6.x, p6.x*p6.y, p6.y*p6.y, p6.x, p6.y, 1.f,
 934                  p7.x*p7.x, p7.x*p7.y, p7.y*p7.y, p7.x, p7.y, 1.f,
 935                  p8.x*p8.x, p8.x*p8.y, p8.y*p8.y, p8.x, p8.y, 1.f,
 936                  max_loc.x*max_loc.x, max_loc.x*max_loc.y, max_loc.y*max_loc.y, max_loc.x, max_loc.y, 1.f);
 937     cv::Mat fval = (cv::Mat_<float>(9, 1) <<
 938                     get_response_circular(p1, response),
 939                     get_response_circular(p2, response),
 940                     get_response_circular(p3, response),
 941                     get_response_circular(p4, response),
 942                     get_response_circular(p5, response),
 943                     get_response_circular(p6, response),
 944                     get_response_circular(p7, response),
 945                     get_response_circular(p8, response),
 946                     get_response_circular(max_loc, response));
 947     // clang-format on
 948     cv::Mat x;
 949     cv::solve(A, fval, x, cv::DECOMP_SVD);
 950
 951     double a = x.at<float>(0), b = x.at<float>(1), c = x.at<float>(2),
 952            d = x.at<float>(3), e = x.at<float>(4);
 953
 954     cv::Point2f sub_peak(max_loc.x, max_loc.y);
 955     if (b > 0 || b < 0) {
 956         sub_peak.y = ((2.f * a * e) / b - d) / (b - (4 * a * c) / b);
 957         sub_peak.x = (-2 * c * sub_peak.y - e) / b;
 958     }
 959
 960     return sub_peak;
 961 }
 962
 963 double KCF_Tracker::sub_grid_scale(std::vector<double> & responses, int index)
 964 {
 965     cv::Mat A, fval;
 966     if (index < 0 || index > (int)p_scales.size()-1) {
 967         // interpolate from all values
 968         // fit 1d quadratic function f(x) = a*x^2 + b*x + c
 969         A.create(p_scales.size(), 3, CV_32FC1);
 970         fval.create(p_scales.size(), 1, CV_32FC1);
 971         for (size_t i = 0; i < p_scales.size(); ++i) {
 972             A.at<float>(i, 0) = p_scales[i] * p_scales[i];
 973             A.at<float>(i, 1) = p_scales[i];
 974             A.at<float>(i, 2) = 1;
 975             fval.at<float>(i) = responses[i];
 976         }
 977     } else {
 978         //only from neighbours
 979         if (index == 0 || index == (int)p_scales.size()-1)
 980             return p_scales[index];
 981
 982         A = (cv::Mat_<float>(3, 3) <<
 983              p_scales[index-1] * p_scales[index-1], p_scales[index-1], 1,
 984              p_scales[index] * p_scales[index], p_scales[index], 1,
 985              p_scales[index+1] * p_scales[index+1], p_scales[index+1], 1);
 986         fval = (cv::Mat_<float>(3, 1) << responses[index-1], responses[index], responses[index+1]);
 987     }
 988
 989     cv::Mat x;
 990     cv::solve(A, fval, x, cv::DECOMP_SVD);
 991     double a = x.at<float>(0), b = x.at<float>(1);
 992     double scale = p_scales[index];
 993     if (a > 0 || a < 0)
 994         scale = -b / (2 * a);
 995     return scale;
 996 }