text: /*M///////////////////////////////////////////////////////////////////////////////////////
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  //  If you do not agree to this license, do not download, install,
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  //
  //                           License Agreement
  //                For Open Source Computer Vision Library
  //
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  // are permitted provided that the following conditions are met:
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  //     derived from this software without specific prior written permission.
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  // warranties of merchantability and fitness for a particular purpose are disclaimed.
  // In no event shall the Intel Corporation or contributors be liable for any direct,
  // indirect, incidental, special, exemplary, or consequential damages
  // (including, but not limited to, procurement of substitute goods or services;
  // loss of use, data, or profits; or business interruption) however caused
  // and on any theory of liability, whether in contract, strict liability,
  // or tort (including negligence or otherwise) arising in any way out of
  // the use of this software, even if advised of the possibility of such damage.
  //
  //M*/
  
  #include "precomp.hpp"
  #include <algorithm>
  #include <cmath>
  #include <functional>
  #include <fstream>
  #include <limits>
  #include <set>
  
  using namespace cv;
  using namespace std;
  
  /********************************* local utility *********************************/
  
  namespace cv
  {
      using std::log;
      using std::max;
      using std::min;
      using std::sqrt;
  }
  namespace
  {
      const static Scalar colors[] =
      {
          CV_RGB(255,   0,   0),
          CV_RGB(  0, 255,   0),
          CV_RGB(  0,   0, 255),
          CV_RGB(255, 255,   0),
          CV_RGB(255,   0, 255),
          CV_RGB(  0, 255, 255),
          CV_RGB(255, 127, 127),
          CV_RGB(127, 127, 255),
          CV_RGB(127, 255, 127),
          CV_RGB(255, 255, 127),
          CV_RGB(127, 255, 255),
          CV_RGB(255, 127, 255),
          CV_RGB(127,   0,   0),
          CV_RGB(  0, 127,   0),
          CV_RGB(  0,   0, 127),
          CV_RGB(127, 127,   0),
          CV_RGB(127,   0, 127),
          CV_RGB(  0, 127, 127)
      };
      size_t colors_mum = sizeof(colors)/sizeof(colors[0]);
  
  template<class FwIt, class T> inline void _iota(FwIt first, FwIt last, T value)
  {
      while(first != last) *first++ = value++;
  }
  
  void computeNormals( const Octree& Octree, const vector<Point3f>& centers, vector<Point3f>& normals,
                      vector<uchar>& mask, float normalRadius, int minNeighbors = 20)
  {
      size_t normals_size = centers.size();
      normals.resize(normals_size);
  
      if (mask.size() != normals_size)
      {
          size_t m = mask.size();
          mask.resize(normals_size);
          if (normals_size > m)
              for(; m < normals_size; ++m)
                  mask[m] = 1;
      }
  
      vector<Point3f> buffer;
      buffer.reserve(128);
      SVD svd;
  
      const static Point3f zero(0.f, 0.f, 0.f);
  
      for(size_t n = 0; n < normals_size; ++n)
      {
          if (mask[n] == 0)
              continue;
  
          const Point3f& center = centers[n];
          Octree.getPointsWithinSphere(center, normalRadius, buffer);
  
          int buf_size = (int)buffer.size();
          if (buf_size < minNeighbors)
          {
              normals[n] = Mesh3D::allzero;
              mask[n] = 0;
              continue;
          }
  
          //find the mean point for normalization
          Point3f mean(Mesh3D::allzero);
          for(int i = 0; i < buf_size; ++i)
              mean += buffer[i];
  
          mean.x /= buf_size;
          mean.y /= buf_size;
          mean.z /= buf_size;
  
          double pxpx = 0;
          double pypy = 0;
          double pzpz = 0;
  
          double pxpy = 0;
          double pxpz = 0;
          double pypz = 0;
  
          for(int i = 0; i < buf_size; ++i)
          {
              const Point3f& p = buffer[i];
  
              pxpx += (p.x - mean.x) * (p.x - mean.x);
              pypy += (p.y - mean.y) * (p.y - mean.y);
              pzpz += (p.z - mean.z) * (p.z - mean.z);
  
              pxpy += (p.x - mean.x) * (p.y - mean.y);
              pxpz += (p.x - mean.x) * (p.z - mean.z);
              pypz += (p.y - mean.y) * (p.z - mean.z);
          }
  
          //create and populate matrix with normalized nbrs
          double M_data[] = { pxpx, pxpy, pxpz, /**/ pxpy, pypy, pypz, /**/ pxpz, pypz, pzpz };
          Mat M(3, 3, CV_64F, M_data);
  
          svd(M, SVD::MODIFY_A);
  
          /*normals[n] = Point3f(  (float)((double*)svd.vt.data)[6],
                                   (float)((double*)svd.vt.data)[7],
                                   (float)((double*)svd.vt.data)[8]  );*/
          normals[n] = reinterpret_cast<Point3d*>(svd.vt.data)[2];
          mask[n] = 1;
      }
  }
  
  void initRotationMat(const Point3f& n, float out[9])
  {
      double pitch = atan2(n.x, n.z);
      double pmat[] = { cos(pitch), 0, -sin(pitch) ,
                          0      , 1,      0      ,
                       sin(pitch), 0,  cos(pitch) };
  
      double roll = atan2((double)n.y, n.x * pmat[3*2+0] + n.z * pmat[3*2+2]);
  
      double rmat[] = { 1,     0,         0,
                       0, cos(roll), -sin(roll) ,
                       0, sin(roll),  cos(roll) };
  
      for(int i = 0; i < 3; ++i)
          for(int j = 0; j < 3; ++j)
              out[3*i+j] = (float)(rmat[3*i+0]*pmat[3*0+j] +
                  rmat[3*i+1]*pmat[3*1+j] + rmat[3*i+2]*pmat[3*2+j]);
  }
  
  void transform(const Point3f& in, float matrix[9], Point3f& out)
  {
      out.x = in.x * matrix[3*0+0] + in.y * matrix[3*0+1] + in.z * matrix[3*0+2];
      out.y = in.x * matrix[3*1+0] + in.y * matrix[3*1+1] + in.z * matrix[3*1+2];
      out.z = in.x * matrix[3*2+0] + in.y * matrix[3*2+1] + in.z * matrix[3*2+2];
  }
  
  #if CV_SSE2
  void convertTransformMatrix(const float* matrix, float* sseMatrix)
  {
      sseMatrix[0] = matrix[0]; sseMatrix[1] = matrix[3]; sseMatrix[2] = matrix[6]; sseMatrix[3] = 0;
      sseMatrix[4] = matrix[1]; sseMatrix[5] = matrix[4]; sseMatrix[6] = matrix[7]; sseMatrix[7] = 0;
      sseMatrix[8] = matrix[2]; sseMatrix[9] = matrix[5]; sseMatrix[10] = matrix[8]; sseMatrix[11] = 0;
  }
  
  inline __m128 transformSSE(const __m128* matrix, const __m128& in)
  {
      assert(((size_t)matrix & 15) == 0);
      __m128 a0 = _mm_mul_ps(_mm_load_ps((float*)(matrix+0)), _mm_shuffle_ps(in,in,_MM_SHUFFLE(0,0,0,0)));
      __m128 a1 = _mm_mul_ps(_mm_load_ps((float*)(matrix+1)), _mm_shuffle_ps(in,in,_MM_SHUFFLE(1,1,1,1)));
      __m128 a2 = _mm_mul_ps(_mm_load_ps((float*)(matrix+2)), _mm_shuffle_ps(in,in,_MM_SHUFFLE(2,2,2,2)));
  
      return _mm_add_ps(_mm_add_ps(a0,a1),a2);
  }
  
  inline __m128i _mm_mullo_epi32_emul(const __m128i& a, __m128i& b)
  {
      __m128i pack = _mm_packs_epi32(a, a);
      return _mm_unpacklo_epi16(_mm_mullo_epi16(pack, b), _mm_mulhi_epi16(pack, b));
  }
  
  #endif
  
  void computeSpinImages( const Octree& Octree, const vector<Point3f>& points, const vector<Point3f>& normals,
                         vector<uchar>& mask, Mat& spinImages, int imageWidth, float binSize)
  {
      float pixelsPerMeter = 1.f / binSize;
      float support = imageWidth * binSize;
  
      assert(normals.size() == points.size());
      assert(mask.size() == points.size());
  
      size_t points_size = points.size();
      mask.resize(points_size);
  
      int height = imageWidth;
      int width  = imageWidth;
  
      spinImages.create( (int)points_size, width*height, CV_32F );
  
      int nthreads = getNumThreads();
      int i;
  
      vector< vector<Point3f> > pointsInSpherePool(nthreads);
      for(i = 0; i < nthreads; i++)
          pointsInSpherePool[i].reserve(2048);
  
      float halfSuppport = support / 2;
      float searchRad = support * sqrt(5.f) / 2;  //  sqrt(sup*sup + (sup/2) * (sup/2) )
  
  #ifdef _OPENMP
      #pragma omp parallel for num_threads(nthreads)
  #endif
      for(i = 0; i < (int)points_size; ++i)
      {
          if (mask[i] == 0)
              continue;
  
          int t = cvGetThreadNum();
          vector<Point3f>& pointsInSphere = pointsInSpherePool[t];
  
          const Point3f& center = points[i];
          Octree.getPointsWithinSphere(center, searchRad, pointsInSphere);
  
          size_t inSphere_size = pointsInSphere.size();
          if (inSphere_size == 0)
          {
              mask[i] = 0;
              continue;
          }
  
          const Point3f& normal = normals[i];
  
          float rotmat[9];
          initRotationMat(normal, rotmat);
          Point3f new_center;
          transform(center, rotmat, new_center);
  
          Mat spinImage = spinImages.row(i).reshape(1, height);
          float* spinImageData = (float*)spinImage.data;
          int step = width;
          spinImage = Scalar(0.);
  
          float alpha, beta;
          size_t j = 0;
  #if CV_SSE2
          if (inSphere_size > 4 && checkHardwareSupport(CV_CPU_SSE2))
          {
              __m128 rotmatSSE[3];
              convertTransformMatrix(rotmat, (float*)rotmatSSE);
  
              __m128 center_x4 = _mm_set1_ps(new_center.x);
              __m128 center_y4 = _mm_set1_ps(new_center.y);
              __m128 center_z4 = _mm_set1_ps(new_center.z + halfSuppport);
              __m128 ppm4 = _mm_set1_ps(pixelsPerMeter);
              __m128i height4m1 = _mm_set1_epi32(spinImage.rows-1);
              __m128i width4m1 = _mm_set1_epi32(spinImage.cols-1);
              assert( spinImage.step <= 0xffff );
              __m128i step4 = _mm_set1_epi16((short)step);
              __m128i zero4 = _mm_setzero_si128();
              __m128i one4i = _mm_set1_epi32(1);
              __m128 zero4f = _mm_setzero_ps();
              __m128 one4f = _mm_set1_ps(1.f);
              //__m128 two4f = _mm_set1_ps(2.f);
              int CV_DECL_ALIGNED(16) o[4];
  
              for (; j <= inSphere_size - 5; j += 4)
              {
                  __m128 pt0 = transformSSE(rotmatSSE, _mm_loadu_ps((float*)&pointsInSphere[j+0])); // x0 y0 z0 .
                  __m128 pt1 = transformSSE(rotmatSSE, _mm_loadu_ps((float*)&pointsInSphere[j+1])); // x1 y1 z1 .
                  __m128 pt2 = transformSSE(rotmatSSE, _mm_loadu_ps((float*)&pointsInSphere[j+2])); // x2 y2 z2 .
                  __m128 pt3 = transformSSE(rotmatSSE, _mm_loadu_ps((float*)&pointsInSphere[j+3])); // x3 y3 z3 .
  
                  __m128 z0 = _mm_unpackhi_ps(pt0, pt1); // z0 z1 . .
                  __m128 z1 = _mm_unpackhi_ps(pt2, pt3); // z2 z3 . .
                  __m128 beta4 = _mm_sub_ps(center_z4, _mm_movelh_ps(z0, z1)); // b0 b1 b2 b3
  
                  __m128 xy0 = _mm_unpacklo_ps(pt0, pt1); // x0 x1 y0 y1
                  __m128 xy1 = _mm_unpacklo_ps(pt2, pt3); // x2 x3 y2 y3
                  __m128 x4 = _mm_movelh_ps(xy0, xy1); // x0 x1 x2 x3
                  __m128 y4 = _mm_movehl_ps(xy1, xy0); // y0 y1 y2 y3
  
                  x4 = _mm_sub_ps(x4, center_x4);
                  y4 = _mm_sub_ps(y4, center_y4);
                  __m128 alpha4 = _mm_sqrt_ps(_mm_add_ps(_mm_mul_ps(x4,x4),_mm_mul_ps(y4,y4)));
  
                  __m128 n1f4 = _mm_mul_ps( beta4, ppm4);  /* beta4 float */
                  __m128 n2f4 = _mm_mul_ps(alpha4, ppm4); /* alpha4 float */
  
                  /* floor */
                  __m128i n1 = _mm_sub_epi32(_mm_cvttps_epi32( _mm_add_ps( n1f4, one4f ) ), one4i);
                  __m128i n2 = _mm_sub_epi32(_mm_cvttps_epi32( _mm_add_ps( n2f4, one4f ) ), one4i);
  
                  __m128 f1 = _mm_sub_ps( n1f4, _mm_cvtepi32_ps(n1) );  /* { beta4  }  */
                  __m128 f2 = _mm_sub_ps( n2f4, _mm_cvtepi32_ps(n2) );  /* { alpha4 }  */
  
                  __m128 f1f2 = _mm_mul_ps(f1, f2);  // f1 * f2
                  __m128 omf1omf2 = _mm_add_ps(_mm_sub_ps(_mm_sub_ps(one4f, f2), f1), f1f2); // (1-f1) * (1-f2)
  
                  __m128i _mask = _mm_and_si128(
                      _mm_andnot_si128(_mm_cmpgt_epi32(zero4, n1), _mm_cmpgt_epi32(height4m1, n1)),
                      _mm_andnot_si128(_mm_cmpgt_epi32(zero4, n2), _mm_cmpgt_epi32(width4m1, n2)));
  
                  __m128 maskf = _mm_cmpneq_ps(_mm_cvtepi32_ps(_mask), zero4f);
  
                  __m128 v00 = _mm_and_ps(        omf1omf2       , maskf); // a00 b00 c00 d00
                  __m128 v01 = _mm_and_ps( _mm_sub_ps( f2, f1f2 ), maskf); // a01 b01 c01 d01
                  __m128 v10 = _mm_and_ps( _mm_sub_ps( f1, f1f2 ), maskf); // a10 b10 c10 d10
                  __m128 v11 = _mm_and_ps(          f1f2         , maskf); // a11 b11 c11 d11
  
                  __m128i ofs4 = _mm_and_si128(_mm_add_epi32(_mm_mullo_epi32_emul(n1, step4), n2), _mask);
                  _mm_store_si128((__m128i*)o, ofs4);
  
                  __m128 t0 = _mm_unpacklo_ps(v00, v01); // a00 a01 b00 b01
                  __m128 t1 = _mm_unpacklo_ps(v10, v11); // a10 a11 b10 b11
                  __m128 u0 = _mm_movelh_ps(t0, t1); // a00 a01 a10 a11
                  __m128 u1 = _mm_movehl_ps(t1, t0); // b00 b01 b10 b11
  
                  __m128 x0 = _mm_loadl_pi(u0, (__m64*)(spinImageData+o[0])); // x00 x01
                  x0 = _mm_loadh_pi(x0, (__m64*)(spinImageData+o[0]+step));   // x00 x01 x10 x11
                  x0 = _mm_add_ps(x0, u0);
                  _mm_storel_pi((__m64*)(spinImageData+o[0]), x0);
                  _mm_storeh_pi((__m64*)(spinImageData+o[0]+step), x0);
  
                  x0 = _mm_loadl_pi(x0, (__m64*)(spinImageData+o[1]));        // y00 y01
                  x0 = _mm_loadh_pi(x0, (__m64*)(spinImageData+o[1]+step));   // y00 y01 y10 y11
                  x0 = _mm_add_ps(x0, u1);
                  _mm_storel_pi((__m64*)(spinImageData+o[1]), x0);
                  _mm_storeh_pi((__m64*)(spinImageData+o[1]+step), x0);
  
                  t0 = _mm_unpackhi_ps(v00, v01); // c00 c01 d00 d01
                  t1 = _mm_unpackhi_ps(v10, v11); // c10 c11 d10 d11
                  u0 = _mm_movelh_ps(t0, t1); // c00 c01 c10 c11
                  u1 = _mm_movehl_ps(t1, t0); // d00 d01 d10 d11
  
                  x0 = _mm_loadl_pi(x0, (__m64*)(spinImageData+o[2]));        // z00 z01
                  x0 = _mm_loadh_pi(x0, (__m64*)(spinImageData+o[2]+step));   // z00 z01 z10 z11
                  x0 = _mm_add_ps(x0, u0);
                  _mm_storel_pi((__m64*)(spinImageData+o[2]), x0);
                  _mm_storeh_pi((__m64*)(spinImageData+o[2]+step), x0);
  
                  x0 = _mm_loadl_pi(x0, (__m64*)(spinImageData+o[3]));        // w00 w01
                  x0 = _mm_loadh_pi(x0, (__m64*)(spinImageData+o[3]+step));   // w00 w01 w10 w11
                  x0 = _mm_add_ps(x0, u1);
                  _mm_storel_pi((__m64*)(spinImageData+o[3]), x0);
                  _mm_storeh_pi((__m64*)(spinImageData+o[3]+step), x0);
              }
          }
  #endif
          for (; j < inSphere_size; ++j)
          {
              Point3f pt;
              transform(pointsInSphere[j], rotmat, pt);
  
              beta = halfSuppport - (pt.z - new_center.z);
              if (beta >= support || beta < 0)
                  continue;
  
              alpha = sqrt( (new_center.x - pt.x) * (new_center.x - pt.x) +
                            (new_center.y - pt.y) * (new_center.y - pt.y) );
  
              float n1f = beta  * pixelsPerMeter;
              float n2f = alpha * pixelsPerMeter;
  
              int n1 = cvFloor(n1f);
              int n2 = cvFloor(n2f);
  
              float f1 = n1f - n1;
              float f2 = n2f - n2;
  
              if  ((unsigned)n1 >= (unsigned)(spinImage.rows-1) ||
                   (unsigned)n2 >= (unsigned)(spinImage.cols-1))
                  continue;
  
              float *cellptr = spinImageData + step * n1 + n2;
              float f1f2 = f1*f2;
              cellptr[0] += 1 - f1 - f2 + f1f2;
              cellptr[1] += f2 - f1f2;
              cellptr[step] += f1 - f1f2;
              cellptr[step+1] += f1f2;
          }
          mask[i] = 1;
      }
  }
  
  }
  
  /********************************* Mesh3D *********************************/
  
  const Point3f cv::Mesh3D::allzero(0.f, 0.f, 0.f);
  
  cv::Mesh3D::Mesh3D() { resolution = -1; }
  cv::Mesh3D::Mesh3D(const vector<Point3f>& _vtx)
  {
      resolution = -1;
      vtx.resize(_vtx.size());
      std::copy(_vtx.begin(), _vtx.end(), vtx.begin());
  }
  cv::Mesh3D::~Mesh3D() {}
  
  void cv::Mesh3D::buildOctree() { if (octree.getNodes().empty()) octree.buildTree(vtx); }
  void cv::Mesh3D::clearOctree(){ octree = Octree(); }
  
  float cv::Mesh3D::estimateResolution(float /*tryRatio*/)
  {
  #if 0
      const int neighbors = 3;
      const int minReasonable = 10;
  
      int tryNum = static_cast<int>(tryRatio * vtx.size());
      tryNum = min(max(tryNum, minReasonable), (int)vtx.size());
  
      CvMat desc = cvMat((int)vtx.size(), 3, CV_32F, &vtx[0]);
      CvFeatureTree* tr = cvCreateKDTree(&desc);
  
      vector<double> dist(tryNum * neighbors);
      vector<int>    inds(tryNum * neighbors);
      vector<Point3f> query;
  
      RNG& rng = theRNG();
      for(int i = 0; i < tryNum; ++i)
          query.push_back(vtx[rng.next() % vtx.size()]);
  
      CvMat cvinds  = cvMat( (int)tryNum, neighbors, CV_32S,  &inds[0] );
      CvMat cvdist  = cvMat( (int)tryNum, neighbors, CV_64F,  &dist[0] );
      CvMat cvquery = cvMat( (int)tryNum,         3, CV_32F, &query[0] );
      cvFindFeatures(tr, &cvquery, &cvinds, &cvdist, neighbors, 50);
      cvReleaseFeatureTree(tr);
  
      const int invalid_dist = -2;
      for(int i = 0; i < tryNum; ++i)
          if (inds[i] == -1)
              dist[i] = invalid_dist;
  
      dist.resize(remove(dist.begin(), dist.end(), invalid_dist) - dist.begin());
  
      sort(dist, less<double>());
  
      return resolution = (float)dist[ dist.size() / 2 ];
  #else
      CV_Error(CV_StsNotImplemented, "");
      return 1.f;
  #endif
  }
  
  
  void cv::Mesh3D::computeNormals(float normalRadius, int minNeighbors)
  {
      buildOctree();
      vector<uchar> mask;
      ::computeNormals(octree, vtx, normals, mask, normalRadius, minNeighbors);
  }
  
  void cv::Mesh3D::computeNormals(const vector<int>& subset, float normalRadius, int minNeighbors)
  {
      buildOctree();
      vector<uchar> mask(vtx.size(), 0);
      for(size_t i = 0; i < subset.size(); ++i)
          mask[subset[i]] = 1;
      ::computeNormals(octree, vtx, normals, mask, normalRadius, minNeighbors);
  }
  
  void cv::Mesh3D::writeAsVrml(const String& file, const vector<Scalar>& _colors) const
  {
      ofstream ofs(file.c_str());
  
      ofs << "#VRML V2.0 utf8" << endl;
      ofs << "Shape" << std::endl << "{" << endl;
      ofs << "geometry PointSet" << endl << "{" << endl;
      ofs << "coord Coordinate" << endl << "{" << endl;
      ofs << "point[" << endl;
  
      for(size_t i = 0; i < vtx.size(); ++i)
          ofs << vtx[i].x << " " << vtx[i].y << " " << vtx[i].z << endl;
  
      ofs << "]" << endl; //point[
      ofs << "}" << endl; //Coordinate{
  
      if (vtx.size() == _colors.size())
      {
          ofs << "color Color" << endl << "{" << endl;
          ofs << "color[" << endl;
  
          for(size_t i = 0; i < _colors.size(); ++i)
              ofs << (float)_colors[i][2] << " " << (float)_colors[i][1] << " " << (float)_colors[i][0] << endl;
  
          ofs << "]" << endl; //color[
          ofs << "}" << endl; //color Color{
      }
  
      ofs << "}" << endl; //PointSet{
      ofs << "}" << endl; //Shape{
  }
  
  
  /********************************* SpinImageModel *********************************/
  
  
  bool cv::SpinImageModel::spinCorrelation(const Mat& spin1, const Mat& spin2, float lambda, float& result)
  {
      struct Math { static double atanh(double x) { return 0.5 * std::log( (1 + x) / (1 - x) ); } };
  
      const float* s1 = spin1.ptr<float>();
      const float* s2 = spin2.ptr<float>();
  
      int spin_sz = spin1.cols * spin1.rows;
      double sum1 = 0.0, sum2 = 0.0, sum12 = 0.0, sum11 = 0.0, sum22 = 0.0;
  
      int N = 0;
      int i = 0;
  #if CV_SSE2//____________TEMPORARY_DISABLED_____________
      float CV_DECL_ALIGNED(16) su1[4], su2[4], su11[4], su22[4], su12[4], n[4];
  
      __m128 zerof4 = _mm_setzero_ps();
      __m128 onef4  = _mm_set1_ps(1.f);
      __m128 Nf4 = zerof4;
      __m128 sum1f4  = zerof4;
      __m128 sum2f4  = zerof4;
      __m128 sum11f4 = zerof4;
      __m128 sum22f4 = zerof4;
      __m128 sum12f4 = zerof4;
      for(; i < spin_sz - 5; i += 4)
      {
          __m128 v1f4 = _mm_loadu_ps(s1 + i);
          __m128 v2f4 = _mm_loadu_ps(s2 + i);
  
          __m128 mskf4 = _mm_and_ps(_mm_cmpneq_ps(v1f4, zerof4), _mm_cmpneq_ps(v2f4, zerof4));
          if( !_mm_movemask_ps(mskf4) )
              continue;
  
          Nf4 = _mm_add_ps(Nf4, _mm_and_ps(onef4, mskf4));
  
          v1f4 = _mm_and_ps(v1f4, mskf4);
          v2f4 = _mm_and_ps(v2f4, mskf4);
  
          sum1f4 = _mm_add_ps(sum1f4, v1f4);
          sum2f4 = _mm_add_ps(sum2f4, v2f4);
          sum11f4 = _mm_add_ps(sum11f4, _mm_mul_ps(v1f4, v1f4));
          sum22f4 = _mm_add_ps(sum22f4, _mm_mul_ps(v2f4, v2f4));
          sum12f4 = _mm_add_ps(sum12f4, _mm_mul_ps(v1f4, v2f4));
      }
      _mm_store_ps( su1,  sum1f4 );
      _mm_store_ps( su2,  sum2f4 );
      _mm_store_ps(su11, sum11f4 );
      _mm_store_ps(su22, sum22f4 );
      _mm_store_ps(su12, sum12f4 );
      _mm_store_ps(n, Nf4 );
  
      N = static_cast<int>(n[0] + n[1] + n[2] + n[3]);
      sum1  =  su1[0] +  su1[1] +  su1[2] +  su1[3];
      sum2  =  su2[0] +  su2[1] +  su2[2] +  su2[3];
      sum11 = su11[0] + su11[1] + su11[2] + su11[3];
      sum22 = su22[0] + su22[1] + su22[2] + su22[3];
      sum12 = su12[0] + su12[1] + su12[2] + su12[3];
  #endif
  
      for(; i < spin_sz; ++i)
      {
          float v1 = s1[i];
          float v2 = s2[i];
  
          if( !v1 || !v2 )
              continue;
          N++;
  
          sum1  += v1;
          sum2  += v2;
          sum11 += v1 * v1;
          sum22 += v2 * v2;
          sum12 += v1 * v2;
      }
      if( N < 4 )
          return false;
  
      double sum1sum1 = sum1 * sum1;
      double sum2sum2 = sum2 * sum2;
  
      double Nsum12 = N * sum12;
      double Nsum11 = N * sum11;
      double Nsum22 = N * sum22;
  
      if (Nsum11 == sum1sum1 || Nsum22 == sum2sum2)
          return false;
  
      double corr = (Nsum12 - sum1 * sum2) / sqrt( (Nsum11 - sum1sum1) * (Nsum22 - sum2sum2) );
      double atanh = Math::atanh(corr);
      result = (float)( atanh * atanh - lambda * ( 1.0 / (N - 3) ) );
      return true;
  }
  
  inline Point2f cv::SpinImageModel::calcSpinMapCoo(const Point3f& p, const Point3f& v, const Point3f& n)
  {
      /*Point3f PmV(p.x - v.x, p.y - v.y, p.z - v.z);
      float normalNorm = (float)norm(n);
      float beta = PmV.dot(n) / normalNorm;
      float pmcNorm = (float)norm(PmV);
      float alpha = sqrt( pmcNorm * pmcNorm - beta * beta);
      return Point2f(alpha, beta);*/
  
      float pmv_x = p.x - v.x, pmv_y = p.y - v.y, pmv_z = p.z - v.z;
  
      float beta = (pmv_x * n.x + pmv_y + n.y + pmv_z * n.z) / sqrt(n.x * n.x + n.y * n.y + n.z * n.z);
      float alpha = sqrt( pmv_x * pmv_x + pmv_y * pmv_y + pmv_z * pmv_z - beta * beta);
      return Point2f(alpha, beta);
  }
  
  inline float cv::SpinImageModel::geometricConsistency(const Point3f& pointScene1, const Point3f& normalScene1,
                                                        const Point3f& pointModel1, const Point3f& normalModel1,
                                                        const Point3f& pointScene2, const Point3f& normalScene2,
                                                        const Point3f& pointModel2, const Point3f& normalModel2)
  {
      Point2f Sm2_to_m1, Ss2_to_s1;
      Point2f Sm1_to_m2, Ss1_to_s2;
  
      double n_Sm2_to_m1 = norm(Sm2_to_m1 = calcSpinMapCoo(pointModel2, pointModel1, normalModel1));
      double n_Ss2_to_s1 = norm(Ss2_to_s1 = calcSpinMapCoo(pointScene2, pointScene1, normalScene1));
  
      double gc21 = 2 * norm(Sm2_to_m1 - Ss2_to_s1) / (n_Sm2_to_m1 + n_Ss2_to_s1 ) ;
  
      double n_Sm1_to_m2 = norm(Sm1_to_m2 = calcSpinMapCoo(pointModel1, pointModel2, normalModel2));
      double n_Ss1_to_s2 = norm(Ss1_to_s2 = calcSpinMapCoo(pointScene1, pointScene2, normalScene2));
  
      double gc12 = 2 * norm(Sm1_to_m2 - Ss1_to_s2) / (n_Sm1_to_m2 + n_Ss1_to_s2 ) ;
  
      return (float)max(gc12, gc21);
  }
  
  inline float cv::SpinImageModel::groupingCreteria(const Point3f& pointScene1, const Point3f& normalScene1,
                                                    const Point3f& pointModel1, const Point3f& normalModel1,
                                                    const Point3f& pointScene2, const Point3f& normalScene2,
                                                    const Point3f& pointModel2, const Point3f& normalModel2,
                                                    float gamma)
  {
      Point2f Sm2_to_m1, Ss2_to_s1;
      Point2f Sm1_to_m2, Ss1_to_s2;
  
      float gamma05_inv =  0.5f/gamma;
  
      double n_Sm2_to_m1 = norm(Sm2_to_m1 = calcSpinMapCoo(pointModel2, pointModel1, normalModel1));
      double n_Ss2_to_s1 = norm(Ss2_to_s1 = calcSpinMapCoo(pointScene2, pointScene1, normalScene1));
  
      double gc21 = 2 * norm(Sm2_to_m1 - Ss2_to_s1) / (n_Sm2_to_m1 + n_Ss2_to_s1 );
      double wgc21 = gc21 / (1 - exp( -(n_Sm2_to_m1 + n_Ss2_to_s1) * gamma05_inv ) );
  
      double n_Sm1_to_m2 = norm(Sm1_to_m2 = calcSpinMapCoo(pointModel1, pointModel2, normalModel2));
      double n_Ss1_to_s2 = norm(Ss1_to_s2 = calcSpinMapCoo(pointScene1, pointScene2, normalScene2));
  
      double gc12 = 2 * norm(Sm1_to_m2 - Ss1_to_s2) / (n_Sm1_to_m2 + n_Ss1_to_s2 );
      double wgc12 = gc12 / (1 - exp( -(n_Sm1_to_m2 + n_Ss1_to_s2) * gamma05_inv ) );
  
      return (float)max(wgc12, wgc21);
  }
  
  
  cv::SpinImageModel::SpinImageModel(const Mesh3D& _mesh) : mesh(_mesh) , out(0)
  {
       if (mesh.vtx.empty())
           throw Mesh3D::EmptyMeshException();
      defaultParams();
  }
  cv::SpinImageModel::SpinImageModel() : out(0) { defaultParams(); }
  cv::SpinImageModel::~SpinImageModel() {}
  
  void cv::SpinImageModel::setLogger(ostream* log) { out = log; }
  
  void cv::SpinImageModel::defaultParams()
  {
      normalRadius = 0.f;
      minNeighbors = 20;
  
      binSize    = 0.f; /* autodetect according to mesh resolution */
      imageWidth = 32;
  
      lambda = 0.f; /* autodetect according to medan non zero images bin */
      gamma  = 0.f; /* autodetect according to mesh resolution */
  
      T_GeometriccConsistency = 0.25f;
      T_GroupingCorespondances = 0.25f;
  }
  
  Mat cv::SpinImageModel::packRandomScaledSpins(bool separateScale, size_t xCount, size_t yCount) const
  {
      int spinNum = (int)getSpinCount();
      int num = min(spinNum, (int)(xCount * yCount));
  
      if (num == 0)
          return Mat();
  
      RNG& rng = theRNG();
  
      vector<Mat> spins;
      for(int i = 0; i < num; ++i)
          spins.push_back(getSpinImage( rng.next() % spinNum ).reshape(1, imageWidth));
  
      if (separateScale)
          for(int i = 0; i < num; ++i)
          {
              double max;
              Mat spin8u;
              minMaxLoc(spins[i], 0, &max);
              spins[i].convertTo(spin8u, CV_8U, -255.0/max, 255.0);
              spins[i] = spin8u;
          }
      else
      {
          double totalMax = 0;
          for(int i = 0; i < num; ++i)
          {
              double m;
              minMaxLoc(spins[i], 0, &m);
              totalMax = max(m, totalMax);
          }
  
          for(int i = 0; i < num; ++i)
          {
              Mat spin8u;
              spins[i].convertTo(spin8u, CV_8U, -255.0/totalMax, 255.0);
              spins[i] = spin8u;
          }
      }
  
      int sz = spins.front().cols;
  
      Mat result((int)(yCount * sz + (yCount - 1)), (int)(xCount * sz + (xCount - 1)), CV_8UC3);
      result = colors[(static_cast<int64>(cvGetTickCount()/cvGetTickFrequency())/1000) % colors_mum];
  
      int pos = 0;
      for(int y = 0; y < (int)yCount; ++y)
          for(int x = 0; x < (int)xCount; ++x)
              if (pos < num)
              {
                  int starty = (y + 0) * sz + y;
                  int endy   = (y + 1) * sz + y;
  
                  int startx = (x + 0) * sz + x;
                  int endx   = (x + 1) * sz + x;
  
                  Mat color;
                  cvtColor(spins[pos++], color, CV_GRAY2BGR);
                  Mat roi = result(Range(starty, endy), Range(startx, endx));
                  color.copyTo(roi);
              }
      return result;
  }
  
  void cv::SpinImageModel::selectRandomSubset(float ratio)
  {
      ratio = min(max(ratio, 0.f), 1.f);
  
      size_t vtxSize = mesh.vtx.size();
      size_t setSize  = static_cast<size_t>(vtxSize * ratio);
  
      if (setSize == 0)
      {
          subset.clear();
      }
      else if (setSize == vtxSize)
      {
          subset.resize(vtxSize);
          _iota(subset.begin(), subset.end(), 0);
      }
      else
      {
          RNG& rnd = theRNG();
  
          vector<size_t> left(vtxSize);
          _iota(left.begin(), left.end(), (size_t)0);
  
          subset.resize(setSize);
          for(size_t i = 0; i < setSize; ++i)
          {
              int pos = rnd.next() % (int)left.size();
              subset[i] = (int)left[pos];
  
              left[pos] = left.back();
              left.resize(left.size() - 1);
          }
          sort(subset, less<int>());
      }
  }
  
  void cv::SpinImageModel::setSubset(const vector<int>& ss)
  {
      subset = ss;
  }
  
  void cv::SpinImageModel::repackSpinImages(const vector<uchar>& mask, Mat& _spinImages, bool reAlloc) const
  {
      if (reAlloc)
      {
          size_t spinCount = mask.size() - count(mask.begin(), mask.end(), (uchar)0);
          Mat newImgs((int)spinCount, _spinImages.cols, _spinImages.type());
  
          int pos = 0;
          for(size_t t = 0; t < mask.size(); ++t)
              if (mask[t])
              {
                  Mat row = newImgs.row(pos++);
                  _spinImages.row((int)t).copyTo(row);
              }
          _spinImages = newImgs;
      }
      else
      {
          int last = (int)mask.size();
  
          int dest = (int)(find(mask.begin(), mask.end(), (uchar)0) - mask.begin());
          if (dest == last)
              return;
  
          int first = dest + 1;
          for (; first != last; ++first)
              if (mask[first] != 0)
              {
                  Mat row = _spinImages.row(dest);
                  _spinImages.row(first).copyTo(row);
                  ++dest;
              }
          _spinImages = _spinImages.rowRange(0, dest);
      }
  }
  
  void cv::SpinImageModel::compute()
  {
      /* estimate binSize */
      if (binSize == 0.f)
      {
           if (mesh.resolution == -1.f)
              mesh.estimateResolution();
          binSize = mesh.resolution;
      }
      /* estimate normalRadius */
      normalRadius = normalRadius != 0.f ? normalRadius : binSize * imageWidth / 2;
  
      mesh.buildOctree();
      if (subset.empty())
      {
          mesh.computeNormals(normalRadius, minNeighbors);
          subset.resize(mesh.vtx.size());
          _iota(subset.begin(), subset.end(), 0);
      }
      else
          mesh.computeNormals(subset, normalRadius, minNeighbors);
  
      vector<uchar> mask(mesh.vtx.size(), 0);
      for(size_t i = 0; i < subset.size(); ++i)
          if (mesh.normals[subset[i]] == Mesh3D::allzero)
              subset[i] = -1;
          else
              mask[subset[i]] = 1;
      subset.resize( remove(subset.begin(), subset.end(), -1) - subset.begin() );
  
      vector<Point3f> vtx;
      vector<Point3f> normals;
      for(size_t i = 0; i < mask.size(); ++i)
          if(mask[i])
          {
              vtx.push_back(mesh.vtx[i]);
              normals.push_back(mesh.normals[i]);
          }
  
      vector<uchar> spinMask(vtx.size(), 1);
      computeSpinImages( mesh.octree, vtx, normals, spinMask, spinImages, imageWidth, binSize);
      repackSpinImages(spinMask, spinImages);
  
      size_t mask_pos = 0;
      for(size_t i = 0; i < mask.size(); ++i)
          if(mask[i])
              if (spinMask[mask_pos++] == 0)
                  subset.resize( remove(subset.begin(), subset.end(), (int)i) - subset.begin() );
  }
  
  void cv::SpinImageModel::matchSpinToModel(const Mat& spin, vector<int>& indeces, vector<float>& corrCoeffs, bool useExtremeOutliers) const
  {
      const SpinImageModel& model = *this;
  
      indeces.clear();
      corrCoeffs.clear();
  
      vector<float> corrs(model.spinImages.rows);
      vector<uchar>  masks(model.spinImages.rows);
      vector<float> cleanCorrs;
      cleanCorrs.reserve(model.spinImages.rows);
  
      for(int i = 0; i < model.spinImages.rows; ++i)
      {
          masks[i] = spinCorrelation(spin, model.spinImages.row(i), model.lambda, corrs[i]);
          if (masks[i])
              cleanCorrs.push_back(corrs[i]);
      }
  
      /* Filtering by measure histogram */
      size_t total = cleanCorrs.size();
      if(total < 5)
          return;
  
      sort(cleanCorrs, less<float>());
  
      float lower_fourth = cleanCorrs[(1 * total) / 4 - 1];
      float upper_fourth = cleanCorrs[(3 * total) / 4 - 0];
      float fourth_spread = upper_fourth - lower_fourth;
  
      //extreme or moderate?
      float coef = useExtremeOutliers ? 3.0f : 1.5f;
  
      float histThresHi = upper_fourth + coef * fourth_spread;
      //float histThresLo = lower_fourth - coef * fourth_spread;
  
      for(size_t i = 0; i < corrs.size(); ++i)
          if (masks[i])
              if (/* corrs[i] < histThresLo || */ corrs[i] > histThresHi)
              {
                  indeces.push_back((int)i);
                  corrCoeffs.push_back(corrs[i]);
              }
  }
  
  namespace
  {
  
  struct Match
  {
      int sceneInd;
      int modelInd;
      float measure;
  
      Match(){}
      Match(int sceneIndex, int modelIndex, float coeff) : sceneInd(sceneIndex), modelInd(modelIndex), measure(coeff) {}
      operator float() const { return measure; }
  };
  
  typedef set<size_t> group_t;
  typedef group_t::iterator iter;
  typedef group_t::const_iterator citer;
  
  struct WgcHelper
  {
      const group_t& grp;
      const Mat& mat;
      WgcHelper(const group_t& group, const Mat& groupingMat) : grp(group), mat(groupingMat){}
      float operator()(size_t leftInd) const { return Wgc(leftInd, grp); }
  
      /* Wgc( correspondence_C, group_{C1..Cn} ) = max_i=1..n_( Wgc(C, Ci) ) */
      float Wgc(const size_t corespInd, const group_t& group) const
      {
          const float* wgcLine = mat.ptr<float>((int)corespInd);
          float maximum = numeric_limits<float>::min();
  
          for(citer pos = group.begin(); pos != group.end(); ++pos)
              maximum = max(wgcLine[*pos], maximum);
  
          return maximum;
      }
  private:
      WgcHelper& operator=(const WgcHelper& helper);
  };
  
  }
  
   void cv::SpinImageModel::match(const SpinImageModel& scene, vector< vector<Vec2i> >& result)
  {
      if (mesh.vtx.empty())
          throw Mesh3D::EmptyMeshException();
  
      result.clear();
  
      SpinImageModel& model = *this;
      const float infinity = numeric_limits<float>::infinity();
      const float float_max = numeric_limits<float>::max();
  
      /* estimate gamma */
      if (model.gamma == 0.f)
      {
          if (model.mesh.resolution == -1.f)
              model.mesh.estimateResolution();
          model.gamma = 4 * model.mesh.resolution;
      }
  
      /* estimate lambda */
      if (model.lambda == 0.f)
      {
          vector<int> nonzero(model.spinImages.rows);
          for(int i = 0; i < model.spinImages.rows; ++i)
              nonzero[i] = countNonZero(model.spinImages.row(i));
          sort(nonzero, less<int>());
          model.lambda = static_cast<float>( nonzero[ nonzero.size()/2 ] ) / 2;
      }
  
      TickMeter corr_timer;
      corr_timer.start();
      vector<Match> allMatches;
      for(int i = 0; i < scene.spinImages.rows; ++i)
      {
          vector<int> indeces;
          vector<float> coeffs;
          matchSpinToModel(scene.spinImages.row(i), indeces, coeffs);
          for(size_t t = 0; t < indeces.size(); ++t)
              allMatches.push_back(Match(i, indeces[t], coeffs[t]));
  
          if (out) if (i % 100 == 0) *out << "Comparing scene spinimage " << i << " of " << scene.spinImages.rows << endl;
      }
      corr_timer.stop();
      if (out) *out << "Spin correlation time  = " << corr_timer << endl;
      if (out) *out << "Matches number = " << allMatches.size() << endl;
  
      if(allMatches.empty())
          return;
  
      /* filtering by similarity measure */
      const float fraction = 0.5f;
      float maxMeasure = max_element(allMatches.begin(), allMatches.end(), less<float>())->measure;
      allMatches.erase(
          remove_if(allMatches.begin(), allMatches.end(), bind2nd(less<float>(), maxMeasure * fraction)),
          allMatches.end());
      if (out) *out << "Matches number [filtered by similarity measure] = " << allMatches.size() << endl;
  
      int matchesSize = (int)allMatches.size();
      if(matchesSize == 0)
          return;
  
      /* filtering by geometric consistency */
      for(int i = 0; i < matchesSize; ++i)
      {
          int consistNum = 1;
          float gc = float_max;
  
          for(int j = 0; j < matchesSize; ++j)
              if (i != j)
              {
                  const Match& mi = allMatches[i];
                  const Match& mj = allMatches[j];
  
                  if (mi.sceneInd == mj.sceneInd || mi.modelInd == mj.modelInd)
                      gc = float_max;
                  else
                  {
                      const Point3f& pointSceneI  = scene.getSpinVertex(mi.sceneInd);
                      const Point3f& normalSceneI = scene.getSpinNormal(mi.sceneInd);
  
                      const Point3f& pointModelI  = model.getSpinVertex(mi.modelInd);
                      const Point3f& normalModelI = model.getSpinNormal(mi.modelInd);
  
                      const Point3f& pointSceneJ  = scene.getSpinVertex(mj.sceneInd);
                      const Point3f& normalSceneJ = scene.getSpinNormal(mj.sceneInd);
  
                      const Point3f& pointModelJ  = model.getSpinVertex(mj.modelInd);
                      const Point3f& normalModelJ = model.getSpinNormal(mj.modelInd);
  
                      gc = geometricConsistency(pointSceneI, normalSceneI, pointModelI, normalModelI,
                                                pointSceneJ, normalSceneJ, pointModelJ, normalModelJ);
                  }
  
                  if (gc < model.T_GeometriccConsistency)
                      ++consistNum;
              }
  
  
          if (consistNum < matchesSize / 4) /* failed consistensy test */
              allMatches[i].measure = infinity;
      }
      allMatches.erase(
        remove_if(allMatches.begin(), allMatches.end(), bind2nd(equal_to<float>(), infinity)),
        allMatches.end());
      if (out) *out << "Matches number [filtered by geometric consistency] = " << allMatches.size() << endl;
  
  
      matchesSize = (int)allMatches.size();
      if(matchesSize == 0)
          return;
  
      if (out) *out << "grouping ..." << endl;
  
      Mat groupingMat((int)matchesSize, (int)matchesSize, CV_32F);
      groupingMat = Scalar(0);
  
      /* grouping */
      for(int j = 0; j < matchesSize; ++j)
          for(int i = j + 1; i < matchesSize; ++i)
          {
              const Match& mi = allMatches[i];
              const Match& mj = allMatches[j];
  
              if (mi.sceneInd == mj.sceneInd || mi.modelInd == mj.modelInd)
              {
                  groupingMat.ptr<float>(i)[j] = float_max;
                  groupingMat.ptr<float>(j)[i] = float_max;
                  continue;
              }
  
              const Point3f& pointSceneI  = scene.getSpinVertex(mi.sceneInd);
              const Point3f& normalSceneI = scene.getSpinNormal(mi.sceneInd);
  
              const Point3f& pointModelI  = model.getSpinVertex(mi.modelInd);
              const Point3f& normalModelI = model.getSpinNormal(mi.modelInd);
  
              const Point3f& pointSceneJ  = scene.getSpinVertex(mj.sceneInd);
              const Point3f& normalSceneJ = scene.getSpinNormal(mj.sceneInd);
  
              const Point3f& pointModelJ  = model.getSpinVertex(mj.modelInd);
              const Point3f& normalModelJ = model.getSpinNormal(mj.modelInd);
  
              float wgc = groupingCreteria(pointSceneI, normalSceneI, pointModelI, normalModelI,
                                           pointSceneJ, normalSceneJ, pointModelJ, normalModelJ,
                                           model.gamma);
  
              groupingMat.ptr<float>(i)[j] = wgc;
              groupingMat.ptr<float>(j)[i] = wgc;
          }
  
      group_t allMatchesInds;
      for(int i = 0; i < matchesSize; ++i)
          allMatchesInds.insert(i);
  
      vector<float> buf(matchesSize);
      float *buf_beg = &buf[0];
      vector<group_t> groups;
  
      for(int g = 0; g < matchesSize; ++g)
      {
          if (out) if (g % 100 == 0) *out << "G = " << g << endl;
  
          group_t left = allMatchesInds;
          group_t group;
  
          left.erase(g);
          group.insert(g);
  
          for(;;)
          {
              size_t left_size = left.size();
              if (left_size == 0)
                  break;
  
              std::transform(left.begin(), left.end(), buf_beg,  WgcHelper(group, groupingMat));
              size_t minInd = min_element(buf_beg, buf_beg + left_size) - buf_beg;
  
              if (buf[minInd] < model.T_GroupingCorespondances) /* can add corespondance to group */
              {
                  iter pos = left.begin();
                  advance(pos, minInd);
  
                  group.insert(*pos);
                  left.erase(pos);
              }
              else
                  break;
          }
  
          if (group.size() >= 4)
              groups.push_back(group);
      }
  
      /* converting the data to final result */
      for(size_t i = 0; i < groups.size(); ++i)
      {
          const group_t& group = groups[i];
  
          vector< Vec2i > outgrp;
          for(citer pos = group.begin(); pos != group.end(); ++pos)
          {
              const Match& m = allMatches[*pos];
              outgrp.push_back(Vec2i(subset[m.modelInd], scene.subset[m.sceneInd]));
          }
          result.push_back(outgrp);
      }
  }
  
  cv::TickMeter::TickMeter() { reset(); }
  int64 cv::TickMeter::getTimeTicks() const { return sumTime; }
  double cv::TickMeter::getTimeSec()   const { return (double)getTimeTicks()/getTickFrequency(); }
  double cv::TickMeter::getTimeMilli() const { return getTimeSec()*1e3; }
  double cv::TickMeter::getTimeMicro() const { return getTimeMilli()*1e3; }
  int64 cv::TickMeter::getCounter() const { return counter; }
  void  cv::TickMeter::reset() {startTime = 0; sumTime = 0; counter = 0; }
  
  void cv::TickMeter::start(){ startTime = getTickCount(); }
  void cv::TickMeter::stop()
  {
      int64 time = getTickCount();
      if ( startTime == 0 )
          return;
  
      ++counter;
  
      sumTime += ( time - startTime );
      startTime = 0;
  }
  
  std::ostream& cv::operator<<(std::ostream& out, const TickMeter& tm){ return out << tm.getTimeSec() << "sec"; }
  