PatchFinder.cc

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// Copyright 2008 Isis Innovation Limited
#include "ptam/PatchFinder.h"
#include "ptam/SmallMatrixOpts.h"
#include "ptam/KeyFrame.h"

#include <cvd/vision.h>
#include <cvd/vector_image_ref.h>
#include <cvd/image_interpolate.h>
#include <TooN/Cholesky.h>
// tmmintrin.h contains SSE3<> instrinsics, used for the ZMSSD search at the bottom..
// If this causes problems, just do #define CVD_HAVE_XMMINTRIN 0
#if CVD_HAVE_XMMINTRIN
#include <tmmintrin.h>
#endif

using namespace CVD;
using namespace std;

PatchFinder::PatchFinder(int nPatchSize)
: mimTemplate(ImageRef(nPatchSize,nPatchSize))
{
  mnPatchSize = nPatchSize;
  mirCenter = ImageRef(nPatchSize/2, nPatchSize/2);
  int nMaxSSDPerPixel = 500; // Pretty arbitrary... could make a GVar out of this.
  mnMaxSSD = mnPatchSize * mnPatchSize * nMaxSSDPerPixel;
  // Populate the speed-up caches with bogus values:
  mm2LastWarpMatrix = 9999.9 * Identity;
};


// Find the warping matrix and search level
int PatchFinder::CalcSearchLevelAndWarpMatrix(MapPoint::Ptr p,
                                              SE3<> se3CFromW,
                                              Matrix<2> &m2CamDerivs)
{
  // Calc point pos in new view camera frame
  // Slightly dumb that we re-calculate this here when the tracker's already done this!
  Vector<3> v3Cam = se3CFromW * p->v3WorldPos;
  double dOneOverCameraZ = 1.0 / v3Cam[2];
  // Project the source keyframe's one-pixel-right and one-pixel-down vectors into the current view
  Vector<3> v3MotionRight = se3CFromW.get_rotation() * p->v3PixelRight_W;
  Vector<3> v3MotionDown = se3CFromW.get_rotation() * p->v3PixelDown_W;
  // Calculate in-image derivatives of source image pixel motions:
  mm2WarpInverse.T()[0] = m2CamDerivs * (v3MotionRight.slice<0,2>() - v3Cam.slice<0,2>() * v3MotionRight[2] * dOneOverCameraZ) * dOneOverCameraZ;
  mm2WarpInverse.T()[1] = m2CamDerivs * (v3MotionDown.slice<0,2>() - v3Cam.slice<0,2>() * v3MotionDown[2] * dOneOverCameraZ) * dOneOverCameraZ;
  double dDet = mm2WarpInverse[0][0] * mm2WarpInverse[1][1] - mm2WarpInverse[0][1] * mm2WarpInverse[1][0];
  mnSearchLevel = 0;

  // This warp matrix is likely not appropriate for finding at level zero, which is 
  // the level at which it has been calculated. Vary the search level until the 
  // at that level would be appropriate (does not actually modify the matrix.)
  while(dDet > 3 && mnSearchLevel < LEVELS-1)
  {
    mnSearchLevel++;
    dDet *= 0.25;
  };

  // Some warps are inappropriate, e.g. too near the camera, too far, or reflected, 
  // or zero area.. reject these!
  if(dDet > 3 || dDet < 0.25)
  {
    mbTemplateBad = true;
    return -1;
  }
  else
    return mnSearchLevel;
}

// This is just a convenience function wich caluclates the warp matrix and generates
// the template all in one call.
void PatchFinder::MakeTemplateCoarse(MapPoint::Ptr p,
                                     SE3<> se3CFromW,
                                     Matrix<2> &m2CamDerivs)
{
  CalcSearchLevelAndWarpMatrix(p, se3CFromW, m2CamDerivs);
  MakeTemplateCoarseCont(p);
};

// This function generates the warped search template.
void PatchFinder::MakeTemplateCoarseCont(MapPoint::Ptr p)
{
  // Get the warping matrix appropriate for use with CVD::transform...
  Matrix<2> m2 = M2Inverse(mm2WarpInverse) * LevelScale(mnSearchLevel); 
  // m2 now represents the number of pixels in the source image for one 
  // pixel of template image

  // Optimisation: Don't re-gen the coarse template if it's going to be substantially the 
  // same as was made last time. This saves time when the camera is not moving. For this, 
  // check that (a) this patchfinder is still working on the same map point and (b) the 
  // warping matrix has not changed much.

  bool bNeedToRefreshTemplate = false;
  if(p != mpLastTemplateMapPoint)
    bNeedToRefreshTemplate = true;
  // Still the same map point? Then compare warping matrix..
  for(int i=0; !bNeedToRefreshTemplate && i<2; i++)
  {
    Vector<2> v2Diff = m2.T()[i] - mm2LastWarpMatrix.T()[i];
    const double dRefreshLimit = 0.07;  // Sort of works out as half a pixel displacement in src img
    if(v2Diff * v2Diff > dRefreshLimit * dRefreshLimit)
      bNeedToRefreshTemplate = true;
  }

  // Need to regen template? Then go ahead.
  if(bNeedToRefreshTemplate)
  {
    int nOutside;  // Use CVD::transform to warp the patch according the the warping matrix m2
    // This returns the number of pixels outside the source image hit, which should be zero.
    nOutside = CVD::transform(p->pPatchSourceKF->aLevels[p->nSourceLevel].im,
                              mimTemplate,
                              m2,
                              vec(p->irCenter),
                              vec(mirCenter));

    if(nOutside)
      mbTemplateBad = true;
    else
      mbTemplateBad = false;

    MakeTemplateSums();

    // Store the parameters which allow us to determine if we need to re-calculate
    // the patch next time round.
    mpLastTemplateMapPoint = p;
    mm2LastWarpMatrix = m2;
  }
};

// This makes a template without warping. Used for epipolar search, where we don't really know 
// what the warping matrix should be. (Although to be fair, I should do rotation for epipolar,
// which we could approximate without knowing patch depth!)
void PatchFinder::MakeTemplateCoarseNoWarp(KeyFrame::Ptr k, int nLevel, ImageRef irLevelPos)
{
  mnSearchLevel = nLevel;
  Image<CVD::byte> &im = k->aLevels[nLevel].im;
  if(!im.in_image_with_border(irLevelPos, mnPatchSize / 2 + 1))
  {
    mbTemplateBad = true;
    return;
  }
  mbTemplateBad = false;
  copy(im,
       mimTemplate,
       mimTemplate.size(),
       irLevelPos - mirCenter);

  MakeTemplateSums();
}

// Convenient wrapper for the above
void PatchFinder::MakeTemplateCoarseNoWarp(MapPoint::Ptr p)
{
  MakeTemplateCoarseNoWarp(p->pPatchSourceKF, p->nSourceLevel,  p->irCenter);
};

// Finds the sum, and sum-squared, of template pixels. These sums are used
// to calculate the ZMSSD.
inline void PatchFinder::MakeTemplateSums()
{
  int nSum = 0;
  int nSumSq = 0;
  ImageRef ir;
  do
  {
    int b = mimTemplate[ir];
    nSum += b;
    nSumSq +=b * b;
  }
  while(ir.next(mimTemplate.size()));
  mnTemplateSum = nSum;
  mnTemplateSumSq = nSumSq;
}

// One of the main functions of the class! Looks at the appropriate level of 
// the target keyframe to try and find the template. Looks only at FAST corner points
// which are within radius nRange of the center. (Params are supplied in Level0
// coords.) Returns true on patch found.
bool PatchFinder::FindPatchCoarse(ImageRef irPos, KeyFrame::Ptr kf, unsigned int nRange)
{
  mbFound = false;

  // Convert from L0 coords to search level quantities
  int nLevelScale = LevelScale(mnSearchLevel);
  mirPredictedPos = irPos;
  irPos = irPos / nLevelScale;
  nRange = (nRange + nLevelScale - 1) / nLevelScale;

  // Bounding box of search circle
  int nTop = irPos.y - nRange;
  int nBottomPlusOne = irPos.y + nRange + 1;
  int nLeft = irPos.x - nRange;
  int nRight = irPos.x + nRange;

  // Ref variable for the search level
  Level &L = kf->aLevels[mnSearchLevel];

  // Some bounds checks on the bounding box..
  if(nTop < 0)
    nTop = 0;
  if(nTop >= L.im.size().y)
    return false;
  if(nBottomPlusOne <= 0)
    return false;

  // The next section finds all the FAST corners in the target level which 
  // are near enough the search center. It's a bit optimised to use 
  // a corner row look-up-table, since otherwise the routine
  // would spend a long time trawling throught the whole list of FAST corners!
  vector<ImageRef>::iterator i;
  vector<ImageRef>::iterator i_end;

  i = L.vCorners.begin() + L.vCornerRowLUT[nTop];

  if(nBottomPlusOne >= L.im.size().y)
    i_end = L.vCorners.end();
  else 
    i_end = L.vCorners.begin() + L.vCornerRowLUT[nBottomPlusOne];

  ImageRef irBest;             // Best match so far
  int nBestSSD = mnMaxSSD + 1; // Best score so far is beyond the max allowed

  for(; i<i_end; i++)          // For each corner ...
  {
    if( i->x < nLeft || i->x > nRight)
      continue;
    if((irPos - *i).mag_squared() > nRange * nRange)
      continue;              // ... reject all those not close enough..

    int nSSD;                // .. and find the ZMSSD at those near enough.
    nSSD = ZMSSDAtPoint(L.im, *i);
    if(nSSD < nBestSSD)      // Best yet?
    {
      irBest = *i;
      nBestSSD = nSSD;
    }
  } // done looping over corners

  if(nBestSSD < mnMaxSSD)      // Found a valid match?
  {
    mv2CoarsePos= LevelZeroPos(irBest, mnSearchLevel);
    mbFound = true;
  }
  else
    mbFound = false;
  return mbFound;
}

// Makes an inverse composition template out of the coarse template.
// Includes calculating image of derivatives (gradients.) The inverse composition
// used here operates on three variables: x offet, y offset, and difference in patch
// means; hence things like mm3HInv are dim 3, but the trivial mean jacobian 
// (always unity, for each pixel) is not stored.
void PatchFinder::MakeSubPixTemplate()
{
  mimJacs.resize(mimTemplate.size() - ImageRef(2,2));
  Matrix<3> m3H = Zeros; // This stores jTj.
  ImageRef ir;
  for(ir.x = 1; ir.x < mnPatchSize - 1; ir.x++)
    for(ir.y = 1; ir.y < mnPatchSize - 1; ir.y++)
    {
      Vector<2> v2Grad;
      v2Grad[0] = 0.5 * (mimTemplate[ir + ImageRef(1,0)] - mimTemplate[ir - ImageRef(1,0)]);
      v2Grad[1] = 0.5 * (mimTemplate[ir + ImageRef(0,1)] - mimTemplate[ir - ImageRef(0,1)]);
      mimJacs[ir-ImageRef(1,1)].first = v2Grad[0];
      mimJacs[ir-ImageRef(1,1)].second = v2Grad[1];
      Vector<3> v3Grad = unproject(v2Grad); // This adds the mean-difference jacobian..
      m3H += v3Grad.as_col() * v3Grad.as_row(); // Populate JTJ.
    }

  // Invert JTJ..
  Cholesky<3> chol(m3H);
  mm3HInv = chol.get_inverse();
  // TOON2 Does not have a get_rank for cholesky
  // int nRank = chol.get_rank();
  // if(nRank < 3)
  // cout << "BAD RANK IN MAKESUBPIXELTEMPLATE!!!!" << endl; // This does not happen often (almost never!)

  mv2SubPixPos = mv2CoarsePos; // Start the sub-pixel search at the result of the coarse search..
  mdMeanDiff = 0.0;
}

// Iterate inverse composition until convergence. Since it should never have 
// to travel more than a pixel's distance, set a max number of iterations; 
// if this is exceeded, consider the IC to have failed.
bool PatchFinder::IterateSubPixToConvergence(KeyFrame& kf, int nMaxIts)
{
  const double dConvLimit = 0.03;
  bool bConverged = false;
  int nIts;
  for(nIts = 0; nIts < nMaxIts && !bConverged; nIts++)
  {
    double dUpdateSquared = IterateSubPix(kf);
    if(dUpdateSquared < 0) // went off edge of image
      return false;
    if(dUpdateSquared < dConvLimit*dConvLimit)
      return true;
  }
  return false;
}

// Single iteration of inverse composition. This compares integral image positions in the 
// template image to floating point positions in the target keyframe. Interpolation is
// bilinear, and performed manually (rather than using CVD::image_interpolate) since 
// this is a special case where the mixing fractions for each pixel are identical.
double PatchFinder::IterateSubPix(KeyFrame& kf)
{
  // Search level pos of patch center
  Vector<2> v2Center = LevelNPos(mv2SubPixPos, mnSearchLevel);
  BasicImage<CVD::byte> &im = kf.aLevels[mnSearchLevel].im;
  if(!im.in_image_with_border(ir_rounded(v2Center), mnPatchSize / 2 + 1))
    return -1.0;       // Negative return value indicates off edge of image 

  // Position of top-left corner of patch in search level
  Vector<2> v2Base = v2Center - vec(mirCenter);

  // I.C. JT*d accumulator
  Vector<3> v3Accum = Zeros;

  ImageRef ir;

  CVD::byte* pTopLeftPixel;

  // Each template pixel will be compared to an interpolated target pixel
  // The target value is made using bilinear interpolation as the weighted sum
  // of four target image pixels. Calculate mixing fractions:
  double dX = v2Base[0]-floor(v2Base[0]); // Distances from pixel center of TL pixel
  double dY = v2Base[1]-floor(v2Base[1]);
  float fMixTL = (1.0 - dX) * (1.0 - dY);
  float fMixTR = (dX)       * (1.0 - dY);
  float fMixBL = (1.0 - dX) * (dY);
  float fMixBR = (dX)       * (dY);

  // Loop over template image
  unsigned long nRowOffset = &kf.aLevels[mnSearchLevel].im[ImageRef(0,1)] - &kf.aLevels[mnSearchLevel].im[ImageRef(0,0)];
  for(ir.y = 1; ir.y < mnPatchSize - 1; ir.y++)
  {
    pTopLeftPixel = &im[::ir(v2Base) + ImageRef(1,ir.y)]; // n.b. the x=1 offset, as with y
    for(ir.x = 1; ir.x < mnPatchSize - 1; ir.x++)
    {
      float fPixel =   // Calc target interpolated pixel
          fMixTL * pTopLeftPixel[0]          + fMixTR * pTopLeftPixel[1] +
          fMixBL * pTopLeftPixel[nRowOffset] + fMixBR * pTopLeftPixel[nRowOffset + 1];
      pTopLeftPixel++;
      double dDiff = fPixel - mimTemplate[ir] + mdMeanDiff;
      v3Accum[0] += dDiff * mimJacs[ir - ImageRef(1,1)].first;
      v3Accum[1] += dDiff * mimJacs[ir - ImageRef(1,1)].second;
      v3Accum[2] += dDiff;  // Update JT*d
    };
  }

  // All done looping over image - find JTJ^-1 * JTd:
  Vector<3> v3Update = mm3HInv * v3Accum; 
  mv2SubPixPos -= v3Update.slice<0,2>() * LevelScale(mnSearchLevel);
  mdMeanDiff -= v3Update[2];

  double dPixelUpdateSquared = v3Update.slice<0,2>() * v3Update.slice<0,2>();
  return dPixelUpdateSquared;
}

// 
//
//              ZMSSDatpoint, which is SSE optimised, follows
//
// The top version is the SSE version for 8x8 patches. It is compiled
// only if CVD_HAVE_XMMINTRIN is true, also you need to give your 
// compiler the appropriate flags (e.g. -march=core2 -msse3 for g++.)
// The standard c++ version, which is about half as quick (not a disaster
// by any means) is below.
//
// The 8x8 SSE version looks long because it has been unrolled, 
// it just does the same thing eight times. Both versions are one-pass
// and need pre-calculated template sums and sum-squares.
//

#if CVD_HAVE_XMMINTRIN
// Horizontal sum of uint16s stored in an XMM register
inline int SumXMM_16(__m128i &target)
{
  unsigned short int sums_store[8];    
  _mm_storeu_si128((__m128i*)sums_store, target);
  return sums_store[0] + sums_store[1] + sums_store[2] + sums_store[3] +
      sums_store[4] + sums_store[5] + sums_store[6] + sums_store[7];
}
// Horizontal sum of uint32s stored in an XMM register
inline int SumXMM_32(__m128i &target)
{
  unsigned int sums_store[4];    
  _mm_storeu_si128((__m128i*)sums_store, target);
  return sums_store[0] + sums_store[1] + sums_store[2] + sums_store[3];
}
#endif

// Calculate the Zero-mean SSD of the coarse patch and a target imate at a specific 
// point.
int PatchFinder::ZMSSDAtPoint(CVD::BasicImage<CVD::byte> &im, const CVD::ImageRef &ir)
{
  if(!im.in_image_with_border(ir, mirCenter[0]))
    return mnMaxSSD + 1;

  ImageRef irImgBase = ir - mirCenter;
  CVD::byte *imagepointer;
  CVD::byte *templatepointer;

  int nImageSumSq = 0;
  int nImageSum = 0;
  int nCrossSum = 0;

#if CVD_HAVE_XMMINTRIN
  if(mnPatchSize == 8)
  {
    long unsigned int imagepointerincrement;

    __m128i xImageAsEightBytes;
    __m128i xImageAsWords;
    __m128i xTemplateAsEightBytes;
    __m128i xTemplateAsWords;
    __m128i xZero;
    __m128i xImageSums; // These sums are 8xuint16
    __m128i xImageSqSums; // These sums are 4xint32
    __m128i xCrossSums;   // These sums are 4xint32
    __m128i xProduct;


    xImageSums = _mm_setzero_si128();
    xImageSqSums = _mm_setzero_si128();
    xCrossSums = _mm_setzero_si128();
    xZero = _mm_setzero_si128();

    imagepointer = &im[irImgBase + ImageRef(0,0)];
    templatepointer = &mimTemplate[ImageRef(0,0)];
    imagepointerincrement = &im[irImgBase + ImageRef(0,1)] - imagepointer;

    xImageAsEightBytes=_mm_loadl_epi64((__m128i*) imagepointer);
    imagepointer += imagepointerincrement;
    xImageAsWords = _mm_unpacklo_epi8(xImageAsEightBytes,xZero);
    xImageSums = _mm_adds_epu16(xImageAsWords,xImageSums);
    xProduct = _mm_madd_epi16(xImageAsWords, xImageAsWords);
    xImageSqSums = _mm_add_epi32(xProduct, xImageSqSums);
    xTemplateAsEightBytes=_mm_load_si128((__m128i*) templatepointer);
    templatepointer += 16;
    xTemplateAsWords = _mm_unpacklo_epi8(xTemplateAsEightBytes,xZero);
    xProduct = _mm_madd_epi16(xImageAsWords, xTemplateAsWords);
    xCrossSums = _mm_add_epi32(xProduct, xCrossSums);
    xImageAsEightBytes=_mm_loadl_epi64((__m128i*) imagepointer);
    imagepointer += imagepointerincrement;
    xImageAsWords = _mm_unpacklo_epi8(xImageAsEightBytes,xZero);
    xImageSums = _mm_adds_epu16(xImageAsWords,xImageSums);
    xProduct = _mm_madd_epi16(xImageAsWords, xImageAsWords);
    xImageSqSums = _mm_add_epi32(xProduct, xImageSqSums);
    xTemplateAsWords = _mm_unpackhi_epi8(xTemplateAsEightBytes,xZero);
    xProduct = _mm_madd_epi16(xImageAsWords, xTemplateAsWords);
    xCrossSums = _mm_add_epi32(xProduct, xCrossSums);

    xImageAsEightBytes=_mm_loadl_epi64((__m128i*) imagepointer);
    imagepointer += imagepointerincrement;
    xImageAsWords = _mm_unpacklo_epi8(xImageAsEightBytes,xZero);
    xImageSums = _mm_adds_epu16(xImageAsWords,xImageSums);
    xProduct = _mm_madd_epi16(xImageAsWords, xImageAsWords);
    xImageSqSums = _mm_add_epi32(xProduct, xImageSqSums);
    xTemplateAsEightBytes=_mm_load_si128((__m128i*) templatepointer);
    templatepointer += 16;
    xTemplateAsWords = _mm_unpacklo_epi8(xTemplateAsEightBytes,xZero);
    xProduct = _mm_madd_epi16(xImageAsWords, xTemplateAsWords);
    xCrossSums = _mm_add_epi32(xProduct, xCrossSums);
    xImageAsEightBytes=_mm_loadl_epi64((__m128i*) imagepointer);
    imagepointer += imagepointerincrement;
    xImageAsWords = _mm_unpacklo_epi8(xImageAsEightBytes,xZero);
    xImageSums = _mm_adds_epu16(xImageAsWords,xImageSums);
    xProduct = _mm_madd_epi16(xImageAsWords, xImageAsWords);
    xImageSqSums = _mm_add_epi32(xProduct, xImageSqSums);
    xTemplateAsWords = _mm_unpackhi_epi8(xTemplateAsEightBytes,xZero);
    xProduct = _mm_madd_epi16(xImageAsWords, xTemplateAsWords);
    xCrossSums = _mm_add_epi32(xProduct, xCrossSums);

    xImageAsEightBytes=_mm_loadl_epi64((__m128i*) imagepointer);
    imagepointer += imagepointerincrement;
    xImageAsWords = _mm_unpacklo_epi8(xImageAsEightBytes,xZero);
    xImageSums = _mm_adds_epu16(xImageAsWords,xImageSums);
    xProduct = _mm_madd_epi16(xImageAsWords, xImageAsWords);
    xImageSqSums = _mm_add_epi32(xProduct, xImageSqSums);
    xTemplateAsEightBytes=_mm_load_si128((__m128i*) templatepointer);
    templatepointer += 16;
    xTemplateAsWords = _mm_unpacklo_epi8(xTemplateAsEightBytes,xZero);
    xProduct = _mm_madd_epi16(xImageAsWords, xTemplateAsWords);
    xCrossSums = _mm_add_epi32(xProduct, xCrossSums);
    xImageAsEightBytes=_mm_loadl_epi64((__m128i*) imagepointer);
    imagepointer += imagepointerincrement;
    xImageAsWords = _mm_unpacklo_epi8(xImageAsEightBytes,xZero);
    xImageSums = _mm_adds_epu16(xImageAsWords,xImageSums);
    xProduct = _mm_madd_epi16(xImageAsWords, xImageAsWords);
    xImageSqSums = _mm_add_epi32(xProduct, xImageSqSums);
    xTemplateAsWords = _mm_unpackhi_epi8(xTemplateAsEightBytes,xZero);
    xProduct = _mm_madd_epi16(xImageAsWords, xTemplateAsWords);
    xCrossSums = _mm_add_epi32(xProduct, xCrossSums);

    xImageAsEightBytes=_mm_loadl_epi64((__m128i*) imagepointer);
    imagepointer += imagepointerincrement;
    xImageAsWords = _mm_unpacklo_epi8(xImageAsEightBytes,xZero);
    xImageSums = _mm_adds_epu16(xImageAsWords,xImageSums);
    xProduct = _mm_madd_epi16(xImageAsWords, xImageAsWords);
    xImageSqSums = _mm_add_epi32(xProduct, xImageSqSums);
    xTemplateAsEightBytes=_mm_load_si128((__m128i*) templatepointer);
    templatepointer += 16;
    xTemplateAsWords = _mm_unpacklo_epi8(xTemplateAsEightBytes,xZero);
    xProduct = _mm_madd_epi16(xImageAsWords, xTemplateAsWords);
    xCrossSums = _mm_add_epi32(xProduct, xCrossSums);
    xImageAsEightBytes=_mm_loadl_epi64((__m128i*) imagepointer);
    xImageAsWords = _mm_unpacklo_epi8(xImageAsEightBytes,xZero);
    xImageSums = _mm_adds_epu16(xImageAsWords,xImageSums);
    xProduct = _mm_madd_epi16(xImageAsWords, xImageAsWords);
    xImageSqSums = _mm_add_epi32(xProduct, xImageSqSums);
    xTemplateAsWords = _mm_unpackhi_epi8(xTemplateAsEightBytes,xZero);
    xProduct = _mm_madd_epi16(xImageAsWords, xTemplateAsWords);
    xCrossSums = _mm_add_epi32(xProduct, xCrossSums);

    nImageSum = SumXMM_16(xImageSums);
    nCrossSum = SumXMM_32(xCrossSums);
    nImageSumSq = SumXMM_32(xImageSqSums);
  }
  else
#endif 
  {
    for(int nRow = 0; nRow < mnPatchSize; nRow++)
    {
      imagepointer = &im[irImgBase + ImageRef(0,nRow)];
      templatepointer = &mimTemplate[ImageRef(0,nRow)];
      for(int nCol = 0; nCol < mnPatchSize; nCol++)
      {
        int n = imagepointer[nCol];
        nImageSum += n;
        nImageSumSq += n*n;
        nCrossSum += n * templatepointer[nCol];
      };
    }
  };

  int SA = mnTemplateSum;
  int SB = nImageSum;

  int N = mnPatchSize * mnPatchSize;
  return ((2*SA*SB - SA*SA - SB*SB)/N + nImageSumSq + mnTemplateSumSq - 2*nCrossSum);
}