/** Kullback-Leibner divergence */
double getKullbackLeibnerDivergence(MultidimArray<Complex >& Fimg,
MultidimArray<Complex >& Fref, MultidimArray<double>& sigma2,
MultidimArray<double>& p_i, MultidimArray<double>& q_i, int highshell, int lowshell)
{
// First check dimensions are OK
if (!Fimg.sameShape(Fref))
{
REPORT_ERROR("getKullbackLeibnerDivergence ERROR: Fimg and Fref are not of the same shape.");
}
if (highshell < 0)
{
highshell = XSIZE(Fimg) - 1;
}
if (lowshell < 0)
{
lowshell = 0;
}
if (highshell > XSIZE(sigma2))
{
REPORT_ERROR("getKullbackLeibnerDivergence ERROR: highshell is larger than size of sigma2 array.");
}
if (highshell < lowshell)
{
REPORT_ERROR("getKullbackLeibnerDivergence ERROR: highshell is smaller than lowshell.");
}
// Initialize the histogram
MultidimArray<int> histogram;
int histogram_size = 101;
int histogram_origin = histogram_size / 2;
double sigma_max = 10.;
double histogram_factor = histogram_origin / sigma_max;
histogram.initZeros(histogram_size);
// This way this will work in both 2D and 3D
FOR_ALL_ELEMENTS_IN_FFTW_TRANSFORM(Fimg)
{
int ires = ROUND(sqrt(kp * kp + ip * ip + jp * jp));
if (ires >= lowshell && ires <= highshell)
{
// Use FT of masked image for noise estimation!
double diff_real = (DIRECT_A3D_ELEM(Fref, k, i, j)).real - (DIRECT_A3D_ELEM(Fimg, k, i, j)).real;
double diff_imag = (DIRECT_A3D_ELEM(Fref, k, i, j)).imag - (DIRECT_A3D_ELEM(Fimg, k, i, j)).imag;
double sigma = sqrt(DIRECT_A1D_ELEM(sigma2, ires));
// Divide by standard deviation to normalise all the difference
diff_real /= sigma;
diff_imag /= sigma;
// Histogram runs from -10 sigma to +10 sigma
diff_real += sigma_max;
diff_imag += sigma_max;
// Make histogram on-the-fly;
// Real part
int ihis = ROUND(diff_real * histogram_factor);
if (ihis < 0)
{
ihis = 0;
}
else if (ihis >= histogram_size)
{
ihis = histogram_size - 1;
}
histogram(ihis)++;
// Imaginary part
ihis = ROUND(diff_imag * histogram_factor);
if (ihis < 0)
{
ihis = 0;
}
else if (ihis > histogram_size)
{
ihis = histogram_size;
}
histogram(ihis)++;
}
}
// Normalise the histogram and the discretised analytical Gaussian
double norm = (double)histogram.sum();
double gaussnorm = 0.;
for (int i = 0; i < histogram_size; i++)
{
double x = (double)i / histogram_factor;
gaussnorm += gaussian1D(x - sigma_max, 1. , 0.);
}
// Now calculate the actual Kullback-Leibner divergence
double kl_divergence = 0.;
p_i.resize(histogram_size);
q_i.resize(histogram_size);
for (int i = 0; i < histogram_size; i++)
{
// Data distribution
p_i(i) = (double)histogram(i) / norm;
// Theoretical distribution
double x = (double)i / histogram_factor;
q_i(i) = gaussian1D(x - sigma_max, 1. , 0.) / gaussnorm;
if (p_i(i) > 0.)
{
kl_divergence += p_i(i) * log(p_i(i) / q_i(i));
}
}
kl_divergence /= (double)histogram_size;
return kl_divergence;
}
void PolyZernikes::fit(const Matrix1D<int> & coef, MultidimArray<double> & im, MultidimArray<double> &weight,
MultidimArray<bool> & ROI, int verbose)
{
this->create(coef);
size_t xdim = XSIZE(im);
size_t ydim = YSIZE(im);
//int numZer = (size_t)coef.sum();
int numZer = (size_t)coef.sum();
//Actually polOrder corresponds to the polynomial order +1
int polOrder=(int)ZERNIKE_ORDER(coef.size());
im.setXmippOrigin();
Matrix2D<double> polValue(polOrder,polOrder);
//First argument means number of images
//Second argument means number of pixels
WeightedLeastSquaresHelper weightedLeastSquaresHelper;
Matrix2D<double>& zerMat=weightedLeastSquaresHelper.A;
zerMat.resizeNoCopy((size_t)ROI.sum(), numZer);
double iMaxDim2 = 2./std::max(xdim,ydim);
size_t pixel_idx=0;
weightedLeastSquaresHelper.b.resizeNoCopy((size_t)ROI.sum());
weightedLeastSquaresHelper.w.resizeNoCopy(weightedLeastSquaresHelper.b);
FOR_ALL_ELEMENTS_IN_ARRAY2D(im)
{
if ( (A2D_ELEM(ROI,i,j)))
{
//For one i we swap the different j
double y=i*iMaxDim2;
double x=j*iMaxDim2;
//polValue = [ 0 y y2 y3 ...
// x xy xy2 xy3 ...
// x2 x2y x2y2 x2y3 ]
//dMij(polValue,py,px) py es fila, px es columna
for (int py = 0; py < polOrder; ++py)
{
double ypy=std::pow(y,py);
for (int px = 0; px < polOrder; ++px)
dMij(polValue,px,py) = ypy*std::pow(x,px);
}
Matrix2D<int> *fMat;
//We generate the representation of the Zernike polynomials
for (int k=0; k < numZer; ++k)
{
fMat = &fMatV[k];
if (fMat == NULL)
continue;
double temp = 0;
for (size_t px = 0; px < (*fMat).Xdim(); ++px)
for (size_t py = 0; py < (*fMat).Ydim(); ++py)
temp += dMij(*fMat,py,px)*dMij(polValue,py,px);
dMij(zerMat,pixel_idx,k) = temp;
}
VEC_ELEM(weightedLeastSquaresHelper.b,pixel_idx)=A2D_ELEM(im,i,j);
VEC_ELEM(weightedLeastSquaresHelper.w,pixel_idx)=std::abs(A2D_ELEM(weight,i,j));
++pixel_idx;
}
}
Matrix1D<double> zernikeCoefficients;
weightedLeastSquares(weightedLeastSquaresHelper, zernikeCoefficients);
fittedCoeffs = zernikeCoefficients;
// Pointer to the image to be fitted
MultidimArray<double> reconstructed;
reconstructed.resizeNoCopy(im);
pixel_idx=0;
FOR_ALL_ELEMENTS_IN_ARRAY2D(im)
if (A2D_ELEM(ROI,i,j))
{
double temp=0;
for (int k=0; k < numZer; ++k)
temp+=dMij(zerMat,pixel_idx,k)*VEC_ELEM(fittedCoeffs,k);
A2D_ELEM(reconstructed,i,j)=temp;
if ( fabs(A2D_ELEM(reconstructed,i,j)-A2D_ELEM(im,i,j)) > PI)
A2D_ELEM(ROI,i,j) = false;
++pixel_idx;
}
pixel_idx=0;
if (verbose > 0)
{
Image<double> save;
save()=reconstructed;
save.write("reconstructedZernikes.xmp");
ROI.write("ROI.txt");
}
}
