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Zernike.cpp
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Zernike.cpp
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//============================================================================
// Name : Zernike.cpp
// Author : Dailos
// Version :
// Copyright : Your copyright notice
// Description : Hello World in C++, Ansi-style
//============================================================================
#include "Zernike.h"
#include "ToolBox.h"
#include "FITS.h"
#include <iostream>
#include <random>
#include "opencv2/opencv.hpp"
#include "CustomException.h"
#include "OpticalSetup.h"
//Rename as Representation, Rprsnttn, DictionaryBase, Zernike
using namespace std;
const double PI = 3.141592653589793238462643383279502884197169399375105;
Zernike::Zernike(const double& r_c, const int& nph, const int& z_max) :
radious_px_(r_c), side_px_(nph), base_(z_max)
{
cv::Mat c_mask;
circular_mask(radious_px_, side_px_, c_mask);
cv::Scalar c_area = cv::sum(c_mask);
//cv::divide(c_mask, c_area, c_mask);
for(unsigned int j=0;j<z_max;++j)
{
if(false)
{
polynomial(radious_px_, side_px_, j + 1, base_.at(j));
cv::multiply(base_.at(j), c_mask, base_.at(j));
//Be aware that RMS value should be normalized to one!!
double l2 = cv::norm(base_.at(j), cv::NORM_L2);
cv::multiply(base_.at(j), l2/std::sqrt(c_area.val[0]), base_.at(j));
}
else
{
base_.at(j) = phaseMapZernike(j + 1, side_px_, radious_px_).clone();
}
}
}
//The default constructor of the Zernike class
Zernike::Zernike()
{
}
//analysis operator: action analyse; takes the phase signal and gives the sequence of coefficients (representation realm)
//from phase signal space to zernike representation
void Zernike::analyse(const cv::Mat& sig, cv::Mat& z_coeffs)
{
z_coeffs.release();
for(cv::Mat z_j : base_)
{
double l2 = cv::norm(z_j, cv::NORM_L2);
double inner_prod = z_j.dot(sig)/(l2*l2);
z_coeffs.push_back( inner_prod );
}
}
void Zernike::synthesize(const cv::Mat& z_coeffs, cv::Mat& sig)
{
if(z_coeffs.cols != 1) throw CustomException("Coeffs must be single column matrix.");
if(z_coeffs.rows > base_.size()) throw CustomException("Number of coeffs greater than zernike base.");
sig = cv::Mat::zeros(side_px_, side_px_, cv::DataType<double>::type);
auto coeffs_it = z_coeffs.begin<double>();
for(cv::Mat z_j : base_)
{
if(coeffs_it == z_coeffs.end<double>()) break;
if(*coeffs_it != 0.0) sig += (*coeffs_it) * z_j;
coeffs_it++;
}
}
//synthesis operator: action synthesize; takes the sequence of coefficients (representation realm) and gives the phase signal
//Rename as zernike_synthesis: from zernike representation to phase signal space
cv::Mat Zernike::phaseMapZernikeSum(const unsigned int& sideLength, const double& radiousLength, const cv::Mat& coeffs)
{
if(coeffs.cols == 1 && coeffs.type() == cv::DataType<double>::type)
{
cv::Mat thePhaseMapSum = cv::Mat::zeros(sideLength, sideLength, cv::DataType<double>::type);
for(auto cIt = coeffs.begin<double>(), cEnd = coeffs.end<double>(); cIt != cEnd; ++cIt)
{
if((*cIt) != 0.0)
{
//cv::accumulate((*cIt) * phaseMapZernike(std::distance(coeffs.begin<double>(), cIt) + 1, sideLength, radiousLength), thePhaseMapSum);
thePhaseMapSum += (*cIt) * phaseMapZernike(std::distance(coeffs.begin<double>(), cIt) + 1, sideLength, radiousLength);
}
}
return thePhaseMapSum;
}
else
{
throw CustomException("Zernike: coeffs is single column vector of doubles.");
}
}
void Zernike::zernike_mn(const int& j,int &m,int &n) // j=1...
{
n = 0;
int len = 1;
for(int i = 1;len<j;++i) len += (n=i)+1;
int dl = n + 1 - len + j;
m = 2 * ((dl+(n%2))/2)+!(n%2)-1;
}
void Zernike::polynomial(const double& r_c, const int& nph, const int& j, cv::Mat& z_j)
{
double angle = 0.0; //The angle value is set to zero by default. Use it when needed
auto ft2dim = [](const int& x1l, const int& x1h, const int& x2l, const int& x2h) -> double **
{
int nx1=x1h-x1l+1,nx2=x2h-x2l+1;
double **p;
p=new double* [nx1] - x1l;
p[x1l] = new double [nx1*nx2] - x2l;
for(int x1=x1l+1;x1<=x1h;++x1) p[x1]=p[x1-1]+nx2;
return p;
};
auto del_ft2dim = [](double **p,const int& x1l, const int& x1h, const int& x2l, const int& x2h)-> void
{
delete[] (p[x1l]+x2l);
delete[] (p+x1l);
};
auto RC = [](const int& m, const int& n) -> double *
{
int nmm=(n-m)/2,npm=(n+m)/2;
int nmax=std::max(npm,n);
double *f=new double [nmax+1];
f[0]=1.0;
for(int i=1;i<=nmax;++i) f[i]=(double)i*f[i-1];
double *res=new double [nmm+1];
for(int s=0,pm=-1;s<=nmm;++s)
res[s]=(double)((pm*=-1)*f[n-s])/(f[s]*f[npm-s]*f[nmm-s]);
delete[] f;
return res;
};
int xo=1+nph/2,yo=1+nph/2;
//Release array if necesary
z_j.create(nph, nph, cv::DataType<double>::type);
double* z = (double*)z_j.data;
if(j==1)
{
for(int x=1;x<=nph;++x)
for(int y=1;y<=nph;++y) z[(x-1)*nph + (y-1)] = 1.0;
}
else
{ // j>1
int m,n;
zernike_mn(j,m,n);
double *rc=RC(m,n);
double **r=ft2dim(1,nph,1,nph);
double **rs=ft2dim(1,nph,1,nph);
for(int x=1;x<=nph;++x) // s=0
{
for(int y=1;y<=nph;++y)
{
double rr=std::sqrt((double)std::pow(x-xo, 2.0)+(double)std::pow(y-yo, 2.0))/r_c;
rs[x][y]=rr*rr;
r[x][y]=pow(rr,n);
z[(x-1)*nph + (y-1)]=r[x][y]*rc[0];
}
}
rs[xo][yo]=1.0; // avoid divide by 0
for(int s=1;s<=(n-m)/2;++s)
{
for(int x=1;x<=nph;++x)
{
for(int y=1;y<=nph;++y)
{
z[(x-1)*nph + (y-1)]+=(r[x][y]/=rs[x][y])*rc[s];
}
}
if(!(n-2*s)) z[(xo-1)*nph + (yo-1)]+=rc[s]; // dividing 0 by 1 will never give 1...
}
del_ft2dim(rs,1,nph,1,nph);
del_ft2dim(r,1,nph,1,nph);
if(m)
{ // m!=0
double sf=std::sqrt((double)(2.0*(n+1.0))); //CHANGE!
if(j%2)
{ // odd
for(int x=1;x<=nph;++x)
{
for(int y=1;y<=nph;++y) z[(x-1)*nph + (y-1)]*=sf*std::sin(((double)m)*(std::atan2((double)(y-yo),(double)(x-xo))+angle));
}
}
else // even
{
for(int x=1;x<=nph;++x)
{
for(int y=1;y<=nph;++y) z[(x-1)*nph + (y-1)]*=sf*std::cos(((double)m)*(std::atan2((double)(y-yo),(double)(x-xo))+angle));
}
}
}
else
{ // m==0
double sf=std::sqrt((double)(n+1.0)); //CHANGE!
for(int x=1;x<=nph;++x)
{
for(int y=1;y<=nph;++y) z[(x-1)*nph + (y-1)]*=sf;
}
}
delete[] rc;
}
// return cv::Mat(cv::Size(nph, nph), cv::DataType<double>::type, &z[1][1]); //c-like array starts at position (1,1)
}
double Zernike::zernike_covar(int i,int j)
{
auto gammln = [](double xx, double &sign)-> double
{
static double cof[6]={ 7.618009172947146E+01,-8.650532032941677E+01, 2.401409824083091E+01,
-1.231739572450155E+00, 1.208650973866179E-03,-5.395239384953000E-06};
/*
double x=xx;
double y=x;
double tmp=x+5.5;
tmp -= (x+0.5)*log(tmp);
double ser=1.000000000190015;
for (int j=0;j<=5;++j) ser+=cof[j]/++y;
return -tmp+log(2.5066282746310005*ser/x);
*/
double yy = xx;
double res = 1.000000000190015;
while(yy < 1.0)
{
res *= yy;
yy += 1.0;
}
sign = (res >= 0) ? 1.0 : -1.0;
yy -= 1.0;
double tmp = yy + 5.5;
tmp -= (yy + 0.5) * std::log(tmp);
double ser = 1.000000000190015;
for (int jj = 0; jj <= 5; ++jj) ser += cof[jj] / ++yy;
return -tmp + std::log(2.5066282746310005 * ser) - std::log(std::fabs(res));
};
if((i<2)||(j<2)) return 0.0;
int m,n,o,p;
zernike_mn(i,m,n);
zernike_mn(j,o,p);
if(m!=o) return 0.0;
if(m) if((i+j)%2) return 0.0;
// ; Now deal with the numerical terms: Dai
double tmp;
double k = std::pow(4.8 * std::exp(gammln(6.0/5.0,tmp)),5.0/6.0) * std::exp(gammln(14.0/3.0,tmp)+2.0*gammln(11.0/6.0,tmp))/(std::pow(2.0,(8.0/3.0))*PI);
k *= std::pow(-1.0,(double)((n+p-2*m)/2)) * std::sqrt((double)((n+1)*(p+1)));
double g1_sgn,g2_sgn,g3_sgn,g4_sgn;
double g1 = gammln(((double)(n+p)- 5.0/3.0)/2.0,g1_sgn);
double g2 = gammln(((double)(n-p)+17.0/3.0)/2.0,g2_sgn);
double g3 = gammln(((double)(p-n)+17.0/3.0)/2.0,g3_sgn);
double g4 = gammln(((double)(n+p)+23.0/3.0)/2.0,g4_sgn);
return k * std::exp(g1 - g2 - g3 - g4) * g1_sgn * g2_sgn * g3_sgn * g4_sgn;
}
void Zernike::circular_mask(const double& r_c, const int& nph, cv::Mat& c_mask)
{
c_mask.create(nph, nph, cv::DataType<double>::type);
double* z = (double*)c_mask.data;
//Circular mask: zero-valued outside the cicle, one-valued inside,
//the edge pixels has values between 0 and 1 depending on how far lies the center of the pixel from the edge
int xo=1+nph/2,yo=1+nph/2;
double rcs=r_c*r_c,dx=0.5/r_c,dy=0.5/r_c;
for(int x=1;x<=nph;++x){
double xl=fabs((double)(x-xo))/r_c-dx,xh=fabs((double)(x-xo))/r_c+dx;
double xhs=std::pow(xh,2.0);
for(int y=1;y<=nph;++y){
double yl=fabs((double)(y-yo))/r_c-dy,yh=fabs((double)(y-yo))/r_c+dy;
double yhs=std::pow(yh,2.0);
double rsl=std::pow(xl,2.0)+std::pow(yl,2.0),rsh=xhs+yhs;
int ti=(rsl<rcs)+(rsh<rcs);
if(rsl<=1.0)
{ // inside pixel
if(rsh<1.0) // full pixel
{
z[(x-1)*nph + (y-1)] = 1.0;
}
else
{ // partial pixel
double x2 = std::sqrt(max(1.0-yhs,(double)0.0));
double y3 = std::sqrt(max(1.0-xhs,(double)0.0));
double f = (xh>yh)?(yh-yl)*(std::min(xh,std::max(xl,x2))-xl)/(4*dx*dy):
(xh-xl)*(std::min(yh,std::max(yl,y3))-yl)/(4*dx*dy);
z[(x-1)*nph + (y-1)] = f;
}
}
else z[(x-1)*nph + (y-1)] = 0.0; // outside pixel
}
}
}
void Zernike::circular_mask(cv::Mat& c_mask)
{
double r_c(radious_px_);
int nph(side_px_);
c_mask.create(nph, nph, cv::DataType<double>::type);
double* z = (double*)c_mask.data;
//Circular mask: zero-valued outside the cicle, one-valued inside,
//the edge pixels has values between 0 and 1 depending on how far lies the center of the pixel from the edge
int xo=1+nph/2,yo=1+nph/2;
double rcs=r_c*r_c,dx=0.5/r_c,dy=0.5/r_c;
for(int x=1;x<=nph;++x){
double xl=fabs((double)(x-xo))/r_c-dx,xh=fabs((double)(x-xo))/r_c+dx;
double xhs=std::pow(xh,2.0);
for(int y=1;y<=nph;++y){
double yl=fabs((double)(y-yo))/r_c-dy,yh=fabs((double)(y-yo))/r_c+dy;
double yhs=std::pow(yh,2.0);
double rsl=std::pow(xl,2.0)+std::pow(yl,2.0),rsh=xhs+yhs;
int ti=(rsl<rcs)+(rsh<rcs);
if(rsl<=1.0)
{ // inside pixel
if(rsh<1.0) // full pixel
{
z[(x-1)*nph + (y-1)] = 1.0;
}
else
{ // partial pixel
double x2 = std::sqrt(max(1.0-yhs,(double)0.0));
double y3 = std::sqrt(max(1.0-xhs,(double)0.0));
double f = (xh>yh)?(yh-yl)*(std::min(xh,std::max(xl,x2))-xl)/(4*dx*dy):
(xh-xl)*(std::min(yh,std::max(yl,y3))-yl)/(4*dx*dy);
z[(x-1)*nph + (y-1)] = f;
}
}
else z[(x-1)*nph + (y-1)] = 0.0; // outside pixel
}
}
}
cv::Mat Zernike::phaseMapZernike(const unsigned int& j, const unsigned int& sideLength, const double& radiousLength, const bool& unit_rms, const bool& c_mask)
{
//Find the rms for this mode:
auto rms_t = [](const cv::Mat& zf, const cv::Mat& mask) -> double
{
cv::Mat zf2, cmzf2;
cv::multiply(zf, zf, zf2);
cv::multiply(mask, zf2, cmzf2);
cv::Scalar rms2 = cv::sum(cmzf2) / cv::sum(mask);
return std::sqrt(rms2.val[0]);
};
cv::Mat zz;
polynomial(radiousLength, sideLength, j, zz);
cv::Mat pu;
circular_mask(radiousLength, sideLength, pu);
cv::Mat zernike_mode;
if(c_mask) cv::multiply(zz, pu, zernike_mode);
else zernike_mode = zz.clone();
double rms_d = rms(zz, pu);
if(rms_d != rms_t(zz,pu)) throw CustomException("Rms problem in phaseMapZernike.");
if(unit_rms) zernike_mode = zernike_mode/rms_d;
return zernike_mode/10.0; //divide by 10.0 in order to make sparse recovery works
}