QGIS/plugins/georeferencer/qgsleastsquares.cpp

#include <cmath>
#include <stdexcept>

#include <gsl/gsl_linalg.h>

#include "qgsleastsquares.h"


void QgsLeastSquares::linear(std::vector<QgsPoint> mapCoords, 
			     std::vector<QgsPoint> pixelCoords,
			     QgsPoint& origin, double& pixelSize) {
  int n = mapCoords.size();
  if (n < 2) {
    throw std::domain_error("Fit to a linear transform requires at "
			    "least 2 points.");
  }

  double sumPx(0), sumPy(0), sumPx2(0), sumPy2(0), sumPxMx(0), sumPyMy(0),
    sumMx(0), sumMy(0);
  for (int i = 0; i < n; ++i) {
    sumPx += pixelCoords[i].x();
    sumPy += pixelCoords[i].y();
    sumPx2 += std::pow(pixelCoords[i].x(), 2);
    sumPy2 += std::pow(pixelCoords[i].y(), 2);
    sumPxMx += pixelCoords[i].x() * mapCoords[i].x();
    sumPyMy += pixelCoords[i].y() * mapCoords[i].y();
    sumMx += mapCoords[i].x();
    sumMy += mapCoords[i].y();
  }
  
  double deltaX = n * sumPx2 - std::pow(sumPx, 2);
  double deltaY = n * sumPy2 - std::pow(sumPy, 2);
  
  double aX = (sumPx2 * sumMx - sumPx * sumPxMx) / deltaX;
  double aY = (sumPy2 * sumMy - sumPy * sumPyMy) / deltaY;
  double bX = (n * sumPxMx - sumPx * sumMx) / deltaX;
  double bY = (n * sumPyMy - sumPy * sumMy) / deltaY;
  
  origin.setX(aX);
  origin.setY(aY);
  pixelSize = (std::abs(bX) + std::abs(bY)) / 2;
}

  
void QgsLeastSquares::helmert(std::vector<QgsPoint> mapCoords, 
			      std::vector<QgsPoint> pixelCoords,
			      QgsPoint& origin, double& pixelSize, 
			      double& rotation) {
  int n = mapCoords.size();
  if (n < 2) {
    throw std::domain_error("Fit to a Helmert transform requires at "
			    "least 2 points.");
  }
  
  double A = 0, B = 0, C = 0, D = 0, E = 0, F = 0, G = 0, H = 0, I = 0, J = 0;
  for (int i = 0; i < n; ++i) {
    A += pixelCoords[i].x();
    B += pixelCoords[i].y();
    C += mapCoords[i].x();
    D += mapCoords[i].y();
    E += mapCoords[i].x() * pixelCoords[i].x();
    F += mapCoords[i].y() * pixelCoords[i].y();
    G += std::pow(pixelCoords[i].x(), 2);
    H += std::pow(pixelCoords[i].y(), 2);
    I += mapCoords[i].x() * pixelCoords[i].y();
    J += pixelCoords[i].x() * mapCoords[i].y();
  }
  
  /* The least squares fit for the parameters { a, b, x0, y0 } is the solution
     to the matrix equation Mx = b, where M and b is given below. I *think*
     that this is correct but I derived it myself late at night. Look at 
     helmert.jpg if you suspect bugs. */
  
  double MData[] = { A,   -B,    n,    0,
		     B,    A,    0,    n,
		     G+H,  0,    A,    B,		     
		     0,    G+H, -B,    A };

  double bData[] = { C,    D,    E+F,  J-I };
  
  // we want to solve the equation M*x = b, where x = [a b x0 y0]
  gsl_matrix_view M = gsl_matrix_view_array(MData, 4, 4);
  gsl_vector_view b = gsl_vector_view_array(bData, 4);
  gsl_vector* x = gsl_vector_alloc(4);
  gsl_permutation* p = gsl_permutation_alloc(4);
  int s;
  gsl_linalg_LU_decomp(&M.matrix, p, &s);
  gsl_linalg_LU_solve(&M.matrix, p, &b.vector, x);
  gsl_permutation_free(p);
  
  origin.setX(gsl_vector_get(x, 2));
  origin.setY(gsl_vector_get(x, 3));
  pixelSize = std::sqrt(std::pow(gsl_vector_get(x, 0), 2) +
			std::pow(gsl_vector_get(x, 1), 2));
  rotation = std::atan2(gsl_vector_get(x, 1), gsl_vector_get(x, 0));    
}


void QgsLeastSquares::affine(std::vector<QgsPoint> mapCoords,
			     std::vector<QgsPoint> pixelCoords) {
  int n = mapCoords.size();
  if (n < 4) {
    throw std::domain_error("Fit to an affine transform requires at "
			    "least 4 points.");
  }
  
  double A = 0, B = 0, C = 0, D = 0, E = 0, F = 0, 
    G = 0, H = 0, I = 0, J = 0, K = 0;
  for (int i = 0; i < n; ++i) {
    A += pixelCoords[i].x();
    B += pixelCoords[i].y();
    C += mapCoords[i].x();
    D += mapCoords[i].y();
    E += std::pow(pixelCoords[i].x(), 2);
    F += std::pow(pixelCoords[i].y(), 2);
    G += pixelCoords[i].x() * pixelCoords[i].y();
    H += pixelCoords[i].x() * mapCoords[i].x();
    I += pixelCoords[i].y() * mapCoords[i].y();
    J += pixelCoords[i].x() * mapCoords[i].y();
    K += mapCoords[i].x() * pixelCoords[i].y();
  }

  /* The least squares fit for the parameters { a, b, c, d, x0, y0 } is the 
     solution to the matrix equation Mx = b, where M and b is given below. 
     I *think* that this is correct but I derived it myself late at night. 
     Look at affine.jpg if you suspect bugs. */
  
  double MData[] = { A,    B,    0,    0,    n,    0,
		     0,    0,    A,    B,    0,    n,
		     E,    G,    0,    0,    A,    0,
		     G,    F,    0,    0,    B,    0,
		     0,    0,    E,    G,    0,    A,
		     0,    0,    G,    F,    0,    B };

  double bData[] = { C,    D,    H,    K,    J,    I };
  
  // we want to solve the equation M*x = b, where x = [a b c d x0 y0]
  gsl_matrix_view M = gsl_matrix_view_array(MData, 6, 6);
  gsl_vector_view b = gsl_vector_view_array(bData, 6);
  gsl_vector* x = gsl_vector_alloc(6);
  gsl_permutation* p = gsl_permutation_alloc(6);
  int s;
  gsl_linalg_LU_decomp(&M.matrix, p, &s);
  gsl_linalg_LU_solve(&M.matrix, p, &b.vector, x);
  gsl_permutation_free(p);

}