I'm working with OpenCV 5 point Essential Matrix Computation Algorithm and I'm facing Numerical Instability when working with these 2 platforms (Windows Visual Studio and Linux Gcc compiler).
The problem was caused by this function solvePoly and here is a sample code to reproduce the Error with same inputs in two different platforms.
The following code will produce two different outputs in Windows msvc and Linux GCC and here is a Sample Output.
#include <iostream>
#include "opencv2/opencv.hpp"
#include "opencv2/opencv_modules.hpp"
#include <iostream>
#include <fstream>
#include <stdlib.h>
using namespace std;
using namespace cv;
int main(int, char**)
{
double b[3 * 13]= { 43.62899215341317, -142.8659619253204, 182.4526535510934, -62.12438333428298, -9.66204383178342, 76.3870398608554, -116.055365497144, 40.87998289431373, -42.59799056519181, 254.9402120596346, -504.9633997399467, 384.3746161586831, -95.89887859435427,
77.7070672570582, -245.6776216042046, 302.6478282208725, -89.53722757851534, -18.16867987414801, 137.6158773648859, -198.6262187902296, 60.54628991983429, -77.94581368911055, 454.935337437791, -873.484503220278, 629.3372557512528, -141.5849526705521,
59.937068130234, -203.3296090558193, 269.1321546914465, -102.6876384579035, -12.58131418572418, 103.8840936956255, -166.5017038614965, 66.32614093605801, -57.22582537611544, 350.6649163333698, -716.5726353181753, 574.4994715331657, -155.9118381651257 };
Mat B(3, 13, CV_64F, b);
double c[11];
Mat coeffs(1, 11, CV_64F, c);
c[10] = (b[0] * b[17] * b[34] + b[26] * b[4] * b[21] - b[26] * b[17] * b[8] - b[13] * b[4] * b[34] - b[0] * b[21] * b[30] + b[13] * b[30] * b[8]);
c[9] = (b[26] * b[4] * b[22] + b[14] * b[30] * b[8] + b[13] * b[31] * b[8] + b[1] * b[17] * b[34] - b[13] * b[5] * b[34] + b[26] * b[5] * b[21] - b[0] * b[21] * b[31] - b[26] * b[17] * b[9] - b[1] * b[21] * b[30] + b[27] * b[4] * b[21] + b[0] * b[17] * b[35] - b[0] * b[22] * b[30] + b[13] * b[30] * b[9] + b[0] * b[18] * b[34] - b[27] * b[17] * b[8] - b[14] * b[4] * b[34] - b[13] * b[4] * b[35] - b[26] * b[18] * b[8]);
c[8] = (b[14] * b[30] * b[9] + b[14] * b[31] * b[8] + b[13] * b[31] * b[9] - b[13] * b[4] * b[36] - b[13] * b[5] * b[35] + b[15] * b[30] * b[8] - b[13] * b[6] * b[34] + b[13] * b[30] * b[10] + b[13] * b[32] * b[8] - b[14] * b[4] * b[35] - b[14] * b[5] * b[34] + b[26] * b[4] * b[23] + b[26] * b[5] * b[22] + b[26] * b[6] * b[21] - b[26] * b[17] * b[10] - b[15] * b[4] * b[34] - b[26] * b[18] * b[9] - b[26] * b[19] * b[8] + b[27] * b[4] * b[22] + b[27] * b[5] * b[21] - b[27] * b[17] * b[9] - b[27] * b[18] * b[8] - b[1] * b[21] * b[31] - b[0] * b[23] * b[30] - b[0] * b[21] * b[32] + b[28] * b[4] * b[21] - b[28] * b[17] * b[8] + b[2] * b[17] * b[34] + b[0] * b[18] * b[35] - b[0] * b[22] * b[31] + b[0] * b[17] * b[36] + b[0] * b[19] * b[34] - b[1] * b[22] * b[30] + b[1] * b[18] * b[34] + b[1] * b[17] * b[35] - b[2] * b[21] * b[30]);
c[7] = (b[14] * b[30] * b[10] + b[14] * b[32] * b[8] - b[3] * b[21] * b[30] + b[3] * b[17] * b[34] + b[13] * b[32] * b[9] + b[13] * b[33] * b[8] - b[13] * b[4] * b[37] - b[13] * b[5] * b[36] + b[15] * b[30] * b[9] + b[15] * b[31] * b[8] - b[16] * b[4] * b[34] - b[13] * b[6] * b[35] - b[13] * b[7] * b[34] + b[13] * b[30] * b[11] + b[13] * b[31] * b[10] + b[14] * b[31] * b[9] - b[14] * b[4] * b[36] - b[14] * b[5] * b[35] - b[14] * b[6] * b[34] + b[16] * b[30] * b[8] - b[26] * b[20] * b[8] + b[26] * b[4] * b[24] + b[26] * b[5] * b[23] + b[26] * b[6] * b[22] + b[26] * b[7] * b[21] - b[26] * b[17] * b[11] - b[15] * b[4] * b[35] - b[15] * b[5] * b[34] - b[26] * b[18] * b[10] - b[26] * b[19] * b[9] + b[27] * b[4] * b[23] + b[27] * b[5] * b[22] + b[27] * b[6] * b[21] - b[27] * b[17] * b[10] - b[27] * b[18] * b[9] - b[27] * b[19] * b[8] + b[0] * b[17] * b[37] - b[0] * b[23] * b[31] - b[0] * b[24] * b[30] - b[0] * b[21] * b[33] - b[29] * b[17] * b[8] + b[28] * b[4] * b[22] + b[28] * b[5] * b[21] - b[28] * b[17] * b[9] - b[28] * b[18] * b[8] + b[29] * b[4] * b[21] + b[1] * b[19] * b[34] - b[2] * b[21] * b[31] + b[0] * b[20] * b[34] + b[0] * b[19] * b[35] + b[0] * b[18] * b[36] - b[0] * b[22] * b[32] - b[1] * b[23] * b[30] - b[1] * b[21] * b[32] + b[1] * b[18] * b[35] - b[1] * b[22] * b[31] - b[2] * b[22] * b[30] + b[2] * b[17] * b[35] + b[1] * b[17] * b[36] + b[2] * b[18] * b[34]);
c[6] = (-b[14] * b[6] * b[35] - b[14] * b[7] * b[34] - b[3] * b[22] * b[30] - b[3] * b[21] * b[31] + b[3] * b[17] * b[35] + b[3] * b[18] * b[34] + b[13] * b[32] * b[10] + b[13] * b[33] * b[9] - b[13] * b[4] * b[38] - b[13] * b[5] * b[37] - b[15] * b[6] * b[34] + b[15] * b[30] * b[10] + b[15] * b[32] * b[8] - b[16] * b[4] * b[35] - b[13] * b[6] * b[36] - b[13] * b[7] * b[35] + b[13] * b[31] * b[11] + b[13] * b[30] * b[12] + b[14] * b[32] * b[9] + b[14] * b[33] * b[8] - b[14] * b[4] * b[37] - b[14] * b[5] * b[36] + b[16] * b[30] * b[9] + b[16] * b[31] * b[8] - b[26] * b[20] * b[9] + b[26] * b[4] * b[25] + b[26] * b[5] * b[24] + b[26] * b[6] * b[23] + b[26] * b[7] * b[22] - b[26] * b[17] * b[12] + b[14] * b[30] * b[11] + b[14] * b[31] * b[10] + b[15] * b[31] * b[9] - b[15] * b[4] * b[36] - b[15] * b[5] * b[35] - b[26] * b[18] * b[11] - b[26] * b[19] * b[10] - b[27] * b[20] * b[8] + b[27] * b[4] * b[24] + b[27] * b[5] * b[23] + b[27] * b[6] * b[22] + b[27] * b[7] * b[21] - b[27] * b[17] * b[11] - b[27] * b[18] * b[10] - b[27] * b[19] * b[9] - b[16] * b[5] * b[34] - b[29] * b[17] * b[9] - b[29] * b[18] * b[8] + b[28] * b[4] * b[23] + b[28] * b[5] * b[22] + b[28] * b[6] * b[21] - b[28] * b[17] * b[10] - b[28] * b[18] * b[9] - b[28] * b[19] * b[8] + b[29] * b[4] * b[22] + b[29] * b[5] * b[21] - b[2] * b[23] * b[30] + b[2] * b[18] * b[35] - b[1] * b[22] * b[32] - b[2] * b[21] * b[32] + b[2] * b[19] * b[34] + b[0] * b[19] * b[36] - b[0] * b[22] * b[33] + b[0] * b[20] * b[35] - b[0] * b[23] * b[32] - b[0] * b[25] * b[30] + b[0] * b[17] * b[38] + b[0] * b[18] * b[37] - b[0] * b[24] * b[31] + b[1] * b[17] * b[37] - b[1] * b[23] * b[31] - b[1] * b[24] * b[30] - b[1] * b[21] * b[33] + b[1] * b[20] * b[34] + b[1] * b[19] * b[35] + b[1] * b[18] * b[36] + b[2] * b[17] * b[36] - b[2] * b[22] * b[31]);
c[5] = (-b[14] * b[6] * b[36] - b[14] * b[7] * b[35] + b[14] * b[31] * b[11] - b[3] * b[23] * b[30] - b[3] * b[21] * b[32] + b[3] * b[18] * b[35] - b[3] * b[22] * b[31] + b[3] * b[17] * b[36] + b[3] * b[19] * b[34] + b[13] * b[32] * b[11] + b[13] * b[33] * b[10] - b[13] * b[5] * b[38] - b[15] * b[6] * b[35] - b[15] * b[7] * b[34] + b[15] * b[30] * b[11] + b[15] * b[31] * b[10] + b[16] * b[31] * b[9] - b[13] * b[6] * b[37] - b[13] * b[7] * b[36] + b[13] * b[31] * b[12] + b[14] * b[32] * b[10] + b[14] * b[33] * b[9] - b[14] * b[4] * b[38] - b[14] * b[5] * b[37] - b[16] * b[6] * b[34] + b[16] * b[30] * b[10] + b[16] * b[32] * b[8] - b[26] * b[20] * b[10] + b[26] * b[5] * b[25] + b[26] * b[6] * b[24] + b[26] * b[7] * b[23] + b[14] * b[30] * b[12] + b[15] * b[32] * b[9] + b[15] * b[33] * b[8] - b[15] * b[4] * b[37] - b[15] * b[5] * b[36] + b[29] * b[5] * b[22] + b[29] * b[6] * b[21] - b[26] * b[18] * b[12] - b[26] * b[19] * b[11] - b[27] * b[20] * b[9] + b[27] * b[4] * b[25] + b[27] * b[5] * b[24] + b[27] * b[6] * b[23] + b[27] * b[7] * b[22] - b[27] * b[17] * b[12] - b[27] * b[18] * b[11] - b[27] * b[19] * b[10] - b[28] * b[20] * b[8] - b[16] * b[4] * b[36] - b[16] * b[5] * b[35] - b[29] * b[17] * b[10] - b[29] * b[18] * b[9] - b[29] * b[19] * b[8] + b[28] * b[4] * b[24] + b[28] * b[5] * b[23] + b[28] * b[6] * b[22] + b[28] * b[7] * b[21] - b[28] * b[17] * b[11] - b[28] * b[18] * b[10] - b[28] * b[19] * b[9] + b[29] * b[4] * b[23] - b[2] * b[22] * b[32] - b[2] * b[21] * b[33] - b[1] * b[24] * b[31] + b[0] * b[18] * b[38] - b[0] * b[24] * b[32] + b[0] * b[19] * b[37] + b[0] * b[20] * b[36] - b[0] * b[25] * b[31] - b[0] * b[23] * b[33] + b[1] * b[19] * b[36] - b[1] * b[22] * b[33] + b[1] * b[20] * b[35] + b[2] * b[19] * b[35] - b[2] * b[24] * b[30] - b[2] * b[23] * b[31] + b[2] * b[20] * b[34] + b[2] * b[17] * b[37] - b[1] * b[25] * b[30] + b[1] * b[18] * b[37] + b[1] * b[17] * b[38] - b[1] * b[23] * b[32] + b[2] * b[18] * b[36]);
c[4] = (-b[14] * b[6] * b[37] - b[14] * b[7] * b[36] + b[14] * b[31] * b[12] + b[3] * b[17] * b[37] - b[3] * b[23] * b[31] - b[3] * b[24] * b[30] - b[3] * b[21] * b[33] + b[3] * b[20] * b[34] + b[3] * b[19] * b[35] + b[3] * b[18] * b[36] - b[3] * b[22] * b[32] + b[13] * b[32] * b[12] + b[13] * b[33] * b[11] - b[15] * b[6] * b[36] - b[15] * b[7] * b[35] + b[15] * b[31] * b[11] + b[15] * b[30] * b[12] + b[16] * b[32] * b[9] + b[16] * b[33] * b[8] - b[13] * b[6] * b[38] - b[13] * b[7] * b[37] + b[14] * b[32] * b[11] + b[14] * b[33] * b[10] - b[14] * b[5] * b[38] - b[16] * b[6] * b[35] - b[16] * b[7] * b[34] + b[16] * b[30] * b[11] + b[16] * b[31] * b[10] - b[26] * b[19] * b[12] - b[26] * b[20] * b[11] + b[26] * b[6] * b[25] + b[26] * b[7] * b[24] + b[15] * b[32] * b[10] + b[15] * b[33] * b[9] - b[15] * b[4] * b[38] - b[15] * b[5] * b[37] + b[29] * b[5] * b[23] + b[29] * b[6] * b[22] + b[29] * b[7] * b[21] - b[27] * b[20] * b[10] + b[27] * b[5] * b[25] + b[27] * b[6] * b[24] + b[27] * b[7] * b[23] - b[27] * b[18] * b[12] - b[27] * b[19] * b[11] - b[28] * b[20] * b[9] - b[16] * b[4] * b[37] - b[16] * b[5] * b[36] + b[0] * b[19] * b[38] - b[0] * b[24] * b[33] + b[0] * b[20] * b[37] - b[29] * b[17] * b[11] - b[29] * b[18] * b[10] - b[29] * b[19] * b[9] + b[28] * b[4] * b[25] + b[28] * b[5] * b[24] + b[28] * b[6] * b[23] + b[28] * b[7] * b[22] - b[28] * b[17] * b[12] - b[28] * b[18] * b[11] - b[28] * b[19] * b[10] - b[29] * b[20] * b[8] + b[29] * b[4] * b[24] + b[2] * b[18] * b[37] - b[0] * b[25] * b[32] + b[1] * b[18] * b[38] - b[1] * b[24] * b[32] + b[1] * b[19] * b[37] + b[1] * b[20] * b[36] - b[1] * b[25] * b[31] + b[2] * b[17] * b[38] + b[2] * b[19] * b[36] - b[2] * b[24] * b[31] - b[2] * b[22] * b[33] - b[2] * b[23] * b[32] + b[2] * b[20] * b[35] - b[1] * b[23] * b[33] - b[2] * b[25] * b[30]);
c[3] = (-b[14] * b[6] * b[38] - b[14] * b[7] * b[37] + b[3] * b[19] * b[36] - b[3] * b[22] * b[33] + b[3] * b[20] * b[35] - b[3] * b[23] * b[32] - b[3] * b[25] * b[30] + b[3] * b[17] * b[38] + b[3] * b[18] * b[37] - b[3] * b[24] * b[31] - b[15] * b[6] * b[37] - b[15] * b[7] * b[36] + b[15] * b[31] * b[12] + b[16] * b[32] * b[10] + b[16] * b[33] * b[9] + b[13] * b[33] * b[12] - b[13] * b[7] * b[38] + b[14] * b[32] * b[12] + b[14] * b[33] * b[11] - b[16] * b[6] * b[36] - b[16] * b[7] * b[35] + b[16] * b[31] * b[11] + b[16] * b[30] * b[12] + b[15] * b[32] * b[11] + b[15] * b[33] * b[10] - b[15] * b[5] * b[38] + b[29] * b[5] * b[24] + b[29] * b[6] * b[23] - b[26] * b[20] * b[12] + b[26] * b[7] * b[25] - b[27] * b[19] * b[12] - b[27] * b[20] * b[11] + b[27] * b[6] * b[25] + b[27] * b[7] * b[24] - b[28] * b[20] * b[10] - b[16] * b[4] * b[38] - b[16] * b[5] * b[37] + b[29] * b[7] * b[22] - b[29] * b[17] * b[12] - b[29] * b[18] * b[11] - b[29] * b[19] * b[10] + b[28] * b[5] * b[25] + b[28] * b[6] * b[24] + b[28] * b[7] * b[23] - b[28] * b[18] * b[12] - b[28] * b[19] * b[11] - b[29] * b[20] * b[9] + b[29] * b[4] * b[25] - b[2] * b[24] * b[32] + b[0] * b[20] * b[38] - b[0] * b[25] * b[33] + b[1] * b[19] * b[38] - b[1] * b[24] * b[33] + b[1] * b[20] * b[37] - b[2] * b[25] * b[31] + b[2] * b[20] * b[36] - b[1] * b[25] * b[32] + b[2] * b[19] * b[37] + b[2] * b[18] * b[38] - b[2] * b[23] * b[33]);
c[2] = (b[3] * b[18] * b[38] - b[3] * b[24] * b[32] + b[3] * b[19] * b[37] + b[3] * b[20] * b[36] - b[3] * b[25] * b[31] - b[3] * b[23] * b[33] - b[15] * b[6] * b[38] - b[15] * b[7] * b[37] + b[16] * b[32] * b[11] + b[16] * b[33] * b[10] - b[16] * b[5] * b[38] - b[16] * b[6] * b[37] - b[16] * b[7] * b[36] + b[16] * b[31] * b[12] + b[14] * b[33] * b[12] - b[14] * b[7] * b[38] + b[15] * b[32] * b[12] + b[15] * b[33] * b[11] + b[29] * b[5] * b[25] + b[29] * b[6] * b[24] - b[27] * b[20] * b[12] + b[27] * b[7] * b[25] - b[28] * b[19] * b[12] - b[28] * b[20] * b[11] + b[29] * b[7] * b[23] - b[29] * b[18] * b[12] - b[29] * b[19] * b[11] + b[28] * b[6] * b[25] + b[28] * b[7] * b[24] - b[29] * b[20] * b[10] + b[2] * b[19] * b[38] - b[1] * b[25] * b[33] + b[2] * b[20] * b[37] - b[2] * b[24] * b[33] - b[2] * b[25] * b[32] + b[1] * b[20] * b[38]);
c[1] = (b[29] * b[7] * b[24] - b[29] * b[20] * b[11] + b[2] * b[20] * b[38] - b[2] * b[25] * b[33] - b[28] * b[20] * b[12] + b[28] * b[7] * b[25] - b[29] * b[19] * b[12] - b[3] * b[24] * b[33] + b[15] * b[33] * b[12] + b[3] * b[19] * b[38] - b[16] * b[6] * b[38] + b[3] * b[20] * b[37] + b[16] * b[32] * b[12] + b[29] * b[6] * b[25] - b[16] * b[7] * b[37] - b[3] * b[25] * b[32] - b[15] * b[7] * b[38] + b[16] * b[33] * b[11]);
c[0] = -b[29] * b[20] * b[12] + b[29] * b[7] * b[25] + b[16] * b[33] * b[12] - b[16] * b[7] * b[38] + b[3] * b[20] * b[38] - b[3] * b[25] * b[33];
std::vector<Complex<double>> roots;
/* finds complex roots of a polynomial using Durand-Kerner method:
http://en.wikipedia.org/wiki/Durand%E2%80%93Kerner_method */
solvePoly(coeffs, roots, 200);
cout << "coeffs:\n"<< coeffs <<"\n";
cout << "B:\n" << B << "\n";
ofstream Debug_Output("Results_EssentialMatrix_Roots.csv", ios::out);
if (!Debug_Output.is_open())
{
cout << "[Error] Unable to Create File.\n";
return 0;
}
Debug_Output << "coeffs:\n";
Debug_Output << format(coeffs, cv::Formatter::FMT_CSV);
Debug_Output << "\n";
Debug_Output << "B:\n";
Debug_Output << format(B, cv::Formatter::FMT_CSV);
Debug_Output << "\n";
Debug_Output << "roots:\n";
Debug_Output << format(roots, cv::Formatter::FMT_CSV);
Debug_Output << "\n";
Debug_Output.close();
waitKey(0);
return 0;
}