solvePnP fails with perfect coordinates (and cvPOSIT passes)

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Hi,

I have found a set of parameters for which solvePnP does not give correct results although :

• the image points are perfect coordinates obtained with projectPoints applied to the objectPoints (no error at all in the image points)
• the objects points consist of 4 non coplanar points
• the parameters are quite innocent looking
• cvPOSIT is perfectly able to reconstruct the pose, when solvePnp seems not to be able to do so

This problem occurs with opencv 2.4.1 and 3.1.0, under osx and windows

When I reproject the point using the rotation and translation provided by solvePnP, I have a total error of about 8 pixels (I have tried all flags : ITERATIVE, P3P and EPNP)

If instead I use the rotation and translation provided by cvPOSIT the reprojection error can be reduced to 0.00014 pixels !

Here is a short program that demonstrates the error : I simply instantiate a camera matrix, some object points and their corresponding image points obtained through projectPoints. Then I compare the reprojection and I get 8 pixels of error!

#include <opencv2/core/core.hpp>
#include <opencv2/calib3d/calib3d.hpp>
#include <iostream>

void TestSolvePnp()
{
  std::vector<cv::Point3f> objectPoints;

  objectPoints.push_back(cv::Point3f(0.f, 0.f, 0.f));
  objectPoints.push_back(cv::Point3f(62.3174629f, 15.7940502f, 0.819983721f));
  objectPoints.push_back(cv::Point3f(-62.1225319f, 15.7540569f, 0.819464564f));
  objectPoints.push_back(cv::Point3f(-0.372639507f, 16.4230633f,  -36.5060043f));

  cv::Mat_<double> cameraIntrinsicParams(cv::Size(3, 3));
  cameraIntrinsicParams = 0.;
  cameraIntrinsicParams(0, 0) = 3844.4400000000001f;
  cameraIntrinsicParams(1, 1) = 3841.0599999999999f;
  cameraIntrinsicParams(0, 2) = 640.f;
  cameraIntrinsicParams(1, 2) = 380.f;
  cameraIntrinsicParams(2, 2) = 1.f;

  cv::Mat_<double> distCoeffs(cv::Size(1, 4));
  distCoeffs = 0.f;


  cv::Mat_<double> rotation(cv::Size(3, 1));
  rotation(0,0) = 0.07015543380659847f;
  rotation(0,1) = 0.06922079477774973f;
  rotation(0,2) = -0.00254676088325f;

  cv::Mat_<double> translation(cv::Size(3, 1));
  translation(0,0) = -35.3236f;
  translation(0,1) = -48.1699f;
  translation(0,2) = 769.068f;

  std::vector<cv::Point2f> imagePoints;
  cv::projectPoints(objectPoints, rotation, translation, cameraIntrinsicParams, distCoeffs, imagePoints);


  cv::Mat_<double> rotation2(cv::Size(3, 1));
  cv::Mat_<double> translation2(cv::Size(3, 1));

  cv::solvePnP(objectPoints, imagePoints,                 
               cameraIntrinsicParams, distCoeffs,
               rotation2, translation2,
               //false,//useExtrinsicGuess

               //Choose solvepnp flag below
               //cv::SOLVEPNP_UPNP
               //cv::SOLVEPNP_DLS
               //cv::SOLVEPNP_EPNP
               //cv::SOLVEPNP_P3P
               cv::SOLVEPNP_ITERATIVE
  );

  std::vector<cv::Point2f> imagePoints_Reproj(3);
  cv::projectPoints(objectPoints, rotation2, translation2, cameraIntrinsicParams, distCoeffs, imagePoints_Reproj);

  float sum = 0.;
  for (size_t i = 0; i < imagePoints.size(); i++)
    sum += DistPoint(imagePoints_Reproj[i], imagePoints[i]);

  std::cout << "sum=" << sum << std::endl;
}

int main(int argc, char **argv)
{
  TestSolvePnp();
}

However, if I replace the call to solvePnp by a call to cvPOSIT, the reprojection error goes down to 0.00014 pixels !

Below is the implementation of a function named MySolvePnpPosit() that reproduces the behavior of solvePnP, but uses cvPOSIT internally => when I use it, the error goes down almost zero.

namespace
{
  void Posit_IdealCameraCoords(const std::vector<cv::Point3f> & objectPoints, const std::vector<cv::Point2f> & imagePoints,
             cv::Mat &outRotationEstimated, cv::Mat & outTranslationEstimated)
  {

    CvPoint2D32f * imagePoints_c = (CvPoint2D32f ...