Absolute bundle adjustment with GPS is very slow
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San Jiang
2016年6月21日 06:00:242016/6/21
收件人 Ceres Solver
Hi,
thanks for releasing the usefull library. Recently, I have tried to integrate ceres into an existed sfm workflow and added position constrains for each image with help of GPS information, just like the cost function in following topic. however, the difference is that my workflow can be divided into tow steps:
1) relative sfm without GPS information. In this step, the first image' pose is identify and translation is zero. and only reprojection residuals are considered.
2) absolute sfm with GPS information. In this step, the extra residual blocks are added besides the reprojection residual, which estmate the offset between image position and GPS position.
according to these two step, I could successfully do bundle adjustment in step one. But very slow iteration speed has been identified as following and termination status is no convergent!
Then, anyone could provide some tips on how to accelate this iteration.
Thanks! any help is highly appreciated!
San Jiang.
===============================================================================================
https://groups.google.com/forum/#!starred/ceres-solver/-Cq37gjICL0
bool operator()(const T* const qvec, const T* const tvec,
T* residuals) const {
// Calculate pose center.
//const Eigen::Quaternion<T> quat(qvec[0], qvec[1], qvec[2], qvec[3]);
//Eigen::Matrix<T, 3, 1> tran(tvec[0], tvec[1], tvec[2]);
//Eigen::Matrix<T, 3, 1> imgC = quat * -tran;
//residuals[0] = imgC[0] - T(gpsC_(0));
//residuals[1] = imgC[1] - T(gpsC_(1));
//residuals[2] = imgC[2] - T(gpsC_(2));
residuals[0] = tvec[0] - T(gpsC_(0));
residuals[1] = tvec[1] - T(gpsC_(1));
residuals[2] = tvec[2] - T(gpsC_(2));
if (weight_ > 0.0)
{
residuals[0] *= T(weight_);
residuals[1] *= T(weight_);
residuals[2] *= T(weight_);
}
return true;
}
===============================================================================================
==============================================================================
Absolute bundle adjustment
==============================================================================
iter cost cost_change |gradient| |step| tr_ratio tr_radius ls_iter iter_time total_time
0 2.502760e+007 0.00e+000 2.06e+005 0.00e+000 0.00e+000 1.00e+004 0 6.12e-001 4.32e+000
1 2.502713e+007 4.69e+002 2.62e+003 1.60e-002 1.00e+000 3.00e+004 1 2.80e+000 7.12e+000
2 2.502713e+007 3.63e+000 4.20e+002 2.31e-002 1.00e+000 9.00e+004 1 1.42e+000 8.54e+000
3 2.502712e+007 6.49e+000 1.58e+003 6.25e-002 1.00e+000 2.70e+005 1 1.39e+000 9.93e+000
4 2.502711e+007 1.45e+001 3.14e+003 1.85e-001 1.00e+000 8.10e+005 1 1.29e+000 1.12e+001
5 2.502707e+007 4.04e+001 1.50e+004 5.71e-001 9.97e-001 2.43e+006 1 1.44e+000 1.27e+001
6 2.502696e+007 1.12e+002 1.33e+005 1.73e+000 9.20e-001 5.96e+006 1 1.39e+000 1.40e+001
7 2.502696e+007 -4.67e+001 0.00e+000 4.25e+000 -1.52e-001 2.98e+006 1 7.97e-001 1.48e+001
8 2.502682e+007 1.36e+002 2.01e+005 2.13e+000 8.60e-001 4.76e+006 1 1.36e+000 1.62e+001
9 2.502670e+007 1.16e+002 5.12e+005 3.40e+000 4.46e-001 4.76e+006 1 1.40e+000 1.76e+001
10 2.502647e+007 2.38e+002 5.10e+005 3.39e+000 6.26e-001 4.83e+006 1 1.32e+000 1.89e+001
11 2.502623e+007 2.32e+002 5.25e+005 3.45e+000 6.06e-001 4.88e+006 1 1.24e+000 2.02e+001
12 2.502600e+007 2.38e+002 5.33e+005 3.48e+000 6.04e-001 4.92e+006 1 1.25e+000 2.14e+001
13 2.502576e+007 2.40e+002 5.41e+005 3.51e+000 5.99e-001 4.96e+006 1 1.28e+000 2.27e+001
14 2.502551e+007 2.43e+002 5.48e+005 3.54e+000 5.96e-001 5.00e+006 1 1.27e+000 2.40e+001
15 2.502527e+007 2.45e+002 5.54e+005 3.57e+000 5.93e-001 5.03e+006 1 1.28e+000 2.52e+001
16 2.502502e+007 2.47e+002 5.59e+005 3.59e+000 5.90e-001 5.06e+006 1 1.28e+000 2.65e+001
17 2.502477e+007 2.49e+002 5.63e+005 3.61e+000 5.88e-001 5.09e+006 1 1.27e+000 2.78e+001
18 2.502452e+007 2.51e+002 5.67e+005 3.63e+000 5.86e-001 5.12e+006 1 1.31e+000 2.91e+001
19 2.502427e+007 2.52e+002 5.70e+005 3.65e+000 5.85e-001 5.14e+006 1 1.23e+000 3.03e+001
20 2.502401e+007 2.54e+002 5.73e+005 3.67e+000 5.83e-001 5.16e+006 1 1.27e+000 3.16e+001
21 2.502376e+007 2.55e+002 5.76e+005 3.68e+000 5.82e-001 5.19e+006 1 1.28e+000 3.29e+001
22 2.502350e+007 2.56e+002 5.78e+005 3.70e+000 5.82e-001 5.21e+006 1 1.29e+000 3.42e+001
23 2.502324e+007 2.58e+002 5.80e+005 3.72e+000 5.81e-001 5.23e+006 1 1.29e+000 3.55e+001
24 2.502299e+007 2.59e+002 5.81e+005 3.73e+000 5.80e-001 5.25e+006 1 1.27e+000 3.67e+001
25 2.502273e+007 2.60e+002 5.83e+005 3.75e+000 5.80e-001 5.28e+006 1 1.28e+000 3.80e+001
26 2.502246e+007 2.61e+002 5.84e+005 3.76e+000 5.80e-001 5.30e+006 1 1.29e+000 3.93e+001
27 2.502220e+007 2.62e+002 5.85e+005 3.78e+000 5.80e-001 5.32e+006 1 1.28e+000 4.06e+001
28 2.502194e+007 2.63e+002 5.85e+005 3.79e+000 5.80e-001 5.34e+006 1 1.25e+000 4.18e+001
29 2.502167e+007 2.65e+002 5.86e+005 3.81e+000 5.80e-001 5.36e+006 1 1.28e+000 4.31e+001
30 2.502141e+007 2.66e+002 5.86e+005 3.82e+000 5.80e-001 5.38e+006 1 1.26e+000 4.44e+001
31 2.502114e+007 2.67e+002 5.86e+005 3.84e+000 5.80e-001 5.41e+006 1 1.28e+000 4.57e+001
32 2.502087e+007 2.68e+002 5.86e+005 3.85e+000 5.81e-001 5.43e+006 1 1.27e+000 4.69e+001
33 2.502060e+007 2.69e+002 5.86e+005 3.87e+000 5.81e-001 5.45e+006 1 1.28e+000 4.82e+001
34 2.502033e+007 2.70e+002 5.86e+005 3.89e+000 5.82e-001 5.48e+006 1 1.24e+000 4.95e+001
35 2.502006e+007 2.72e+002 5.86e+005 3.90e+000 5.83e-001 5.50e+006 1 1.28e+000 5.07e+001
36 2.501979e+007 2.73e+002 5.85e+005 3.92e+000 5.83e-001 5.53e+006 1 1.23e+000 5.20e+001
37 2.501952e+007 2.74e+002 5.84e+005 3.94e+000 5.84e-001 5.55e+006 1 1.27e+000 5.32e+001
38 2.501924e+007 2.75e+002 5.84e+005 3.96e+000 5.85e-001 5.58e+006 1 1.47e+000 5.47e+001
39 2.501896e+007 2.77e+002 5.83e+005 3.98e+000 5.86e-001 5.61e+006 1 1.61e+000 5.63e+001
40 2.501869e+007 2.78e+002 5.82e+005 4.00e+000 5.87e-001 5.64e+006 1 1.42e+000 5.77e+001
41 2.501841e+007 2.80e+002 5.81e+005 4.02e+000 5.88e-001 5.67e+006 1 1.30e+000 5.90e+001
42 2.501812e+007 2.81e+002 5.79e+005 4.04e+000 5.90e-001 5.70e+006 1 1.37e+000 6.04e+001
43 2.501784e+007 2.83e+002 5.79e+005 4.07e+000 5.91e-001 5.74e+006 1 1.44e+000 6.18e+001
44 2.501756e+007 2.85e+002 5.79e+005 4.09e+000 5.92e-001 5.78e+006 1 1.42e+000 6.33e+001
45 2.501727e+007 2.86e+002 5.79e+005 4.12e+000 5.94e-001 5.81e+006 1 1.29e+000 6.46e+001
46 2.501698e+007 2.88e+002 5.79e+005 4.15e+000 5.95e-001 5.85e+006 1 1.29e+000 6.58e+001
47 2.501669e+007 2.90e+002 5.79e+005 4.18e+000 5.97e-001 5.90e+006 1 1.28e+000 6.71e+001
48 2.501640e+007 2.92e+002 5.79e+005 4.21e+000 5.98e-001 5.94e+006 1 1.29e+000 6.84e+001
49 2.501610e+007 2.95e+002 5.79e+005 4.24e+000 6.00e-001 5.99e+006 1 1.27e+000 6.97e+001
50 2.501581e+007 2.97e+002 5.79e+005 4.27e+000 6.02e-001 6.04e+006 1 1.28e+000 7.10e+001
51 2.501551e+007 2.99e+002 5.79e+005 4.31e+000 6.04e-001 6.09e+006 1 1.29e+000 7.23e+001
52 2.501521e+007 3.02e+002 5.79e+005 4.35e+000 6.05e-001 6.15e+006 1 1.29e+000 7.36e+001
……………………………………
491 2.487564e+007 4.68e+002 7.55e+005 7.07e+000 5.60e-001 6.13e+006 1 1.37e+000 6.56e+002
492 2.487517e+007 4.70e+002 7.55e+005 7.09e+000 5.60e-001 6.14e+006 1 1.34e+000 6.57e+002
493 2.487470e+007 4.71e+002 7.56e+005 7.11e+000 5.60e-001 6.15e+006 1 1.39e+000 6.58e+002
494 2.487422e+007 4.72e+002 7.56e+005 7.12e+000 5.60e-001 6.16e+006 1 1.31e+000 6.60e+002
495 2.487375e+007 4.73e+002 7.57e+005 7.14e+000 5.60e-001 6.17e+006 1 1.31e+000 6.61e+002
496 2.487328e+007 4.75e+002 7.57e+005 7.16e+000 5.60e-001 6.19e+006 1 1.32e+000 6.62e+002
497 2.487280e+007 4.76e+002 7.58e+005 7.18e+000 5.60e-001 6.20e+006 1 1.29e+000 6.64e+002
498 2.487232e+007 4.77e+002 7.58e+005 7.20e+000 5.60e-001 6.21e+006 1 1.30e+000 6.65e+002
499 2.487184e+007 4.78e+002 7.59e+005 7.22e+000 5.60e-001 6.22e+006 1 1.30e+000 6.66e+002
500 2.487136e+007 4.80e+002 7.59e+005 7.24e+000 5.60e-001 6.23e+006 1 1.31e+000 6.68e+002
Absolute Bundle Adjustment Report
---------------------------------
Residuals : 1591579
Parameters : 521610
Iterations : 500
Time : 667.579107 [s]
Initial cost : 3.965478 [px]
Final cost : 3.953081 [px]
Termination : No convergence
thanks for releasing the usefull library. Recently, I have tried to integrate ceres into an existed sfm workflow and added position constrains for each image with help of GPS information, just like the cost function in following topic. however, the difference is that my workflow can be divided into tow steps:
1) relative sfm without GPS information. In this step, the first image' pose is identify and translation is zero. and only reprojection residuals are considered.
2) absolute sfm with GPS information. In this step, the extra residual blocks are added besides the reprojection residual, which estmate the offset between image position and GPS position.
according to these two step, I could successfully do bundle adjustment in step one. But very slow iteration speed has been identified as following and termination status is no convergent!
Then, anyone could provide some tips on how to accelate this iteration.
Thanks! any help is highly appreciated!
San Jiang.
===============================================================================================
https://groups.google.com/forum/#!starred/ceres-solver/-Cq37gjICL0
bool operator()(const T* const qvec, const T* const tvec,
T* residuals) const {
// Calculate pose center.
//const Eigen::Quaternion<T> quat(qvec[0], qvec[1], qvec[2], qvec[3]);
//Eigen::Matrix<T, 3, 1> tran(tvec[0], tvec[1], tvec[2]);
//Eigen::Matrix<T, 3, 1> imgC = quat * -tran;
//residuals[0] = imgC[0] - T(gpsC_(0));
//residuals[1] = imgC[1] - T(gpsC_(1));
//residuals[2] = imgC[2] - T(gpsC_(2));
residuals[0] = tvec[0] - T(gpsC_(0));
residuals[1] = tvec[1] - T(gpsC_(1));
residuals[2] = tvec[2] - T(gpsC_(2));
if (weight_ > 0.0)
{
residuals[0] *= T(weight_);
residuals[1] *= T(weight_);
residuals[2] *= T(weight_);
}
return true;
}
===============================================================================================
==============================================================================
Absolute bundle adjustment
==============================================================================
iter cost cost_change |gradient| |step| tr_ratio tr_radius ls_iter iter_time total_time
0 2.502760e+007 0.00e+000 2.06e+005 0.00e+000 0.00e+000 1.00e+004 0 6.12e-001 4.32e+000
1 2.502713e+007 4.69e+002 2.62e+003 1.60e-002 1.00e+000 3.00e+004 1 2.80e+000 7.12e+000
2 2.502713e+007 3.63e+000 4.20e+002 2.31e-002 1.00e+000 9.00e+004 1 1.42e+000 8.54e+000
3 2.502712e+007 6.49e+000 1.58e+003 6.25e-002 1.00e+000 2.70e+005 1 1.39e+000 9.93e+000
4 2.502711e+007 1.45e+001 3.14e+003 1.85e-001 1.00e+000 8.10e+005 1 1.29e+000 1.12e+001
5 2.502707e+007 4.04e+001 1.50e+004 5.71e-001 9.97e-001 2.43e+006 1 1.44e+000 1.27e+001
6 2.502696e+007 1.12e+002 1.33e+005 1.73e+000 9.20e-001 5.96e+006 1 1.39e+000 1.40e+001
7 2.502696e+007 -4.67e+001 0.00e+000 4.25e+000 -1.52e-001 2.98e+006 1 7.97e-001 1.48e+001
8 2.502682e+007 1.36e+002 2.01e+005 2.13e+000 8.60e-001 4.76e+006 1 1.36e+000 1.62e+001
9 2.502670e+007 1.16e+002 5.12e+005 3.40e+000 4.46e-001 4.76e+006 1 1.40e+000 1.76e+001
10 2.502647e+007 2.38e+002 5.10e+005 3.39e+000 6.26e-001 4.83e+006 1 1.32e+000 1.89e+001
11 2.502623e+007 2.32e+002 5.25e+005 3.45e+000 6.06e-001 4.88e+006 1 1.24e+000 2.02e+001
12 2.502600e+007 2.38e+002 5.33e+005 3.48e+000 6.04e-001 4.92e+006 1 1.25e+000 2.14e+001
13 2.502576e+007 2.40e+002 5.41e+005 3.51e+000 5.99e-001 4.96e+006 1 1.28e+000 2.27e+001
14 2.502551e+007 2.43e+002 5.48e+005 3.54e+000 5.96e-001 5.00e+006 1 1.27e+000 2.40e+001
15 2.502527e+007 2.45e+002 5.54e+005 3.57e+000 5.93e-001 5.03e+006 1 1.28e+000 2.52e+001
16 2.502502e+007 2.47e+002 5.59e+005 3.59e+000 5.90e-001 5.06e+006 1 1.28e+000 2.65e+001
17 2.502477e+007 2.49e+002 5.63e+005 3.61e+000 5.88e-001 5.09e+006 1 1.27e+000 2.78e+001
18 2.502452e+007 2.51e+002 5.67e+005 3.63e+000 5.86e-001 5.12e+006 1 1.31e+000 2.91e+001
19 2.502427e+007 2.52e+002 5.70e+005 3.65e+000 5.85e-001 5.14e+006 1 1.23e+000 3.03e+001
20 2.502401e+007 2.54e+002 5.73e+005 3.67e+000 5.83e-001 5.16e+006 1 1.27e+000 3.16e+001
21 2.502376e+007 2.55e+002 5.76e+005 3.68e+000 5.82e-001 5.19e+006 1 1.28e+000 3.29e+001
22 2.502350e+007 2.56e+002 5.78e+005 3.70e+000 5.82e-001 5.21e+006 1 1.29e+000 3.42e+001
23 2.502324e+007 2.58e+002 5.80e+005 3.72e+000 5.81e-001 5.23e+006 1 1.29e+000 3.55e+001
24 2.502299e+007 2.59e+002 5.81e+005 3.73e+000 5.80e-001 5.25e+006 1 1.27e+000 3.67e+001
25 2.502273e+007 2.60e+002 5.83e+005 3.75e+000 5.80e-001 5.28e+006 1 1.28e+000 3.80e+001
26 2.502246e+007 2.61e+002 5.84e+005 3.76e+000 5.80e-001 5.30e+006 1 1.29e+000 3.93e+001
27 2.502220e+007 2.62e+002 5.85e+005 3.78e+000 5.80e-001 5.32e+006 1 1.28e+000 4.06e+001
28 2.502194e+007 2.63e+002 5.85e+005 3.79e+000 5.80e-001 5.34e+006 1 1.25e+000 4.18e+001
29 2.502167e+007 2.65e+002 5.86e+005 3.81e+000 5.80e-001 5.36e+006 1 1.28e+000 4.31e+001
30 2.502141e+007 2.66e+002 5.86e+005 3.82e+000 5.80e-001 5.38e+006 1 1.26e+000 4.44e+001
31 2.502114e+007 2.67e+002 5.86e+005 3.84e+000 5.80e-001 5.41e+006 1 1.28e+000 4.57e+001
32 2.502087e+007 2.68e+002 5.86e+005 3.85e+000 5.81e-001 5.43e+006 1 1.27e+000 4.69e+001
33 2.502060e+007 2.69e+002 5.86e+005 3.87e+000 5.81e-001 5.45e+006 1 1.28e+000 4.82e+001
34 2.502033e+007 2.70e+002 5.86e+005 3.89e+000 5.82e-001 5.48e+006 1 1.24e+000 4.95e+001
35 2.502006e+007 2.72e+002 5.86e+005 3.90e+000 5.83e-001 5.50e+006 1 1.28e+000 5.07e+001
36 2.501979e+007 2.73e+002 5.85e+005 3.92e+000 5.83e-001 5.53e+006 1 1.23e+000 5.20e+001
37 2.501952e+007 2.74e+002 5.84e+005 3.94e+000 5.84e-001 5.55e+006 1 1.27e+000 5.32e+001
38 2.501924e+007 2.75e+002 5.84e+005 3.96e+000 5.85e-001 5.58e+006 1 1.47e+000 5.47e+001
39 2.501896e+007 2.77e+002 5.83e+005 3.98e+000 5.86e-001 5.61e+006 1 1.61e+000 5.63e+001
40 2.501869e+007 2.78e+002 5.82e+005 4.00e+000 5.87e-001 5.64e+006 1 1.42e+000 5.77e+001
41 2.501841e+007 2.80e+002 5.81e+005 4.02e+000 5.88e-001 5.67e+006 1 1.30e+000 5.90e+001
42 2.501812e+007 2.81e+002 5.79e+005 4.04e+000 5.90e-001 5.70e+006 1 1.37e+000 6.04e+001
43 2.501784e+007 2.83e+002 5.79e+005 4.07e+000 5.91e-001 5.74e+006 1 1.44e+000 6.18e+001
44 2.501756e+007 2.85e+002 5.79e+005 4.09e+000 5.92e-001 5.78e+006 1 1.42e+000 6.33e+001
45 2.501727e+007 2.86e+002 5.79e+005 4.12e+000 5.94e-001 5.81e+006 1 1.29e+000 6.46e+001
46 2.501698e+007 2.88e+002 5.79e+005 4.15e+000 5.95e-001 5.85e+006 1 1.29e+000 6.58e+001
47 2.501669e+007 2.90e+002 5.79e+005 4.18e+000 5.97e-001 5.90e+006 1 1.28e+000 6.71e+001
48 2.501640e+007 2.92e+002 5.79e+005 4.21e+000 5.98e-001 5.94e+006 1 1.29e+000 6.84e+001
49 2.501610e+007 2.95e+002 5.79e+005 4.24e+000 6.00e-001 5.99e+006 1 1.27e+000 6.97e+001
50 2.501581e+007 2.97e+002 5.79e+005 4.27e+000 6.02e-001 6.04e+006 1 1.28e+000 7.10e+001
51 2.501551e+007 2.99e+002 5.79e+005 4.31e+000 6.04e-001 6.09e+006 1 1.29e+000 7.23e+001
52 2.501521e+007 3.02e+002 5.79e+005 4.35e+000 6.05e-001 6.15e+006 1 1.29e+000 7.36e+001
……………………………………
491 2.487564e+007 4.68e+002 7.55e+005 7.07e+000 5.60e-001 6.13e+006 1 1.37e+000 6.56e+002
492 2.487517e+007 4.70e+002 7.55e+005 7.09e+000 5.60e-001 6.14e+006 1 1.34e+000 6.57e+002
493 2.487470e+007 4.71e+002 7.56e+005 7.11e+000 5.60e-001 6.15e+006 1 1.39e+000 6.58e+002
494 2.487422e+007 4.72e+002 7.56e+005 7.12e+000 5.60e-001 6.16e+006 1 1.31e+000 6.60e+002
495 2.487375e+007 4.73e+002 7.57e+005 7.14e+000 5.60e-001 6.17e+006 1 1.31e+000 6.61e+002
496 2.487328e+007 4.75e+002 7.57e+005 7.16e+000 5.60e-001 6.19e+006 1 1.32e+000 6.62e+002
497 2.487280e+007 4.76e+002 7.58e+005 7.18e+000 5.60e-001 6.20e+006 1 1.29e+000 6.64e+002
498 2.487232e+007 4.77e+002 7.58e+005 7.20e+000 5.60e-001 6.21e+006 1 1.30e+000 6.65e+002
499 2.487184e+007 4.78e+002 7.59e+005 7.22e+000 5.60e-001 6.22e+006 1 1.30e+000 6.66e+002
500 2.487136e+007 4.80e+002 7.59e+005 7.24e+000 5.60e-001 6.23e+006 1 1.31e+000 6.68e+002
Absolute Bundle Adjustment Report
---------------------------------
Residuals : 1591579
Parameters : 521610
Iterations : 500
Time : 667.579107 [s]
Initial cost : 3.965478 [px]
Final cost : 3.953081 [px]
Termination : No convergence
Sameer Agarwal
2016年6月21日 08:19:432016/6/21
收件人 ceres-...@googlegroups.com
San,
My comments are inline.
1) relative sfm without GPS information. In this step, the first image' pose is identify and translation is zero. and only reprojection residuals are considered.
2) absolute sfm with GPS information. In this step, the extra residual blocks are added besides the reprojection residual, which estmate the offset between image position and GPS position.
according to these two step, I could successfully do bundle adjustment in step one. But very slow iteration speed has been identified as following and termination status is no convergent!
Then, anyone could provide some tips on how to accelate this iteration.
I believe the problem here is that the absolute pose constraints that you have added to the problem work as regularizers, preventing your images from moving too much. Which will naturally slow the convergence down.
But I have a question for you. When you did the relative sfm with no gps information, your sfm reconstruction will have a translation, rotation and scale ambiguity. I imagine you did a similarity transform from your relative reconstruction to the gps locations of the cameras.
my guess is that the positions of the cameras do not match the gps positions well. It would be a good idea to see what the starting residuals for your image position term are. If they are large then you either have to do some outlier pruning, or anneal the terms which enforce the gps positions, by starting with a small weight, optimizing, increasing the weight and optimizing again.
Sameer
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William Rucklidge
2016年6月21日 12:13:582016/6/21
收件人 ceres-...@googlegroups.com
Depending on your coordinate frame, you may want to consider doing some manual preconditioning of the GPS positions, by changing the values Ceres is adjusting from being absolute positions to relative positions.
More detail: If your positions are in ECEF, then their absolute magnitudes are going to be roughly 6e6 (radius of the Earth). The other parameters you adjust are likely to have much smaller magnitudes - for example, rotation quaternion components are always in [-1, 1]. Consider using the original GPS positions as a base, and have Ceres adjust corrections to that base. That is (in pseudocode; in reality this would be >1 cost functor):
MyCostFunctor(const double* absolute_position, const double* rotation_quaternion, double* residuals) {
current_pose = Pose(absolute_position, rotation_quaternion);
... compute reprojection residuals based on current_pose ...
pose_error = absolute_position - GPS_position
... add terms to residuals based on pose_error
}
you'd do
MyCostFunctor(const double* position_correction, const double* rotation_quaternion, double* residuals) {
current_pose = Pose(GPS_position + position_correction, rotation_quaternion);
... compute reprojection residuals based on current_pose ...
... add terms to residuals based on position_correction
}
The values in the position_correction vector will be much smaller than the values in absolute_position would have been.
If your coordinate system isn't ECEF then this may not be a concern for you.
-wjr
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San Jiang
2016年6月22日 20:04:142016/6/22
收件人 Ceres Solver
Sameer,
thanks for providing some useful advises. After checking the similarity transformation from relative orientation to coarse absolute orientation, I found that some mistakes in this process. Now, the bundle adjustment process could be convergent to rational value as following.
thanks for providing some useful advises. After checking the similarity transformation from relative orientation to coarse absolute orientation, I found that some mistakes in this process. Now, the bundle adjustment process could be convergent to rational value as following.
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San Jiang
2016年6月22日 20:36:072016/6/22
收件人 Ceres Solver
iter cost cost_change |gradient| |step| tr_ratio tr_radius ls_iter iter_time total_time
0 4.027004e+005 0.00e+000 1.89e+003 0.00e+000 0.00e+000 1.00e+004 0 6.22e-001 4.52e+000
1 4.022521e+005 4.48e+002 2.60e+001 2.43e+000 1.00e+000 3.00e+004 1 2.65e+000 7.18e+000
2 4.022483e+005 3.81e+000 1.91e+000 3.85e+000 1.00e+000 9.00e+004 1 1.31e+000 8.49e+000
3 4.022433e+005 5.02e+000 3.99e+000 6.90e+000 1.00e+000 2.70e+005 1 1.25e+000 9.73e+000
4 4.022384e+005 4.84e+000 5.20e+000 9.11e+000 1.00e+000 8.10e+005 1 1.27e+000 1.10e+001
5 4.022366e+005 1.85e+000 1.04e+001 5.57e+000 1.00e+000 2.43e+006 1 1.41e+000 1.24e+001
6 4.022363e+005 3.27e-001 6.75e+000 7.22e+000 1.00e+000 7.29e+006 1 1.29e+000 1.37e+001
7 4.022361e+005 1.28e-001 2.26e+000 9.97e+000 1.00e+000 2.19e+007 1 1.27e+000 1.50e+001
8 4.022361e+005 4.21e-002 1.94e+000 7.00e+000 1.00e+000 6.56e+007 1 1.29e+000 1.63e+001
9 4.022361e+005 7.64e-003 2.19e+000 3.71e+000 9.97e-001 1.97e+008 1 1.27e+000 1.75e+001
10 4.022361e+005 3.78e-003 3.77e+000 5.00e+000 9.60e-001 5.90e+008 1 1.37e+000 1.89e+001
11 4.022361e+005 2.51e-003 5.39e+000 6.27e+000 8.65e-001 9.68e+008 1 1.34e+000 2.02e+001
12 4.022361e+005 8.81e-004 1.86e+000 3.13e+000 9.71e-001 2.91e+009 1 1.27e+000 2.15e+001
13 4.022361e+005 7.52e-005 1.86e+000 1.19e+000 9.89e-001 8.72e+009 1 1.34e+000 2.29e+001
14 4.022361e+005 1.28e-006 1.90e+000 1.59e-001 9.95e-001 2.61e+010 1 1.29e+000 2.42e+001
1 4.022521e+005 4.48e+002 2.60e+001 2.43e+000 1.00e+000 3.00e+004 1 2.65e+000 7.18e+000
2 4.022483e+005 3.81e+000 1.91e+000 3.85e+000 1.00e+000 9.00e+004 1 1.31e+000 8.49e+000
3 4.022433e+005 5.02e+000 3.99e+000 6.90e+000 1.00e+000 2.70e+005 1 1.25e+000 9.73e+000
4 4.022384e+005 4.84e+000 5.20e+000 9.11e+000 1.00e+000 8.10e+005 1 1.27e+000 1.10e+001
5 4.022366e+005 1.85e+000 1.04e+001 5.57e+000 1.00e+000 2.43e+006 1 1.41e+000 1.24e+001
6 4.022363e+005 3.27e-001 6.75e+000 7.22e+000 1.00e+000 7.29e+006 1 1.29e+000 1.37e+001
7 4.022361e+005 1.28e-001 2.26e+000 9.97e+000 1.00e+000 2.19e+007 1 1.27e+000 1.50e+001
8 4.022361e+005 4.21e-002 1.94e+000 7.00e+000 1.00e+000 6.56e+007 1 1.29e+000 1.63e+001
9 4.022361e+005 7.64e-003 2.19e+000 3.71e+000 9.97e-001 1.97e+008 1 1.27e+000 1.75e+001
10 4.022361e+005 3.78e-003 3.77e+000 5.00e+000 9.60e-001 5.90e+008 1 1.37e+000 1.89e+001
11 4.022361e+005 2.51e-003 5.39e+000 6.27e+000 8.65e-001 9.68e+008 1 1.34e+000 2.02e+001
12 4.022361e+005 8.81e-004 1.86e+000 3.13e+000 9.71e-001 2.91e+009 1 1.27e+000 2.15e+001
13 4.022361e+005 7.52e-005 1.86e+000 1.19e+000 9.89e-001 8.72e+009 1 1.34e+000 2.29e+001
14 4.022361e+005 1.28e-006 1.90e+000 1.59e-001 9.95e-001 2.61e+010 1 1.29e+000 2.42e+001
Absolute Bundle Adjustment Report
---------------------------------
Residuals : 1591757
Parameters : 521745
Iterations : 15
Time : 25.546804 [s]
Initial cost : 0.502982 [px]
Final cost : 0.502692 [px]
Termination : Convergence
Elapsed time: 19.15 [minutes]
Parameters : 521745
Iterations : 15
Time : 25.546804 [s]
Initial cost : 0.502982 [px]
Final cost : 0.502692 [px]
Termination : Convergence
Elapsed time: 19.15 [minutes]
San Jiang
2016年6月24日 09:27:072016/6/24
收件人 Ceres Solver
Hi, wjr
Thanks for sharing your experience on gps assisted bundle adjustment. and I have test bundle adjustment in ECEF coordinate system. However, the orientation bias is large between relative sfm and absolute sfm. then the convergence speed is also slow and even the termination state is NOT CONVERGENT.
I think the preprocessing, like similairty transformation from relative sfm to absolute sfm using image projection center and gps information, is necessary. However, three correspondings are needed for 3D similarity transformation. then, if only two images are to be processed, the similarity transformation is not possible. So, I would try to add gps constrains to the first bundle adjustment step. If you have some good ideal or information about how to construct the cost function, I would highly appreciated！
San Jiang!
Thanks for sharing your experience on gps assisted bundle adjustment. and I have test bundle adjustment in ECEF coordinate system. However, the orientation bias is large between relative sfm and absolute sfm. then the convergence speed is also slow and even the termination state is NOT CONVERGENT.
I think the preprocessing, like similairty transformation from relative sfm to absolute sfm using image projection center and gps information, is necessary. However, three correspondings are needed for 3D similarity transformation. then, if only two images are to be processed, the similarity transformation is not possible. So, I would try to add gps constrains to the first bundle adjustment step. If you have some good ideal or information about how to construct the cost function, I would highly appreciated！
San Jiang!
William Rucklidge
2016年6月24日 12:08:392016/6/24
收件人 ceres-...@googlegroups.com
One easy-to-miss pitfall of working in ECEF is that if any of your values ever pass through a variable of type "float", you're going to have a bad day. 24 bits of mantissa means a precision of about 1 in 16 million - for values in the 6 million range, your representation quantum is in the 10s of cm. This can badly mess up your calculations, especially the Jacobians. If everything in sight is a double (including any third party libraries), then you're fine.
The cost function you gave earlier seemed fine - apply a cost for any adjustment of the pose away from the GPS-provided initial position. As Sameer suggested, you should try a large range of weights for the GPS-related costs.
I'm not sure why you're doing this in two passes of SFM rather than a single pass. It seems to add complexity; what's the intended benefit?
-wjr
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