This repository is intended to provide practical examples of basic Ceres usage, as well as the infrastructure for a sample project which includes the library. This is not intended as a replacement for the excellent and comprehensive Ceres Documentation, but rather as a pedogogical tool and starting template for optimization projects.
To build this project you will need a compiler and CMake 3.15 or later (available here). Once complete you can then build the project via the following commands:
cmake ..
cmake --build . --config Release
This will build the ceres_example executable, which you can test
by simply typing:
./ceres_example
This should fit to a randomly generated dataset, resulting in console output that looks like that shown below:
Numeric differentiation:
iter cost cost_change |gradient| |step| tr_ratio tr_radius ls_iter iter_time total_time
0 6.765364e+03 0.00e+00 3.00e+04 0.00e+00 0.00e+00 1.00e+04 0 5.01e-05 3.85e-04
1 1.233953e+03 5.53e+03 4.02e+03 5.94e-01 8.18e-01 1.34e+04 1 4.35e-04 1.18e-03
2 2.062309e+02 1.03e+03 5.50e+02 6.93e-01 8.33e-01 1.91e+04 1 1.34e-04 1.48e-03
3 2.901531e+01 1.77e+02 7.86e+01 7.82e-01 8.60e-01 3.04e+04 1 1.25e-04 1.72e-03
4 2.824528e+00 2.62e+01 1.17e+01 8.08e-01 9.05e-01 6.48e+04 1 1.62e-04 2.06e-03
5 1.702931e-01 2.65e+00 1.50e+00 5.70e-01 9.65e-01 1.94e+05 1 1.37e-04 2.36e-03
6 7.276579e-02 9.75e-02 7.72e-02 1.84e-01 9.97e-01 5.83e+05 1 1.14e-04 2.58e-03
7 7.244271e-02 3.23e-04 3.18e-04 1.50e-02 1.00e+00 1.75e+06 1 1.26e-04 2.80e-03
trust_region_minimizer.cc:745 Terminating: Function tolerance reached. |cost_change|/cost: 2.005580e-07 <= 1.000000e-06
Ceres Solver Report: Iterations: 8, Initial cost: 6.765364e+03, Final cost: 7.244271e-02, Termination: CONVERGENCE
Initial: (h=0.1, k=0.3, a=0.9, b=1.2)
Final: (h=-0.262104, k=0.465688, a=4.24418, b=2.12967)
Target: (h=-0.3, k=0.5, a=4.3, b=2.1)
This repository shows how to use Ceres via the example of fitting an ellipse to a noisy arc of points, as seen below:
In ceres_example.cpp you can view examples of:
- Numeric cost functions
- Autodiff cost functions
- Analytic cost functions
- Gradient checking
- Solver callbacks
- Solver customization
To learn more about Ceres and this example repository, please take a look at the tutorial slides