Ceres Solver 2020 文档.pdf-资料库

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Docs » Why? Why? Code Quality - Ceres Solver has been used in production at Google for more than four years now. It is clean, extensively tested and well documented code that is actively developed and supported. Modeling API - It is rarely the case that one starts with the exact and complete formulation of the problem that one is trying to solve. Ceres’s modeling API has been designed so that the user can easily build and modify the objective function, one term at a time. And to do so without worrying about how the solver is going to deal with the resulting changes in the sparsity/structure of the underlying problem. Derivatives Supplying derivatives is perhaps the most tedious and error prone part of using an optimization library. Ceres ships with automatic and numeric differentiation. So you never have to compute derivatives by hand (unless you really want to). Not only this, Ceres allows you to mix automatic, numeric and analytical derivatives in any combination that you want. Robust Loss Functions Most non-linear least squares problems involve data. If there is data, there will be outliers. Ceres allows the user to shape their residuals using a LossFunction LossFunction to reduce the inﬂuence of outliers. Local Parameterization In many cases, some parameters lie on a manifold other than Euclidean space, e.g., rotation matrices. In such cases, the user can specify the geometry of the local tangent space by specifying a LocalParameterization object. LocalParameterization

Solver Choice Depending on the size, sparsity structure, time & memory budgets, and solution quality requiremnts, different optimization algorithms will suit different needs. To this end, Ceres Solver comes with a variety of optimization algorithms: Trust Region Solvers - Ceres supports Levenberg- Marquardt, Powell’s Dogleg, and Subspace dogleg methods. The key computational cost in all of these methods is the solution of a linear system. To this end Ceres ships with a variety of linear solvers - dense QR and dense Cholesky factorization (using Eigen or LAPACK) for dense problems, sparse Cholesky factorization (SuiteSparse, CXSparse or Eigen) for large sparse problems custom Schur complement based dense, sparse, and iterative linear solvers for bundle adjustment problems. Line Search Solvers - When the problem size is so large that storing and factoring the Jacobian is not feasible or a low accuracy solution is required cheaply, Ceres offers a number of line search based algorithms. This includes a number of variants of Non-linear Conjugate Gradients, BFGS and LBFGS. Speed - Ceres Solver has been extensively optimized, with C++ templating, hand written linear algebra routines and OpenMP or TBB based multithreading of the Jacobian evaluation and the linear solvers. Solution Quality Ceres is the best performing solver on the NIST problem set used by Mondragon and Borchers for benchmarking non-linear least squares solvers. Covariance estimation - Evaluate the sensitivity/uncertainty of the solution by evaluating all or part of the covariance matrix. Ceres is one of the few solvers that allows you to to do this analysis at scale. Community Since its release as an open source software, Ceres has developed an active developer community that contributes new features, bug ﬁxes and support.

Portability - Runs on Linux, Windows, Mac OS X, Android and iOS. BSD Licensed The BSD license offers the ﬂexibility to ship your application

Docs » Installation Installation Getting the source code You can start with the latest stable release . Or if you want the latest version, you can clone the git repository git clone https://ceres-solver.googlesource.com/ceres-solver Dependencies Ceres relies on a number of open source libraries, some of which are optional. For details on customizing the build process, see Customizing the build . Eigen 3.2.2 or later strongly recommended, 3.1.0 or later required. ! Note Ceres can also use Eigen as a sparse linear algebra library. Please see the documentation for EIGENSPARSE for more details. CMake 2.8.0 or later. Required on all platforms except for Android. glog 0.3.1 or later. Recommended glog is used extensively throughout Ceres for logging detailed information about memory allocations and time consumed in various parts of the solve, internal error conditions etc. The Ceres developers use it extensively to observe and analyze Ceres’s performance. glog allows you to control its behaviour from the command line. Starting with -logtostderr you can add -v=N for increasing values of N to get more and more verbose and detailed information about Ceres internals. Unfortunately, the current version of google-glog does not build using the Android NDK. So, Ceres also ships with a minimal replacement of glog called miniglog that can be enabled with the MINIGLOG build option.

So, in an attempt to reduce dependencies, it is tempting to use miniglog on platforms other than Android. While there is nothing preventing the user from doing so, we strongly recommend against it. miniglog has worse performance than glog and is much harder to control and use. ! Note If you are compiling glog from source, please note that currently, the unit tests for glog (which are enabled by default) do not compile against a default build of gflags 2.1 as the gﬂags namespace changed from google:: to gflags:: . A patch to ﬁx this is available from here. gﬂags. Needed to build examples and tests. SuiteSparse. Needed for solving large sparse linear systems. Optional; strongly recomended for large scale bundle adjustment CXSparse. Similar to SuiteSparse but simpler and slower. CXSparse has no dependencies on LAPACK and BLAS . This makes for a simpler build process and a smaller binary. Optional BLAS and LAPACK routines are needed by SuiteSparse , and optionally used by Ceres directly for some operations. TBB is a C++11 template library for parallel programming that optionally can be used as an alternative to OpenMP. Optional On UNIX OSes other than Mac OS X we recommend ATLAS, which includes BLAS and LAPACK routines. It is also possible to use OpenBLAS . However, one needs to be careful to turn off the threading inside OpenBLAS as it conﬂicts with use of threads in Ceres. Mac OS X ships with an optimized LAPACK and BLAS implementation as part of the Accelerate framework. The Ceres build system will automatically detect and use it. For Windows things are much more complicated. LAPACK For Windows has detailed instructions.. Optional but required for SuiteSparse . Linux We will use Ubuntu as our example linux distribution.

! Note Up to at least Ubuntu 14.04, the SuiteSparse package in the ofﬁcial package repository (built from SuiteSparse v3.4.0) cannot be used to build Ceres as a shared library. Thus if you want to build Ceres as a shared library using SuiteSparse, you must perform a source install of SuiteSparse or use an external PPA (see bug report here). It is recommended that you use the current version of SuiteSparse (4.2.1 at the time of writing). Start by installing all the dependencies. # CMake sudo apt-get install cmake # google-glog + gflags sudo apt-get install libgoogle-glog-dev # BLAS & LAPACK sudo apt-get install libatlas-base-dev # Eigen3 sudo apt-get install libeigen3-dev # SuiteSparse and CXSparse (optional) # - If you want to build Ceres as a *static* library (the default) # you can use the SuiteSparse package in the main Ubuntu package # repository: sudo apt-get install libsuitesparse-dev # - However, if you want to build Ceres as a *shared* library, you must # add the following PPA: sudo add-apt-repository ppa:bzindovic/suitesparse-bugfix-1319687 sudo apt-get update sudo apt-get install libsuitesparse-dev We are now ready to build, test, and install Ceres. tar zxf ceres-solver-1.14.0.tar.gz mkdir ceres-bin cd ceres-bin cmake ../ceres-solver-1.14.0 make -j3 make test # Optionally install Ceres, it can also be exported using CMake which # allows Ceres to be used without requiring installation, see the documentation # for the EXPORT_BUILD_DIR option for more information. make install

You can also try running the command line bundling application with one of the included problems, which comes from the University of Washington’s BAL dataset [Agarwal]. bin/simple_bundle_adjuster ../ceres-solver-1.14.0/data/problem-16-22106- pre.txt This runs Ceres for a maximum of 10 iterations using the DENSE_SCHUR linear solver. The output should look something like this. iter cost cost_change |gradient| |step| tr_ratio tr_radius ls_iter iter_time total_time 0 4.185660e+06 0.00e+00 1.09e+08 0.00e+00 0.00e+00 1.00e+04 0 7.59e-02 3.37e-01 1 1.062590e+05 4.08e+06 8.99e+06 5.36e+02 9.82e-01 3.00e+04 1 1.65e-01 5.03e-01 2 4.992817e+04 5.63e+04 8.32e+06 3.19e+02 6.52e-01 3.09e+04 1 1.45e-01 6.48e-01 3 1.899774e+04 3.09e+04 1.60e+06 1.24e+02 9.77e-01 9.26e+04 1 1.43e-01 7.92e-01 4 1.808729e+04 9.10e+02 3.97e+05 6.39e+01 9.51e-01 2.78e+05 1 1.45e-01 9.36e-01 5 1.803399e+04 5.33e+01 1.48e+04 1.23e+01 9.99e-01 8.33e+05 1 1.45e-01 1.08e+00 6 1.803390e+04 9.02e-02 6.35e+01 8.00e-01 1.00e+00 2.50e+06 1 1.50e-01 1.23e+00 Ceres Solver v1.14.0 Solve Report ---------------------------------- Original Reduced Parameter blocks 22122 22122 Parameters 66462 66462 Residual blocks 83718 83718 Residual 167436 167436 Minimizer TRUST_REGION Dense linear algebra library EIGEN Trust region strategy LEVENBERG_MARQUARDT Given Used Linear solver DENSE_SCHUR DENSE_SCHUR Threads 1 1 Linear solver threads 1 1 Linear solver ordering AUTOMATIC 22106, 16 Cost: Initial 4.185660e+06

Final 1.803390e+04 Change 4.167626e+06 Minimizer iterations 6 Successful steps 6 Unsuccessful steps 0 Time ((in seconds)): Preprocessor 0.261 Residual evaluation 0.082 Jacobian evaluation 0.412 Linear solver 0.442 Minimizer 1.051 Postprocessor 0.002 Total 1.357 Termination: CONVERGENCE ((Function tolerance reached. |cost_change|/cost: 1.769766e-09 <== 1.000000e-06)) Mac OS X ! Note Ceres will not compile using Xcode 4.5.x (Clang version 4.1) due to a bug in that version of Clang. If you are running Xcode 4.5.x, please update to Xcode >= 4.6.x before attempting to build Ceres. On OS X, you can either use MacPorts or Homebrew to install Ceres Solver. If using MacPorts, then sudo port install ceres-solver will install the latest version. If using Homebrew and assuming that you have the homebrew/science [1] tap enabled, then brew install ceres-solver

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