Se Sync

An implementation of the SE-Sync algorithm for synchronization over the special Euclidean group.
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SE-Sync is a certifiably correct algorithm for performing synchronization over the special Euclidean group: estimate the values of a set of unknown poses (positions and orientations in Euclidean space) given noisy measurements of a subset of their pairwise relative transforms. This problem frequently arises in the context of 2D and 3D geometric estimation; for example, the foundational problems of pose-graph SLAM (in robotics), camera motion estimation (in computer vision), and sensor network localization (in distributed sensing) all require synchronization over the special Euclidean group. SE-Sync improves upon prior methods by exploiting a novel (convex) semidefinite relaxation of the special Euclidean synchronization problem to directly search for globally optimal solutions, and is capable of producing a computational certificate of correctness (global optimality) in the (typical) case that a global minimizer is found.

A detailed description of the algorithm and its implementation can be found in our journal article and its companion technical report.

Getting Started


To use the MATLAB implementation of SE-Sync, simply place the 'MATLAB' folder in any convenient (permanent) location, and then run the script MATLAB/import_SE_Sync.m. Congrats! SE-Sync is now ready to go :-). For a minimal working example, see MATLAB/examples/main.m


The C++ implementation of SE-Sync can be built and exported as a CMake project. For a minimal working example, see C++/examples/main, which provides a simple command-line utility for processing .g2o files.

C++ quick installation guide

The following installation instructions have been verified on Ubuntu 22.04:

Step 1: Install dependencies

$ sudo apt-get install build-essential cmake-gui libeigen3-dev liblapack-dev libblas-dev libsuitesparse-dev

Step 2: Clone the repository

$ git clone SESync

Step 3: Initialize Git submodules

$ cd SESync
$ git submodule init
$ git submodule update

Step 4: Create build directory

$ cd C++ && mkdir build

Step 5: Configure build and generate Makefiles

$ cd build && cmake ..

Step 6: Build code

$ make -j

Step 7: Run the example command-line utility on some tasty data :-D!

$ cd bin
$ ./SE-Sync ../../../data/sphere2500.g2o 


Python bindings for the C++ SE-Sync library can also be built using pybind11. To do so, install the additional Python dependencies using the command:

$ sudo apt-get install python3 python3-numpy python3-matplotlib python3-dev pybind11-dev jupyter-notebook 

and then set BUILD_PYTHON_BINDINGS when configuring the CMake project. See this notebook for a minimal working example demonstrating the use of SE-Sync's Python interface.


We are making this software freely available in the hope that it will be useful to others. If you use SE-Sync in your own work, please cite our papers:

title = {{SE-Sync}:  A Certifiably Correct Algorithm for Synchronization over the Special {Euclidean} Group},
author = {Rosen, D.M. and Carlone, L. and Bandeira, A.S. and Leonard, J.J.},
journal = {Intl. J. of Robotics Research},
volume = {38},
number = {2--3},
pages = {95--125},
month = mar,
year = {2019},

title = {{SE-Sync}: A Certifiably Correct Algorithm for Synchronization over the Special {Euclidean} Group},
author = {Rosen, D.M. and Carlone, L. and Bandeira, A.S. and Leonard, J.J.},
institution = {Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology},
address = {Cambridge, MA},
number = {MIT-CSAIL-TR-2017-002},
year = {2017},
month = feb,

title = {A Certifiably Correct Algorithm for Synchronization over the Special {Euclidean} Group},
author = {Rosen, D.M. and Carlone, L. and Bandeira, A.S. and Leonard, J.J.},
booktitle = {Intl. Workshop on the Algorithmic Foundations of Robotics (WAFR)},
month = dec,
year = {2016},
address = {San Francisco, CA},

title = {Computational Enhancements for Certifiably Correct {SLAM}},
author = {Rosen, D.M. and Carlone, L.},
note = {Presented at the International Conference on Intelligent Robots and Systems (IROS) in the workshop ``Introspective Methods for Reliable Autonomy"},
month = sep,
year = {2017},

  title = {Accelerating Certifiable Estimation with Preconditioned Eigensolvers},
  author = {Rosen, David M.},
  month = may,
  year = {2022},
  publisher = {arXiv},
  doi = {10.48550/ARXIV.2207.05257},
  url = {},

and the following paper of Absil et al., which describes the Riemannian trust-region (RTR) method that SE-Sync employs:

title = {Trust-Region Methods on {Riemannian} Manifolds},
author = {Absil, P.-A. and Baker, C.G. and Gallivan, K.A.},
journal = {Found.\ Comput.\ Math.},
volume = {7},
number = {3},
pages = {303--330},
year = {2007},
month = jul,

If you use the MATLAB implementation of SE-Sync, please also cite the following reference for the Manopt toolbox, which provides the MATLAB implementation of RTR that the SE-Sync toolbox employs:

  title={{Manopt}, a {MATLAB} Toolbox for Optimization on Manifolds.},
  author={Boumal, N. and Mishra, B. and Absil, P.-A. and Sepulchre, R.},
  journal={Journal of Machine Learning Research},

Copyright and License

The C++ and MATLAB implementations of SE-Sync contained herein are copyright (C) 2016-2022 by David M. Rosen, and are distributed under the terms of the GNU Lesser General Public License (LGPL) version 3 (or later). Please see the LICENSE for more information.

Contact: [email protected]

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