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Alternating Direction Graph Matching (ADGM)

This repository contains the code for ADGM introduced in the paper Alternating Direction Graph Matching (CVPR 2017) by D. Khuê Lê-Huu and Nikos Paragios.

A more recent implementation in Python can be found here:

v0.1, 24/02/2017, written by D. Khuê Lê-Huu.

If you use any part of this code, please cite:

 title={Alternating Direction Graph Matching},
 author={L{\^e}-Huu, D. Khu{\^e} and Paragios, Nikos},
 booktitle = {Proceedings of the {IEEE} Conference on Computer Vision and Pattern Recognition ({CVPR})},
 year = {2017}


  • This is a preliminary re-implementation in C++ Eigen and should be considered as pre-release. I haven't tested it on the full benchmark yet and thus the performance is not guaranteed. If you observe some strange behavior then please let me know.

  • Furthermore, some caching part has not been re-implemented yet and thus, the current software might be slow (one can expect 2x-10x speedup in the future release version). If you compare running time in your paper, please indicate that.

  • In the current version, only third-order potentials are supported.


In Matlab, go to the folder ADGM/ and run:



X = FUNCTION(X0, [], [], [], [], indH, valH, rho, MAX_ITER, verbose, eta, iter1, iter2);

where FUNCTION can be one of the following: ADGM1, ADGM2, ADGM1_SYMMETRIC, ADGM2_SYMMETRIC. If the third-order tensor valH is super-symmetric then you should use the _SYMMETRIC versions because they offer several times speedup by exploiting the symmetric structure of the tensor.

The parameters of the above function are:

Output X: the returned assignment matrix (N2 x N1) Intput:

  • X0 the initial solution (N2 x N1)
  • indH: matrix of dimension Nt x 3 representing the indices of the tensor valH (third-order)
  • valH: vector of dimension Nt x 1 representing the values of the potential tensor
  • rho: initial penalty parameter
  • MAX_ITER: maximum number of iterations
  • verbose: 'true' will print out the output
  • eta (> 1.0), iter1, iter2 (denoted by eta, T1, T2 in the paper): parameters for the apdative scheme applied to the penalty parameter.

Typical values are: rho = nP1*nP2/1000; MAX_ITER = 5000; eta = 2.0; iter1 = 200; iter2 = 50;

  • Increasing rho or eta usually results in faster convergence but lower objective (and vice-versa: decreasing them usually offer higher objective values)
  • Decreasing iter1 or iter2 usually results in faster convergence but lower objective (and vice-versa: increasing them usually offer higher objective values)


  • The indices in indH start from 0 (i.e. C++ indices and not Matlab ones)
  • Although ADGM is formulated as a minimzation problem, the above function solves a MAXIMIZATION problem (for the ease of comparison with the other methods). Thus, the input potential tensor valH should represent the similarity between the graphs.


The script demo.m implements a synthetic third-order graph matching problem and solves it using the two variants of ADGM as well as Duchenne's Tensor Matching algorithm (for comparison).

To succesfully run it, follow the steps below:

  1. In Matlab, go to ann_mwrapper/ and run:
  1. Go back to the main folder and run:
mex assignmentoptimal.cpp
  1. Go to TM/ and run:
mex GCC='/usr/bin/g++-4.8' mexSource/mexComputeFeature.cpp -output mex/mexComputeFeature
mex GCC='/usr/bin/g++-4.8' mexSource/mexTensorMatching.cpp -output mex/mexTensorMatching
  1. Go back to the main folder and run:


When running the demo, if you obtain errors like this:

Invalid MEX-file '*.mexa64':
Missing symbol '_ZNSt7__cxx1112basic_stringIcSt11char_traitsIcESaIcEE9_M_assignERKS4_' required by

then probably your C++ compiler is not supported by MATLAB.

To resolve this issue, you can run mex -setup c++ and choose an appropritate compiler, as recommended by MATLAB's official documentation.

Alternatively, you can specify a compiler as an argument for mex. For example, on Linux:

mex GCC='/usr/bin/g++-4.8' <file.cpp>

Make sure to replace mex with mex GCC='/usr/bin/g++-4.8' to all the commands in the previous sections (including those in ADGM/compile.m).

For any questions or bug reports, please send me an email.


Alternating Direction Graph Matching (ADGM)



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