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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: https://github.com/netw0rkf10w/pyADGM

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

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

@inproceedings{lehuu2017adgm,
 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}
}

Note

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.

Installation

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

compile.m

Usage

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)

Important:

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.

Demo

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:

In Matlab, go to ann_mwrapper/ and run:

ann_compile_mex

Go back to the main folder and run:

mex assignmentoptimal.cpp

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

Go back to the main folder and run:

demo

Troubleshooting

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

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

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.