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Higher-order Projected Power Iterations for Scalable Multi-Matching


Bernard,  Florian
Computer Graphics, MPI for Informatics, Max Planck Society;


Swoboda,  Paul
Computer Vision and Multimodal Computing, MPI for Informatics, Max Planck Society;


Theobalt,  Christian
Computer Graphics, MPI for Informatics, Max Planck Society;

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Bernard, F., Thunberg, J., Swoboda, P., & Theobalt, C. (2018). Higher-order Projected Power Iterations for Scalable Multi-Matching. Retrieved from http://arxiv.org/abs/1811.10541.

Cite as: https://hdl.handle.net/21.11116/0000-0002-A8D0-5
The matching of multiple objects (e.g. shapes or images) is a fundamental
problem in vision and graphics. In order to robustly handle ambiguities, noise
and repetitive patterns in challenging real-world settings, it is essential to
take geometric consistency between points into account. Computationally, the
multi-matching problem is difficult. It can be phrased as simultaneously
solving multiple (NP-hard) quadratic assignment problems (QAPs) that are
coupled via cycle-consistency constraints. The main limitations of existing
multi-matching methods are that they either ignore geometric consistency and
thus have limited robustness, or they are restricted to small-scale problems
due to their (relatively) high computational cost. We address these
shortcomings by introducing a Higher-order Projected Power Iteration method,
which is (i) efficient and scales to tens of thousands of points, (ii)
straightforward to implement, (iii) able to incorporate geometric consistency,
and (iv) guarantees cycle-consistent multi-matchings. Experimentally we show
that our approach is superior to existing methods.