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Efficient Feature Matching via Nonnegative Orthogonal Relaxation

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Abstract

Feature matching problem that incorporates pair-wise constraints can be formulated as an Integer Quadratic Programming (IQP) problem with one-to-one matching constraint. Since it is NP-hard, relaxation models are required. One main challenge for optimizing IQP matching is how to incorporate the discrete one-to-one matching constraint in IQP matching optimization. In this paper, we present a new feature matching relaxation model, called Nonnegative Orthogonal Relaxation (NOR), that aims to optimize IQP matching problem in nonnegative orthogonal domain. One important benefit of the proposed NOR model is that it can naturally incorporate the discrete one-to-one matching constraint in its optimization and can return a desired sparse (approximate discrete) solution for the problem. An efficient and effective update algorithm has been developed to solve the proposed NOR model. Promising experimental results on several benchmark datasets demonstrate the effectiveness and efficiency of the proposed NOR method.

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Notes

  1. This is because if \(\mathbf u {} \mathbf v ^{{{\,\mathrm{T}\,}}} = \sum ^n_{i=1} \mathbf u _i\mathbf v _i =0\), then \(\mathbf u _i\mathbf v _i =0\), which implies that for any index i, if \(\mathbf u _i \ne 0\), then \(\mathbf v _i\) must be zero. Thus if \(\Vert \mathbf u \Vert _0 = k\), then there are at least k elements in vector \(\mathbf v \) equal to zero.

  2. Since the nonnegativity of the update is always guaranteed, the nonnegative constraint can be dropped in Lagrangian function.

  3. http://www.pascalnetwork.org/challenges/VOC/voc2007/workshop/index.html.

  4. http://www.ee.cuhk.edu.hk/xgwang/CUHK-identification.html.

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Acknowledgements

This work is supported in part by NSFC Key Projects of International (Regional) Cooperation and Exchanges under Grant (61860206004); National Natural Science Foundation of China (61602001, 61872005, 61671018); Natural Science Foundation of Anhui Province (1708085QF139); Natural Science Foundation of Anhui Higher Education Institutions of China (KJ2016A020).

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  1. School of Computer Science and Technology, Anhui University, No. 111 Jiulong Road, Hefei, China

    Bo Jiang, Jin Tang & Bin Luo

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  1. Bo Jiang
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  2. Jin Tang
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  3. Bin Luo
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Correspondence to Bin Luo.

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Communicated by V. Lepetit.

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Jiang, B., Tang, J. & Luo, B. Efficient Feature Matching via Nonnegative Orthogonal Relaxation. Int J Comput Vis 127, 1345–1360 (2019). https://doi.org/10.1007/s11263-019-01185-1

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