A Fast Semidefinite Approach to Solving Binary Quadratic Problems

authors: Peng Wang, Chunhua Shen, Anton van den Hengel

Segmentation results on the Berkeley dataset. The top row shows the original images with partial labelled pixels. Our SDCut (bottom) achieves better results than BNCut (middle).


Many computer vision problems can be formulated as binary quadratic programs (BQPs). Two classic relaxation methods are widely used for solving BQPs, namely, spectral methods and semidefinite programming (SDP), each with their own advantages and disadvantages. Spectral relaxation is simple and easy to implement, but its bound is loose. Semidefinite relaxation has a tighter bound, but its computational complexity is high for large scale problems.

We present a new SDP formulation for BQPs, with two desirable properties. First, it has a similar relaxation bound to conventional SDP formulations. Second, compared with conventional SDP methods, the new SDP formulation leads to a significantly more efficient and scalable dual optimization approach, which has the same degree of complexity as spectral methods. Extensive experiments on various applications including clustering, image segmentation, co-segmentation and registration demonstrate the usefulness of our SDP formulation for solving large-scale BQPs.

  • A fast semidefinite approach to solving binary quadratic problems.
    P. Wang, C. Shen, A. van den Hengel. Proc. IEEE Conf. Computer Vision and Pattern Recognition (CVPR), 2013.

Other relevant work
  • A scalable dual approach to semidefinite metric learning.
    C. Shen, J. Kim, L. Wang. Proc. IEEE Conf. Computer Vision and Pattern Recognition (CVPR), 2011.


C. Shen's participation in this research was supported by Australian Research Council Future Fellowship FT120100969.

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