A Fast Semidefinite Approach to Solving Binary Quadratic Problems
This work addresses the computational bottleneck of SDP methods for BQPs in computer vision, offering a more efficient approach for researchers and practitioners dealing with large-scale problems.
The paper tackles the problem of solving binary quadratic programs (BQPs) in computer vision by presenting a new semidefinite programming (SDP) formulation that maintains a tight relaxation bound similar to conventional SDP while achieving computational efficiency comparable to spectral methods, enabling scalable solutions for large-scale applications like clustering and image segmentation.
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.