Weakly supervised object detection (WSOD) that only needs image-level annotations has obtained much attention recently. By combining convolutional neural network with multiple instance learning method, Multiple Instance Detection Network (MIDN) has become the most popular method to address the WSOD problem and been adopted as the initial model in many works. We argue that MIDN inclines to converge to the most discriminative object parts, which limits the performance of methods based on it. In this paper, we propose a novel Coupled Multiple Instance Detection Network (C-MIDN) to address this problem. Specifically, we use a pair of MIDNs, which work in a complementary manner with proposal removal. The localization information of the MIDNs is further coupled to obtain tighter bounding boxes and localize multiple objects. We also introduce a Segmentation Guided Proposal Removal (SGPR) algorithm to guarantee the MIL constraint after the removal and ensure the robustness of C-MIDN. Through a simple implementation of the C-MIDN with online detector refinement, we obtain 53.6% and 50.3% mAP on the challenging PASCAL VOC 2007 and 2012 benchmarks respectively, which significantly outperform the previous state-of-the-arts.

The eigen-problem of max-algebraic matrix in the sense of the completely max-algebra is analyzed in detail in this paper. It is proved that \lambda = \varpi(\gamma) must be the eigenvalue of the matrix A in the sense of the completely max-algebra if real number \varpi(\gamma) is the average weight of the critical circuit ? for some strongly connected subgraph G(A\gamma) in the graph G(A).