We focus on grounding (i.e., localizing or linking) referring expressions in images, e.g., ``largest elephant standing behind baby elephant. This is a general yet challenging vision-language task since it does not only require the localization of objects, but also the multimodal comprehension of context -- visual attributes (e.g., ``largest, ``baby) and relationships (e.g., ``behind) that help to distinguish the referent from other objects, especially those of the same category. Due to the exponential complexity involved in modeling the context associated with multiple image regions, existing work oversimplifies this task to pairwise region modeling by multiple instance learning. In this paper, we propose a variational Bayesian method, called Variational Context, to solve the problem of complex context modeling in referring expression grounding. Specifically, our framework exploits the reciprocal relation between the referent and context, i.e., either of them influences estimation of the posterior distribution of the other, and thereby the search space of context can be greatly reduced. In addition to reciprocity, our framework considers the semantic information of context, i.e., the referring expression can be reproduced based on the estimated context. We also extend the model to unsupervised setting where no annotation for the referent is available. Extensive experiments on various benchmarks show consistent improvement over state-of-the-art methods in both supervised and unsupervised settings.
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