A large part of human communication involves referring to entities in the world, and often these entities are objects that are visually present for the interlocutors. A computer system that aims to resolve such references needs to tackle a complex task: objects and their visual features must be determined, the referring expressions must be recognised, extra-linguistic information such as eye gaze or pointing gestures must be incorporated — and the intended connection between words and world must be reconstructed. In this paper, we introduce a discriminative model of reference resolution that processes incrementally (i.e., word for word), is perceptually-grounded, and improves when interpolated with information from gaze and pointing gestures. We evaluated our model and found that it performed robustly in a realistic reference resolution task, when compared to a generative model.