During binocular rivalry, perception alternates between dissimilar images presented dichoptically. Although perception during rivalry is believed to originate from competition at a local level, different rivalry zones are not independent: rival targets that are spaced apart but have similar features tend to be dominant at the same time. We investigated grouping of spatially separated rival targets presented to the same or to different eyes and presented in the same or in different hemifields. We found eye-of-origin to be the strongest cue for grouping during binocular rivalry. Grouping was additionally affected by orientation: identical orientations were grouped longer than dissimilar orientations, even when presented to different eyes. Our results suggest that eye-based and orientation-based grouping is independent and additive in nature. Grouping effects were further modulated by the distribution of the targets across the visual field. That is, grouping within the same hemifield can be stronger or weaker than between hemifields, depending on the eye-of-origin of the grouped targets. We also quantified the contribution of the previous cues to grouping of two images during binocular rivalry. These quantifications can be successfully used to predict the dominance durations of different studies. Incorporating the relative contribution of different cues to grouping, and the dependency on hemifield, into future models of binocular rivalry will prove useful in our understanding of the functional and anatomical basis of the phenomenon of binocular rivalry