A hallmark of human social interaction is the ability to consider other people's mental states, such as what they see, believe, or desire. Prior neuroimaging research has predominantly investigated the neural mechanisms involved in computing one's own or another person's perspective and largely ignored the question of perspective selection. That is, which brain regions are engaged in the process of selecting between self and other perspectives? To address this question, the current fMRI study used a behavioral paradigm that required participants to select between competing visual perspectives. We provide two main extensions to current knowledge. First, we demonstrate that brain regions within dorsolateral prefrontal and parietal cortices respond in a viewpoint-independent manner during the selection of task-relevant over task-irrelevant perspectives. More specifically, following the computation of two competing visual perspectives, common regions of frontoparietal cortex are engaged to select one's own viewpoint over another's as well as select another's viewpoint over one's own. Second, in the absence of conflict between the content of competing perspectives, we showed a reduced engagement of frontoparietal cortex when judging another's visual perspective relative to one's own. This latter finding provides the first brain-based evidence for the hypothesis that, in some situations, another person's perspective is automatically and effortlessly computed, and thus, less cognitive control is required to select it over one's own perspective. In doing so, we provide stronger evidence for the claim that we not only automatically compute what other people see but also, in some cases, we compute this even before we are explicitly aware of our own perspective.