The emergence of virtual reality (VR) and augmented reality (AR) has revolutionized our lives by enabling a 360° artificial sensory stimulation across diverse domains, including, but not limited to, sports, media, healthcare, and gaming. Unlike the conventional planar video processing, where memory access is the main bottleneck, in 360° VR videos the compute is the primary bottleneck and contributes to more than 50% energy consumption in battery-operated VR headsets. Thus, improving the computational efficiency of the video processing pipeline in a VR is critical. While prior efforts have attempted to address this problem through acceleration using a GPU or FPGA, none of them has analyzed the 360° VR pipeline to examine if there is any scope to optimize the computation with known techniques such as memoization. Thus, in this paper, we analyze the VR computation pipeline and observe that there is significant scope to skip computations by leveraging the temporal and spatial locality in head orientation and eye correlations, respectively, resulting in computation reduction and energy efficiency. The proposed Déjà View design takes advantage of temporal reuse by memoizing head orientation and spatial reuse by establishing a relationship between left and right eye projection, and can be implemented either on a GPU or an FPGA. We propose both software modifications for existing compute pipeline and microarchitectural additions for further enhancement. We evaluate our design by implementing the software enhancements on an NVIDIA Jetson TX2 GPU board and our microarchitectural additions on a Xilinx Zynq-7000 FPGA model using five video workloads. Experimental results show that Déjà View can provide 34% computation reduction and 17% energy saving, compared to the state-of-the-art design.