Spatiotemporal sensitivity to high frequency information declines with increased peripheral eccentricity. Foveated rendering exploits this by decreasing the spatial resolution of rendered images in peripheral vision, reducing the rendering cost by omitting high frequency details. As foveation levels increase, the rendering quality is reduced, and traditional foveated rendering systems tend not to preserve samples that were previously rendered at high spatial resolution in previous frames. Additionally, prior research has shown that saccade landing positions are distributed around a target location rather than landing at a single point, and that even during fixations, eyes perform small microsaccades around a fixation point. This creates an opportunity for sampling from temporally neighbouring frames with differing foveal locations to reduce the required rendered size of the foveal region while achieving a higher perceived image quality. We further observe that the temporal presentation of pixels frame-to-frame can be viewed as a data stream, presenting a random sampling problem. Following this intuition, we propose a Weighted Reservoir Sampling technique to efficiently maintain a reservoir of the perceptually relevant high quality pixel samples from previous frames and incorporate them into the computation of the current frame. This allows the renderer to render a smaller region of foveal pixels per frame by temporally reusing pixel samples that are still relevant to reconstruct a higher perceived image quality, while allowing for higher levels of foveation. Our method operates on the output of foveated rendering, and runs in under 1 ms at 4K resolution, making it highly efficient and integrable with real-time VR and AR foveated rendering systems.

Both the marginal contributions needed for the computation of Shapley values and the graph produced by Pearl-Verma theorem rely on the choice of an ordering of the variables. For Shapley values, the marginal contributions are averaged over all orderings, while in causal inference methods, the typical approach is to select orderings producing a graph with a minimal number of edges. We reconcile both approaches by reinterpreting them from a maximum entropy perspective. Namely, Shapley values assume no prior knowledge about the orderings and treat them as equally likely, while causal inference approaches apply Occam’s razor and consider only orderings producing the simplest explanatory graphs. We find that the blind application of Occam’s razor to Shapley values does not produce fully satisfactory explanations. Hence, we propose two variations of Shapley values based on entropy maximization to appropriately incorporate prior information about the model. Hence, we propose a variation of Shapley values based on entropy maximization to appropriately incorporate prior information about the model.