1. An array camera, comprising: a plurality of cameras that capture images of a scene from different viewpoints; memory containing an image processing pipeline application; wherein the image processing pipeline application directs the processor to: obtain image data from a plurality of groups of cameras from within the plurality of cameras, where each group of cameras starts capturing image data at a staggered start time relative to the other groups of cameras; select a reference viewpoint and determine scene-dependent geometric corrections that shift pixels captured from an alternate viewpoint to the reference viewpoint by performing disparity searches to identify the disparity at which pixels from the different viewpoints are most similar; and render frames of video, where a given frame of video is rendered using pixels comprising pixels from at least one group of cameras captured during a given frame capture time interval and by shifting pixels captured from alternate viewpoints to the reference viewpoint using scene-dependent geometric corrections determined for the pixels captured from the alternate viewpoints, wherein the image processing pipeline application further directs the processor to render frames of video using: pixels captured by at least one group of cameras during the given frame capture time interval and determined to be moving during the given frame capture time interval; and pixels from a previously rendered frame that are determined to be non-moving during at least the given frame capture time interval.