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We investigate the relationship between camera design and the problem of recovering the motion and structure of a scene from video data. The visual information that could possibly be obtained is described by the plenoptic function. A camera can be viewed as a device that captures a subset of this function, that is, it measures some of the light rays in some part of the space. The information contained in the subset determines how difficult it is to solve subsequent interpretation processes. By examining the differential structure of the time varying plenoptic function we relate different known and new camera models to the spatiotemporal structure of the observed scene. This allows us to define a hierarchy of camera designs, where the order is determined by the stability and complexity of the computations necessary to estimate structure and motion. At the low end of this hierarchy is the standard planar pinhole camera for which the structure from motion problem is non-linear and ill-posed. At the high end is a new camera, which we call the full field of view polydioptric camera, for which the problem is linear and stable. In between are multiple-view cameras with large fields of view which we have built, as well as catadioptric panoramic sensors and other omni-directional cameras. We develop design suggestions for the polydioptric camera, and based upon this new design we propose a linear algorithm for ego-motion estimation, which in essence combines differential motion estimation with differential stereo.