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Geometry is closely linked to visual perception; yet, very little is known about the geometry of visual processing beyond early retinotopic organization. We present a variety of perceptual phenomena showing that a retinotopic representation is neither sufficient nor necessary to support form perception. We discuss the popular ??object files?? concept as a candidate for nonretinotopic representations and, based on its shortcomings, suggest future directions for research using local manifold representations. We suggest that these manifolds are created by the emergence of dynamic reference-frames that result from motion segmentation. We also suggest that the metric of these manifolds is based on relative motion vectors.