We present a technique for local image representation that is invariant to viewpoint for scenes with arbitrary non-planar shape. We show that generic viewpoint invariance can be achieved, under suitable conditions, although the resulting invariant is not shape-discriminative. Our results serve both to validate existing approaches to local feature detection and description, as well as to complement them where they are not applicable. We illustrate our approach on images of 3-D corners where existing approaches fail. Contents