Transformational invariance - a primer

The shape of objects seen in images depends on the viewpoint. This effect confounds recognition. We demonstrate a theoretical framework within which it is possible to construct descriptors for both curves and surfaces, which do not vary with viewpoint. These descriptors are known as invariants. We use this framework to construct invariant shape descriptors for plane curves. These invariant shape descriptors make it possible to recognise plane curves, without explicitly determining the relationship between the curve reference frame and the camera coordinate system, and can be used to index quickly and efficiently into a large model base of curves. Many of these ideas are demonstrated by experiments on real image data.