Relative motion and pose from invariants

Projectively invariant shape descriptors efficiently identify instances of object models in images without reference to object pose. These descriptions rely on frame independent representations of planar curves, using plane conies. We show that object pose can be determined from coplanar curves, given such a frame independent representation. This result is demonstrated for real image data. The shape of objects in images changes as the camera is moved around. This extremely simple observation represents the dominant problem in model based vision. Nielsen [4, 5] first suggested using projectively invariant labels as landmarks for navigation. Recent papers [1, 2] have shown that it is possible to compute shape descriptors of arbitrary plane objects that are unaffected by camera position. These descriptors are known as transformational invariants. At no stage in this process, however, is the pose of the model determined. In this paper, we show that the available information does in fact determine the pose of the model. In particular, for complex planar objects, pose determination can be reduced to the simpler problem of pose determination for a pair of known planar conies.