Object-image correspondence for curves under finite and affine cameras

We provide criteria for deciding whether a given planar curve is an image of a given spatial curve, taken by a camera with unknown position and parameters. These criteria reduce the projection problem to a certain variation of the equivalence problem of planar curves under affine and projective transformations. The latter problem can be addressed using Cartan's moving frame method. This leads to a novel algorithmic solution of the projection problem for curves. The same approach can be used to decide whether a given finite set of ordered points on a plane is an image of a given finite set of ordered points in R^3.