Model-Based Recognition of 3D Curves From One View

It is well known that there are no geometric invariants of a projection from 3D to 2D. However, given some modeling assumptions about the 3D object, such invariants can be found. The modeling assumptions should be sufficiently strong to enable us to find such invariants, but not stronger than necessary. In this paper we find such modeling assumptions for general 3D curves under affine projection. We show, for example, that if one of the two affine curvatures is known along the 3D curve, the other can be found from the curve's 2D image. We can also derive the point correspondence between the curve and its image. We also deal with point sets and direction vectors.