Optical flow and deformable objects

When a plane undergoes a deformation that can be represented by a planar linear vector field, the projected vector field on the image plane of an optical device is at most quadratic. This 2D motion field has one singular point, with eigenvalues identical to those of the singular point describing the deformation. As a consequence, the nature of the singular point of the deformation is a projective invariant. When the plane moves and experiences a linear deformation at the same time, the associated 2D motion field is still quadratic with at most 3 singular points. In the case of a normal rototranslation, i.e. when the angular velocity is normal to the plane, and of a linear deformation, the 2D motion field has at most one singular point and substantial information on the rigid motion and on the deformation can be recovered from it. Experiments with simulated deformations and real deformable objects show that the proposed analysis can provide accurate results and information on more general 3D deformations