Detecting the motion of a planar surface by line and surface integrals

Abstract A mathematical formulation is presented for detecting the 3D motion of a planar surface from the motion of its perspective image without knowing correspondence of points. The motion is determined explicitly by numerical computation of certain line or surface integrals on the image. The same principle is also used to know the position and orientation of a planar surface fixed in the space by moving the camera or using several appropriately positioned cameras, and no correspondence of points is involved. Some numerical examples are also given.